This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=latex 2010.5.6) 26 MAR 2013 14:54 entering extended mode \write18 enabled. %&-line parsing enabled. **WesterProblemSet.tex (./WesterProblemSet.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia n, swedish, ukenglish, pinyin, loaded. 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LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 77. \plusequivbox=\box27 \nwcodetopsep=\skip43 \nwcodepenalty=\count87 \@original@textwidth=\dimen107 \nwcodecommentsep=\skip44 \@nwlopage=\count88 \@nwhipage=\count89 \@nwlosub=\count90 \@nwhisub=\count91 \@nwpagetemp=\count92 \@nwpagecount=\count93 \sub@page=\count94 \@nwalph@n=\count95 \nw@chunkcount=\count96 \@commacount=\count97 \nwix@counter=\count98 ) (/usr/share/texmf-texlive/tex/latex/base/makeidx.sty Package: makeidx 2000/03/29 v1.0m Standard LaTeX package ) \@indexfile=\write3 \openout3 = `WesterProblemSet.idx'. Writing index file WesterProblemSet.idx (./WesterProblemSet.aux) \openout1 = `WesterProblemSet.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 5. LaTeX Font Info: ... okay on input line 5. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 5. LaTeX Font Info: ... okay on input line 5. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 5. LaTeX Font Info: ... okay on input line 5. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 5. LaTeX Font Info: ... okay on input line 5. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 5. LaTeX Font Info: ... okay on input line 5. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 5. LaTeX Font Info: ... okay on input line 5. LaTeX Font Info: External font `cmex10' loaded for size (Font) <12> on input line 8. LaTeX Font Info: External font `cmex10' loaded for size (Font) <8> on input line 8. LaTeX Font Info: External font `cmex10' loaded for size (Font) <6> on input line 8. [1 ] (./WesterProblemSet.toc [2]) \tf@toc=\write4 \openout4 = `WesterProblemSet.toc'. [3] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n/10 Time: 0.03 (OT) + 0.0 2 (GC) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n/10 x is declared as being in Boolean but has not been given a value.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n/10 x is declared as being in Boolean but has not been given a value.[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n/10 x is declared as being in Boolean but has not been given a value.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] [4] Overfull \hbox (11.99689pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n/10 w is declared as being in Boolean but has not been given a value.[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n/10 x is declared as being in Boolean but has not been given a value.[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 -- Quantifier elimination: See Richard Liska and Stanly Stei nberg, ``Using[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 -- Computer Algebra to Test Stability'', draft of September 25, 1995, and[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 -- Hoon Hong, Richard Liska and Stanly Steinberg, ``Testing Stability by[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 -- Quantifier Elimination'', _Journal of Symbolic Computatio n_, Volume 24,[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 --{implies(-1 <= c <= 1, a**2*(-c**4 - 2*c**3 + 2*c + 1) + c **2 + 2*c + 1 <= 4)}[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 --{implies(v > 0 and y**4 + 4*v*w*y**3 + 2*(2*v**2*w**2 + w* *2 + W**2)*y**2 _[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 -- This quantifier free problem was derived from the above e xample by QEPCAD[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 119--119 [] \OT1/cmtt/m/n/10 Time: 0.40 (IN) + 0.05 (EV) + 0.08 (OT) + 0.0 3 (GC) = 0.57 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 -- => B < 0 and a b > 0 [Liska and Steinberg, p. 49 (equat ion 86)][] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 --thereExists y in C, thereExists n in C, thereExists e in R suchThat _[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 119--119 []\OT1/cmtt/m/n/10 --{real(y) > 0 and real(n) < 0 and y + A*%i*e - B*n = 0 and a*n + b = 0}[] [] [5] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Type: Set OrderedVar iableList [a,b,c][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.05 (EV) + 0.08 (OT) + 0.0 7 (GC) = 0.23 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Type: Set OrderedVar iableList [d,c,b][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Type: Set OrderedV ariableList [b,e][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (EV) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Type : List Set Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Time: 1.20 (IN) + 0.2 0 (OT) = 1.40 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Type: Set Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (EV) = 0.03 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 set reduce(append, [[[A.i, B.j] for j in 1..#B] for i in 1..#A])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/ m/n/10 Type: Void[] [] [6] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Compiling function Cartesian with type (List OrderedVaria bleList [a,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Type : Set List Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 176--176 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.0 8 (OT) = 0.20 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- Let's begin by playing with numbers: infinite precision i ntegers[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- => 30414 0932017133 7804361260 8166064768 8443776415 6896 051200 0000000000[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 (1) 3041409320171337804361260816606476884437764156896051 2000000000000[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.03 (EV) + 0.02 (OT) + 0.0 3 (GC) = 0.08 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- => 2^47 3^22 5^12 7^8 11^4 13^3 17^2 19^2 23^2 29 31 37 4 1 43 47[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: Factored Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.03 (EV) + 0.0 5 (OT) = 0.08 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- Double factorial => 10!! = 10*8*6*4*2 = 3840, 9!! = 9*7*5 *3*1 = 945[] [] [7] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 T ype: Variable abc[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: RadixExpansion 7[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.03 (OT) + 0.0 2 (GC) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: RadixExpansion 16[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 3 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.33 (EV) + 0.12 (OT) + 0.1 2 (GC) = 0.60 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 T ype: PrimeField 7[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 3 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: Union( PrimeField 7,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] [8] Overfull \hbox (11.99689pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 There are 20 exposed and 17 unexposed library operations named **[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named **[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: Union( IntegerMod 6,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (EV) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- Complete decimal expansion of a rational number => 0.1428 57 ...[] [] [9] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: DecimalExpansion[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (EV) = 0.03 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- Multiply two complete decimal expansions and produce an e xact result => 2[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: DecimalExpansion[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.23 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.02 (EV) + 0.0 5 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.10 (EV) + 0.0 2 (OT) = 0.12 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- Try a more complicated example (from the Putnam exam) => 3 + sqrt(2)[] [] [10] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 3 (OT) = 0.08 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- See D.J. Jeffrey and A.D. Rich, ``The nesting habits of r adicals'', draft of[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.22 (EV) + 0.0 2 (OT) = 0.27 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] [11] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.07 (EV) + 0.0 2 (OT) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m /n/10 Type: Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.0 3 (OT) = 0.20 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- See David Jeffrey, ``Current Problems in Computer Algebra Systems'', talk[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 -- A nasty example generated by Axiom => [log(sqrt(2) + 1) + sqrt(2)]/3[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 461--461 []\OT1/cmtt/m/n/10 q:= ((6 - 4*sqrt(2))*log(3 - 2*sqrt(2)) + (3 - 2*sqrt(2))*lo g(17 - 12*sqrt(2)) _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 +-+ +-+ +-+ +-+ +-+[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 (- 4\|2 + 6)log(- 2\|2 + 3) + (- 2\|2 + 3)log(- 12\|2 + 17) - 24\|2 + 32[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 --------------------------------------------------------- --------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.43 (IN) + 0.05 (EV) + 0.0 7 (OT) = 0.55 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 +-+ +-+ +-+ +-+ +-+[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 (- 4\|2 + 6)log(- 2\|2 + 3) + (- 2\|2 + 3)log(- 12\|2 + 17) - 24\|2 + 32[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 --------------------------------------------------------- --------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Ty pe: Complex Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.0 3 (GC) = 0.28 sec[] [] [12] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: Expression Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.35 (IN) + 0.0 5 (OT) = 0.40 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Type: Union(Ca rdinalNumber,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 461--461 [] \OT1/cmtt/m/n/10 Time: 0.1 3 (IN) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: Expression Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.40 (IN) + 0.20 (EV) + 0.22 (OT) + 0. 18 (GC) = 1.0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m /n/10 Type: Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] [13] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m /n/10 Type: Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.03 (OT) + 0.0 3 (GC) = 0.27 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 T ype: List Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 632--632 []\OT1/cmtt/m/n/10 -- Generate a cubic natural spline s from x = [1, 2, 4, 5] a nd y = [1, 4, 2, 3][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: List Lis t PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] [14] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.77 (IN) + 0.68 (EV) + 0.15 (OT) + 0.0 7 (GC) = 1.67 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 0.03 (EV) + 0.0 5 (OT) = 0.35 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.22 (EV) + 0.0 3 (OT) = 0.32 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: Factored E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: MultivariatePolynomial([x],Ex pression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.03 (OT) + 0.0 2 (GC) = 0.12 sec[] [] [15] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: Factored MultivariatePolynomial([x],Ex pression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.32 (EV) + 0.02 (OT) + 0.0 5 (GC) = 0.47 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 p=a(5)*x*(x**4+(a(4)/a(5))*x**3+(a(3)/a(5))*x*x+(a(2)/ a(5))*x+a(1)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.48 (IN) + 0.03 (EV) + 0.1 2 (OT) = 0.63 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 632--632 []\OT1/cmtt/m/n/10 -- Count the number of (floating point) operations needed to compute an[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.10 (EV) + 0.0 5 (OT) = 0.28 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 632--632 []\OT1/cmtt/m/n/10 -- Discretize a PDE: for example, forward differencing time (explicit Euler)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 632--632 []\OT1/cmtt/m/n/10 -- (f[i, j+1] - f[i, j])/dt = (f[i+1, j] - 2 f[i, j] + f[i-1 , j])/dx^2[] [] [16] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 632--632 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.07 (EV) + 0.0 3 (OT) = 0.18 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Compiling function mean with type List PositiveInteger -> Fraction[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (OT) + 0.0 2 (GC) = 0.12 sec[] [] [17] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: Lis t PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Compute the first quartile (25% quantile) of a list of nu mbers => 2 or 5/2[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: Lis t PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Compute the mode (the most frequent item) of a list of n umbers => 7[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: Lis t PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Compute the unbiased sample standard deviation of a list of numbers[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: Lis t PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Discrete distributions---what is the probability of findi ng exactly 12[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- switches that work from a group of 15 where the probabili ty of a single one[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- working is 75%? (Need to use the probability density fun ction [PDF] of the[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Replace `exactly' by `up through' in the above. (Need to use the cumulative[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- probability density function [CDF] of the binomial distri bution.) => 0.76391[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Continuous distributions---if a radiation emission can be modeled by a[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- normal distribution with a mean of 4.35 mrem and a standa rd deviation of[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- 0.59 mrem, what is the probability of being exposed to an ywhere from 4 to 5[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Hypothesis testing---how good of a guess is 5 for the mea n of xx? */[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 T ype: List Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] [18] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 --students_t_distrib((sample_mean(xx) - 5)/(sample_standard_ deviation(xx) /[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- sqrt(length(xx)) ), length(xx) - 1)[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 --standard_normal_distrib((sample_mean(xx) - 5)/(sample_stan dard_deviation(xx) /[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- sqrt(length (xx))))[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Chi-square test---what is the expectation that row charac teristics are[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- independent of column characteristics for a two dimension al array of data?[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 T ype: List Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 T ype: List Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] [19] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: TwoDimensionalArray Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 for i in 1..m repeat for j in 1..n repeat e(i, j):= rowSum(i )*colSum(j)/matSum;[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.02 (EV) + 0.03 (OT) + 0.0 2 (GC) = 0.10 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- chi2:= sum(sum((x(i, j) - e(i, j))**2/e(i, j), i = 1..m), j = 1..n)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Linear regression (age as a function of developmental sco re). See Lambert[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- H. Koopmans, _Introduction to Contemporary Statistical Me thods_, Second[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 t:= [[3.33, 3.25, 3.92, 3.50, 4.33, 4.92, 6.08, 7.42, 8 .33, 8.00, 9.25, _[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 [8.61, 9.40, 9.86, 9.91, 10.53, 10.61, 10.59, 13.28, 12 .76, 13.44, 14.27, _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type : List List Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.03 (OT) + 0.0 2 (GC) = 0.15 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Multiple linear regression (income as a function of age a nd years of[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 [[37, 45, 38, 42, 31], [4, 0, 5, 2, 4], [31200, 26800, 35000 , 30300, 25400]];[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: List List N onNegativeInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] [20] Overfull \hbox (27.74675pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Multiple linear regression using the L1 or Least Absolute Deviations[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- technique rather than the Least Squares technique (minimi zing the sum of the[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- absolute values of the residuals rather than the sum of t he squares of the[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- residuals). Here, the Stack-loss Data is used (percentag e of ammonia lost[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- times 10 from the operation of a plant over 21 days as a function of air[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- flow to the plant, cooling water inlet temperature and ac id concentration).[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- See W. N. Venables and B. D. Ripley, _Modern Applied Stat istics with[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 [[80, 80, 75, 62, 62, 62, 62, 62, 58, 58, 58, 58, 58, 58, 50 , 50, 50, 50, 50, _[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 [27, 27, 25, 24, 22, 23, 24, 24, 23, 18, 18, 17, 18, 19, 18 , 18, 19, 19, 20, _[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 [89, 88, 90, 87, 87, 87, 93, 93, 87, 80, 89, 88, 82, 93, 89 , 86, 72, 79, 80, _[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 [42, 37, 37, 28, 18, 18, 19, 20, 15, 14, 14, 13, 11, 12, 8 , 7, 8, 8, 9, _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type: List Lis t PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- Nonlinear regression (Weight Loss Data from an Obese Pati ent consisting of[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- the time in days and the weight in kilograms of a patient undergoing a[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- weight rehabilitation program). Fit this using least squ ares to weight =[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- b0 + b1 2^(- days/th), starting at (b0, b1, th) = (90, 95 , 120) [Venables[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 -- and Ripley, p. 225] => weight = 81.37375 + 102.6842 2^(- days/141.9105)[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 []\OT1/cmtt/m/n/10 [[ 0, 4, 7, 7, 11, 18, 24, 30, 32, 43, 46, 60 , 64, 70, 71, _[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 71, 73, 74, 84, 88, 95, 102, 106, 109, 115, 122, 133 , 137, 140, 143, _[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 147, 148, 149, 150, 153, 156, 161, 164, 165, 165, 170, 176 , 179, 198, 214, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 [184.35, 182.51, 180.45, 179.91, 177.91, 175.81, 173.11, 17 0.06, 169.31, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 165.10, 163.11, 158.30, 155.80, 154.31, 153.86, 154.20, 15 2.20, 152.80, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 150.30, 147.80, 146.10, 145.60, 142.50, 142.30, 139.40, 13 7.90, 133.70, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 133.70, 133.30, 131.20, 133.00, 132.20, 130.80, 131.30, 12 9.00, 127.90, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 126.90, 127.70, 129.50, 128.40, 125.40, 124.90, 124.90, 11 8.20, 118.20, _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Type : List List Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 850--850 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.0 3 (OT) = 0.33 sec[] [] [21] Overfull \hbox (48.74657pt too wide) in paragraph at lines 927--927 []\OT1/cmtt/m/n/10 -- Pochhammer symbol (a)_n = a (a + 1) ... (a + n - 1) => a (a + 1) (a + 2)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 0.12 (EV) + 0.20 (OT) + 0.1 2 (GC) = 0.70 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Type: Fraction Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.38 (EV) + 0.25 (OT) + 0.0 7 (GC) = 0.82 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.03 (EV) + 0.0 7 (OT) = 0.40 sec[] [] [22] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Time: 0.85 (IN) + 0.02 (EV) + 0.07 (OT) + 0.0 2 (GC) = 0.95 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 927--927 []\OT1/cmtt/m/n/10 -- Partitions of an integer => {1+1+1+1, 1+1+2, 1+3, 2+2, 4} (5 in all)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n /10 Type: Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (EV) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 927--927 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- Display the largest 6-digit prime and the smallest 7-digi t prime[] [] [23] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: Lis t PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.08 (OT) + 0.0 2 (GC) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- (a + b)^p mod p => a^p + b^p for p prime and a, b in Z_p [Chris Hurlburt][] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- See Thomas W. Hungerford, _Algebra_, Springer-Verlag, 197 4, p. 121 for a[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- more general simplification: (a +- b)^(p^n) => a^(p^n) +- b^(p^n)[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- Congruence equations. See Harold M. Stark, _An Introduct ion to Number[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- 9 x = 15 mod 21 => x = 4 mod 7 or {4, 11, 18} mod 21 [Stark, p. 68][] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- 7 x = 22 mod 39 => x = 5 mod 13 or 31 mod 39 [Stark , p. 69][] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] [24] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- x^3 + 2 x^2 + 5 x + 6 = 0 mod 11 => x = 3 mod 11 [Stark , p. 97][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction Polynom ial PrimeField 11[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.72 (IN) + 0.18 (EV) + 0.1 8 (OT) = 1.08 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- {x = 7 mod 9, x = 13 mod 23, x = 1 mod 2} => x = 151 mod 414 [Stark,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.03 (OT) + 0.0 3 (GC) = 0.10 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- {5 x + 4 y = 6 mod 7, 3 x - 2 y = 6 mod 7} => x = 1 mod 7 , y = 2 mod 7[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 solve([5*x + 4*y = 6 :: PrimeField(7), 3*x - 2*y = 6 :: Prim eField(7)], [x, y])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: List List Equation Fraction Polyno mial PrimeField 7[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 1.33 (IN) + 0.08 (EV) + 0.27 (OT) + 0.0 2 (GC) = 1.70 sec[] [] [25] Overfull \hbox (22.4968pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- (x, y) = {(2, 1), (2, 3), (2, 5), (5, 1), (5, 3), (5, 5)} mod 6[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- Diophantine equations => x = 2, y = 5 (Wallis) [Stark, p. 147][] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] [26] Overfull \hbox (22.4968pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- => (x, y, t, z, w) = (3, 4, 5, 12, 13), (7, 24, 25, 312, 313), ...[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: List Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.0 3 (OT) = 0.07 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [27] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- Rational approximation of sqrt(3) with an error tolerance of 1/500 => 26/15[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.05 (EV) + 0.07 (OT) + 0.0 7 (GC) = 0.20 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 3 + +---+ + +----+ + +---+ + +-----+ + +---+ + +---+ + +---+ + +---+[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 | 7 | 15 | 1 | 292 | 1 | 1 | 6 | 2[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: Continue dFraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.03 (EV) + 0.05 (OT) + 0.0 2 (GC) = 0.10 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- => 4 + 1/(1 + 1/(3 + 1/(1 + 1/(8 + 1/(1 + 1/(3 + 1/(1 + 1 /(8 + ...[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 continuedFraction having 1 argument(s) but none was de termined to[] [] [28] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 4 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-- -+ + +---+ + +---+[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 | 1 | 3 | 1 | 8 | 1 | 3 | 1 | 8 | 1[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: Continue dFraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.03 (EV) + 0.03 (OT) + 0.0 3 (GC) = 0.23 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- => 1 + 1/(1 + 1/(1 + 1/(1 + ... See Oskar Perron, _Die Lehre von den[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 1 + +---+ + +---+ + +---+ + +---+ + +---+ + +---+ + +-- -+ + +---+ + +---+[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Type: Continue dFraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 Time: 0.35 (IN) + 0.02 (EV) + 0.0 5 (OT) = 0.42 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- => 1/(2 x + 1/(6 x + 1/(10 x + 1/(14 x + ... [Perron, p . 353][] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 continuedFraction having 1 argument(s) but none was de termined to[] [] [29] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 1243--1243 []\OT1/cmtt/m/n/10 -- => 1/(2 x + 1/(2 x + 1/(2 x + ... (Re x > 0) From Liy ang Xu, ``Method[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 continuedFraction having 1 argument(s) but none was de termined to[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1243--1243 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- One would think that the simplification 2 2^n => 2^(n + 1 ) would happen[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.10 (EV) + 0.17 (OT) + 0.1 2 (GC) = 0.57 sec[] [] [30] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 2 (EV) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.15 (EV) + 0.03 (OT) + 0.0 5 (GC) = 0.32 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Univariate gcd: gcd(p1, p2) => 1, gcd(p1 q, p2 q) => q [Richard Liska][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 5 (OT) = 0.07 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 p2:= 72*x**60 - 25*x**25 - 19*x**23 - 22*x**39 - 83*x**52 + 54*x**10 + 81;[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 7 (IN) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 5 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 7 (EV) = 0.07 sec[] [] [31] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 31.85 (IN) + 0.08 (EV) + 0.02 (OT) + 4.53 (GC) = 36.48 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 31.66 (IN) + 1.42 (EV) + 4.85 (GC) = 37.93 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 120 112 107 99 94 86 85[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 1152x - 1328x + 1512x - 2095x - 4608x + 4850x - 400x[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 83 73 72 70 68 65 60[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 304x + 1408x - 525x + 465x + 9072x + 331 2x - 3330x[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 59 57 52 47 44 39 34[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 1600x - 1468x - 6723x - 1071x - 4468x - 17 82x - 5184x[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 33 31 30 28 25 23 18[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 3150x - 2394x - 1150x - 874x - 2025x - 1 539x + 6804x[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 182.21 (IN) + 184.93 (EV) + 0.07 (OT) + 60.45 (GC) = 427.65 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 p1:= 24*x*y**19*z**8 - 47*x**17*y**5*z**8 + 6*x**15*y**9*z** 2 - 3*x**22 + 5;[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 p2:= 34*x**5*y**8*z**13 + 20*x**7*y**7*z**7 + 12*x**9*y**16* z**4 + 80*y**14*z;[] [] [32] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 3 (OT) = 0.12 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 q:= 11*x**12*y**7*z**13 - 23*x**2*y**8*z**10 + 47*x**17*y**5 *z**8;[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 3 (OT) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (EV) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 6.62 (IN) + 8.73 (EV) + 1.32 (GC) = 16.67 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 9.30 (IN) + 10.72 (EV) + 0.02 (OT) + 1.53 (GC) = 21.57 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 5 (OT) = 0.12 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Resultants. If the resultant of two polynomials is zero, this implies they[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- have a common factor. See Keith O. Geddes, Stephen R. Cz apor and George[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Labahn, _Algorithms for Computer Algebra_, Kluwer Academi c Publishers, 1992,[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 resultant(3*x**4 + 3*x**3 + x**2 - x - 2, x**3 - 3*x**2 + x + 5, x)[] [] [33] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Numbers are nice, but symbols allow for variability---try some high school[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 1.02 (IN) + 0.20 (EV) + 0.15 (OT) + 0.3 5 (GC) = 1.72 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.45 (EV) + 0.0 2 (OT) = 0.52 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 20 19 18 17 16 15 14 13[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 x + 20x + 190x + 1140x + 4845x + 15504x + 3 8760x + 77520x[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 11 10 9 8 7 6[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 125970x + 167960x + 184756x + 167960x + 125970x + 77520x + 38760x[] [] [34] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 19 18 17 16 15 14 13[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 20x + 380x + 3420x + 19380x + 77520x + 232560 x + 542640x[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 11 10 9 8 7[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 1007760x + 1511640x + 1847560x + 1847560x + 1511 640x + 1007760x[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (EV) = 0.02 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Completely factor this polynomial, then try to multiply i t back together![] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 +--------------+2 +- -------------+[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 | +----+ | +----+[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 | |1295 | |1295[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 |9 |---- + 187 |9 |---- + 187[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 +---+ | \| 3 +---+ | \| 3[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 (- \|- 3 + 1) 3|-------------- + (- \|- 3 - 1) 3|- ------------- - 2[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 \| 2 \| 2[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 [x= ----------------------------------------------------- -----------------,[] [] [35] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 +--------------+2 +- -------------+[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 | +----+ | +----+[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 | |1295 | |1295[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 |9 |---- + 187 |9 |---- + 187[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 +---+ | \| 3 +---+ | \| 3[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 (- \|- 3 - 1) 3|-------------- + (- \|- 3 + 1) 3|- ------------- + 2[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 \| 2 \| 2[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 x= ----------------------------------------------------- -----------------,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.12 (EV) + 0.1 3 (OT) = 0.38 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 7 (EV) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] [36] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 (x - 1)(x + 1)(x + 1)(x - x + x - x + 1)(x + x + x + x + 1)[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 6 4 2 20 15 10 5 20 15 10 5[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 (x - x + x - x + 1)(x - x + x - x + 1)(x + x + x + x + 1)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.05 (EV) + 0.0 3 (OT) = 0.08 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 factor(4*x**4 + 8*x**3 + 77*x**2 + 18*x + 153, [rootOf(i**2 + 1)])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored Polynomia l AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 1.65 (EV) + 0.0 3 (OT) = 1.85 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.07 sec[] [] [37] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Fraction Polynomia l AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.40 (IN) + 0.20 (EV) + 0.1 2 (OT) = 0.72 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 0.0 8 (OT) = 0.35 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] [38] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (EV) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored Polyno mial PrimeField 5[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.12 (EV) + 0.02 (OT) + 0.0 5 (GC) = 0.30 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Polyno mial PrimeField 5[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- => (x^2 + x + 1) (x^9 - x^8 + x^6 - x^5 + x^3 - x^2 + 1) mod 65537[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 (42) (x + x + 1)(x + 65536x + x + 65536x + x + 655 36x + 1)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored Polynomial PrimeField 65537[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.13 (EV) + 0.0 3 (OT) = 0.30 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored Polynomia l AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.80 (EV) + 0.0 2 (OT) = 0.82 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] [39] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.55 (EV) + 0.03 (OT) + 0.4 2 (GC) = 1.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.1 3 (EV) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 1.30 (EV) + 0.0 7 (OT) = 1.43 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 60 2 57[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 3486784401tan(z) + (23245229340sin(x) - 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34605737308800cos(y) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 3 10 2[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 69211474617600cos(y) sin(x) - 83053769541120cos(y) sin(x)[] [] [41] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 4 6 6 5[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 7497909750240cos(y) sin(x) - 29991639000960cos(y) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 4 10 3[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 74979097502400cos(y) sin(x) - 119966556003840cos(y ) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 119966556003840cos(y) sin(x) - 68552317716480cos( y) sin(x)[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 4 7 6 6[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 4284519857280cos(y) sin(x) - 19994426000640cos(y) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 5 10 4[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 59983278001920cos(y) sin(x) - 119966556003840cos(y ) sin(x)[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 3 14 2[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 159955408005120cos(y) sin(x) - 137104635432960cos (y) sin(x)[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 4 8 6 7[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 1963738267920cos(y) sin(x) - 10473270762240cos(y) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 6 10 5[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 36656447667840cos(y) sin(x) - 87975474402816cos(y) sin(x)[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 4 14 3[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 146625790671360cos(y) sin(x) - 167572332195840cos (y) sin(x)[] [] [42] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 125679249146880cos(y) sin(x) - 55857444065280cos( y) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 7 10 6[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 17455451270400cos(y) sin(x) - 48875263557120cos(y) sin(x)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 5 14 4[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 97750527114240cos(y) sin(x) - 139643610163200cos( y) sin(x)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 16 3 18 2[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 139643610163200cos(y) sin(x) - 93095740108800cos( y) sin(x)[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 4 10 6 9[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 8 1 0 7[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 6545794226400cos(y) sin(x) - 20946541524480cos(y) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 6 14 5[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 48875263557120cos(y) sin(x) - 83786166097920cos(y ) sin(x)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 16 4 18 3[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 104732707622400cos(y) sin(x) - 93095740108800cos( y) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 55857444065280cos(y) sin(x) - 20311797841920cos(y ) sin(x)[] [] [43] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 9 10 8[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 1939494585600cos(y) sin(x) - 6982180508160cos(y) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 7 14 6[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 18619148021760cos(y) sin(x) - 37238296043520cos(y ) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 16 5 18 4[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 55857444065280cos(y) sin(x) - 62063826739200cos(y ) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 20 3 22 2[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 49651061391360cos(y) sin(x) - 27082397122560cos(y ) sin(x)[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 10 10 9[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 452548736640cos(y) sin(x) - 1810194946560cos(y) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 12 8 14 7[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 5430584839680cos(y) sin(x) - 12412765347840cos(y) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 16 6 18 5[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 21722339358720cos(y) sin(x) - 28963119144960cos(y ) sin(x)[] [] [44] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 20 4 22 3[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 28963119144960cos(y) sin(x) - 21064086650880cos(y ) sin(x)[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 10532043325440cos(y) sin(x) - 3240628715520cos(y) sin(x)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 15 2 14 4 13[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 3767472sin(x) - 113024160cos(y) sin(x) + 158233 8240cos(y) sin(x)[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 6 12 8 11[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 10 10 12 9[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 362038989312cos(y) sin(x) + 1206796631040cos(y ) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 14 8 16 7[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 3103191336960cos(y) sin(x) + 6206382673920cos(y ) sin(x)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 18 6 20 5[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 9654373048320cos(y) sin(x) + 11585247657984cos( y) sin(x)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 22 4 24 3[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 10532043325440cos(y) sin(x) + 7021362216960cos( y) sin(x)[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 3240628715520cos(y) sin(x) + 925893918720cos(y) sin(x)[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 16 2 15 4 14[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 392445sin(x) - 12558240cos(y) sin(x) + 18837360 0cos(y) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 10 11 1 2 10[] [] [45] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 54854392320cos(y) sin(x) + 201132771840cos(y) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 14 9 16 8[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 574665062400cos(y) sin(x) + 1292996390400cos(y) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 18 7 20 6[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 2298660249600cos(y) sin(x) + 3218124349440cos(y ) sin(x)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 22 5 24 4[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 3510681108480cos(y) sin(x) + 2925567590400cos(y ) sin(x)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 26 3 28 2[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 1800349286400cos(y) sin(x) + 771578265600cos(y) sin(x)[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 17 2 16 4 15[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 30780sin(x) - 1046520cos(y) sin(x) + 16744320co s(y) sin(x)[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 10 12 12 11[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 14 10 1 6 9[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 76622008320cos(y) sin(x) + 191555020800cos(y) sin(x)[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 18 8 2 0 7[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 383110041600cos(y) sin(x) + 612976066560cos(y) sin(x)[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 22 6 2 4 5[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 780151357440cos(y) sin(x) + 780151357440cos(y) sin(x)[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 26 4 2 8 3[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 600116428800cos(y) sin(x) + 342923673600cos(y) sin(x)[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 137169469440cos(y) sin(x) + 34292367360cos(y) sin(x)[] [] [46] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 18 2 17 4 16[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 1710sin(x) - 61560cos(y) sin(x) + 1046520cos(y) sin(x)[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 14 11 16 10[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 18 9 20 8[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 22 7 2 4 6[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 111450193920cos(y) sin(x) + 130025226240cos(y) sin(x)[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 26 5 28 4[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 120023285760cos(y) sin(x) + 85730918400cos(y) sin(x)[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 30 3 32 2[] [] [47] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 26 6 28 5[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 34 2 36 38[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 - 1344798720cos(y) sin(x) + 298844160cos(y) sin(x) - 31457280cos(y)[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 20 2 19 4 18 6 17[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 sin(x) - 40cos(y) sin(x) + 760cos(y) sin(x) - 912 0cos(y) sin(x)[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 8 16 10 15 12 14[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 77520cos(y) sin(x) - 496128cos(y) sin(x) + 2480640 cos(y) sin(x)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.8 8 (OT) = 0.90 sec[] [] [48] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- expand[(1 - c^2)^5 (1 - s^2)^5 (c^2 + s^2)^10] => c^10 s^ 10 when[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- c^2 + s^2 = 1 [modification of a problem due to Richard Liska][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.28 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: List P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.17 (EV) + 0.0 2 (OT) = 0.20 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: List Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 There are 20 exposed and 17 unexposed library operations named **[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named **[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- => 1/4 (x + y) (2 x + y [-1 + i sqrt(3)]) (2 x + y [-1 - i sqrt(3)])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Factored Polynomia l AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 2.33 (EV) + 0.07 (OT) + 0.4 3 (GC) = 2.88 sec[] [] [49] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Partial fraction decomposition => 3/(x + 2) - 2/(x + 1) + 2/(x + 1)^2[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Type: Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (143.24574pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 Type: FullPartialFractionExpansion(Fraction Integer,Univaria tePolynomial(x,Fraction Integer))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.20 (EV) + 0.0 5 (OT) = 0.38 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Noncommutative algebra: note that (A B C)^(-1) = C^(-1) B ^(-1) A^(-1)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 A is declared as being in SquareMatrix(2,Integer) but has not been[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- Jacobi's identity: [A, B, C] + [B, C, A] + [C, A, B] = 0 where [A, B, C] =[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2201--2201 []\OT1/cmtt/m/n/10 -- [A, [B, C]] and [A, B] = A B - B A is the commutator of A and B[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] [50] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 A is declared as being in SquareMatrix(2,Integer) but has not been[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 2201--2201 [] \OT1/cmtt/m/n/10 A is declared as being in SquareMatrix(2,Integer) but has not been[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 -- From B. F. Caviness, Robert P. Gilbert, Wolfram Koepf, Ro man Shtokhamer and[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 -- David W. Wood, _An Introduction to Applied Symbolic Compu tation using[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 -- MACSYMA_, University of Delaware, draft of December 14, 1 993, section 2.3.3.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.48 (IN) + 0.18 (EV) + 0.14 (OT) + 0. 20 (GC) = 1.0 sec[] [] [51] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.0 3 (EV) = 0.22 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.20 (EV) + 0.02 (OT) + 0.0 2 (GC) = 0.33 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 1.15 (IN) + 0.02 (EV) + 0.1 7 (OT) = 1.33 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 -- cos(cos(n pi) pi) + sin(cos(n pi) pi/2) => -1 + (-1)^n fo r integer n[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.02 (EV) + 0.0 7 (OT) = 0.20 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.37 (IN) + 0.0 5 (OT) = 0.42 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 -- | cos x |, | sin x | => - cos x, - sin x for - 3 pi < x < - 5/2 pi[] [] [52] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 -- Trigonometric manipulations---these are typically difficu lt for students[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (EV) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 1.45 (EV) + 0.03 (OT) + 0.0 2 (GC) = 1.57 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 1.1 0 (EV) = 1.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: Ruleset(Integer,Integer,Ex pression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.15 (EV) + 0.07 (OT) + 0.0 2 (GC) = 0.48 sec[] [] [53] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.20 (EV) + 0.02 (OT) + 0.0 2 (GC) = 0.25 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.0 7 (EV) = 0.07 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [54] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 0.40 (EV) + 0.27 (OT) + 0.2 0 (GC) = 1.18 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [55] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.45 (EV) + 0.23 (OT) + 0.2 0 (GC) = 1.18 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: Union(OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.35 (IN) + 8.02 (EV) + 0.05 (OT) + 0.5 3 (GC) = 8.95 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.13 (EV) + 0.0 2 (OT) = 0.17 sec[] [] [56] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.12 (EV) + 0.0 3 (OT) = 0.18 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [57] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.37 (IN) + 0.40 (EV) + 0.22 (OT) + 0.2 0 (GC) = 1.18 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2527--2527 [] \OT1/cmtt/m/n/10 Time: 0.15 (EV) + 0.02 (OT) + 0.0 2 (GC) = 0.18 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- Bernoulli numbers: B_16 => -3617/510 [Gradshteyn and Ry zhik 9.71][] [] [58] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.07 (EV) + 0.03 (OT) + 0.0 3 (GC) = 0.15 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- d/dk E(phi, k) => [E(phi, k) - F(phi, k)]/k where F(phi , k) and E(phi, k)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: DoubleFloat[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.03 (OT) + 0.0 2 (GC) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: Expre ssion DoubleFloat[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.68 (IN) + 0.17 (OT) + 0. 15 (GC) = 1.0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- psi(1/3) => - Euler's_constant - pi/2 sqrt(1/3) - 3/2 log 3 where psi(x)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- is the psi function [= d/dx log Gamma(x)] [Gradshteyn a nd Ryzhik 8.366(6)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: DoubleFloat[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: Expre ssion DoubleFloat[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.52 (IN) + 0.10 (EV) + 0.0 5 (OT) = 0.67 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- Bessel function of the first kind of order 2 => 0.04158 + 0.24740 i[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: Co mplex DoubleFloat[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.02 (EV) + 0.05 (OT) + 0.0 3 (GC) = 0.22 sec[] [] [59] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: DoubleFloat[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 3 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: DoubleFloat[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- => sqrt(2/(pi z)) (sin z/z - cos z) [Gradshteyn and Ryz hik 8.464(3)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.33 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.05 (EV) + 0.0 2 (GC) = 0.12 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- Associated Legendre (spherical) function of the 1st kind: P^mu_nu(0)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- => 2^mu sqrt(pi) / [Gamma([nu - mu]/2 + 1) Gamma([- nu - mu + 1]/2)][] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 chebyshevT(1008, x) - 2*x*chebyshevT(1007, x) + chebyshevT(1 006, x)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 30.50 (EV) + 11.38 (GC) = 41.91 sec[] [] [60] Overfull \hbox (6.74693pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 chebyshevT having 2 argument(s) but none was determine d to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 -- => sin(n z)/(n sin z cos z) [Gradshteyn and Ryzhik 9.12 1(17)][] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 2685--2685 []\OT1/cmtt/m/n/10 --integrate(f((x + 2)/5)*delta((x - 2)/3) - g(x)*D(delta(x - 1), x), x = 0..3)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.0 7 (IN) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 2685--2685 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.0 2 (OT) = 0.18 sec[] [] [61] Overfull \hbox (11.99689pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- Complex functions---separate into their real and imaginar y parts.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.55 (IN) + 0.30 (EV) + 0.22 (OT) + 0.2 5 (GC) = 1.32 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.52 (IN) + 0.0 7 (OT) = 0.58 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.10 (EV) + 0.0 5 (OT) = 0.35 sec[] [] [62] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.0 7 (EV) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.78 (IN) + 0.02 (EV) + 0.0 7 (OT) = 0.87 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.12 (EV) + 0.0 2 (GC) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 5 (EV) = 0.08 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- => [sin(x) cos(x) + i sinh(y) cosh(y)] / [cos(x)^2 + sinh (y)^2][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.85 (EV) + 0.03 (OT) + 0.0 3 (GC) = 1.02 sec[] [] [63] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 1.60 (EV) + 0.0 2 (OT) = 1.62 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- Check for branch abuse. See David R. Stoutemyer, ``Crime s and Misdemeanors[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- in the Computer Algebra Trade'', _Notices of the American Mathematical[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- Society_, Volume 38, Number 7, September 1991, 778--785. This first[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- expression can simplify to sqrt(x y)/sqrt(x), but no furt her in general[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- (consider what happens when x, y = -1). sqrt(x y) = sqrt (x) sqrt(y) if[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- either x >= 0 or y >= 0 or both x and y lie in the right- half plane[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.55 (IN) + 0.03 (EV) + 0.02 (OT) + 0.3 5 (GC) = 0.95 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] [64] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.13 (EV) + 0.0 3 (OT) = 0.20 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.0 5 (OT) = 0.15 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Compiling function simp with type Complex Expression Inte ger -> List[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 0.13 (EV) + 0.0 7 (OT) = 0.52 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- Special case: sqrt(x y |z|^2)/(sqrt(x) |z|) => sqrt(y) [P V] for y >= 0[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- sqrt(1/z) = 1/sqrt(z) except when z is real and negative, in which case[] [] [65] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.1 3 (IN) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- sqrt(e^z) = e^(z/2) if and only if Im z is contained in t he interval[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- ((4 n - 1) pi, (4 n + 1) pi] for n an integer: ..., (-5 p i, -3 pi],[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- (-pi, pi], (3 pi, 5 pi], ...; otherwise, sqrt(e^z) = - e^ (z/2) [considering[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.05 (EV) + 0.0 2 (OT) = 0.22 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.42 (EV) + 0.0 3 (OT) = 0.67 sec[] [] [66] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.52 (IN) + 0.07 (EV) + 0.0 7 (OT) = 0.65 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.27 (EV) + 0.0 2 (OT) = 0.28 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- The principal value of this expression is - e^(3 i) = - c os 3 - i sin 3[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.05 (EV) + 0.0 2 (OT) = 0.22 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.15 (EV) + 0.0 2 (OT) = 0.18 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Ty pe: Complex Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.2 0 (IN) = 0.20 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- log(e^z) = z if and only if Im z is contained in the inte rval (-pi, pi][] [] [67] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (EV) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 3 (EV) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.03 (EV) + 0.0 3 (OT) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.07 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Ty pe: Complex Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- (x y)^n = x^n y^n if either x > 0 or y > 0 or both x and y lie in the[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- right-half plane (Re x, Re y > 0) or n is an integer [con sidering principal[] [] [68] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.35 (IN) + 0.02 (EV) + 0.0 5 (OT) = 0.42 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.6 2 (EV) = 0.62 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 0.08 (EV) + 0.0 3 (OT) = 0.38 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 1.18 (EV) + 0.03 (OT) + 0.3 5 (GC) = 1.78 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- Special case: (x y)^(1/n) - x^(1/n) y^(1/n) => 0 [PV] for y > 0[] [] [69] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.0 2 (OT) = 0.20 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.6 2 (EV) = 0.62 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- arctan(tan(z)) = z for z real if and only if z is contain ed in the interval[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 atan(---------------------------------------------- -----)[] [] [70] Overfull \hbox (43.49661pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 - log(------------------------------------------- -------------)[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 4 2 2 4 2[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 sin(z) + (2cos(z) - 2)sin(z) + cos(z) + 2cos(z) + 1[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 log(--------------------------------------------- -----------)[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 4 2 2 4 2[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 sin(z) + (2cos(z) - 2)sin(z) + cos(z) + 2 cos(z) + 1[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.17 (EV) + 0.0 5 (OT) = 0.23 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.23 (EV) + 0.0 2 (OT) = 0.25 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- The principal value of this expression is 11 - 4 pi + 30 i = -1.56637 + 30 i[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (OT) = 0.03 sec[] [] [71] Overfull \hbox (69.74638pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- This is a challenge problem proposed by W. Kahan: simplif y the following[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- expression for complex z. Expanding out the expression p roduces[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 3206--3206 []\OT1/cmtt/m/n/10 -- (z^2 + 1)/(2 z) +- (z + 1)*(z - 1)/(2 z) => z or 1/z in e ach of its branches[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.33 (IN) + 0.08 (EV) + 0.22 (OT) + 0.1 5 (GC) = 0.78 sec[] [] [72] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Type: Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3206--3206 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.05 (EV) + 0.05 (OT) + 0.0 2 (GC) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.27 (EV) + 0.17 (OT) + 0.1 0 (GC) = 0.62 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.08 (EV) + 0.0 2 (OT) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.10 (EV) + 0.0 5 (OT) = 0.22 sec[] [] [73] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type : AlgebraicNumber[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.50 (IN) + 0.02 (OT) + 0.0 2 (GC) = 0.53 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.08 (EV) + 0.0 5 (OT) = 0.28 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.07 (EV) + 0.0 3 (OT) = 0.12 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 3399--3399 []\OT1/cmtt/m/n/10 -- See Joel Moses, ``Algebraic Simplification: A Guide for t he Perplexed'',[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 3399--3399 []\OT1/cmtt/m/n/10 -- _Communications of the Association of Computing Machinery _, Volume 14,[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 3399--3399 []\OT1/cmtt/m/n/10 -- Number 8, August 1971, 527--537. This expression is zero if Re(x) is[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 3399--3399 []\OT1/cmtt/m/n/10 -- contained in the interval ((4 n - 1)/2 pi, (4 n + 1)/2 pi ) for n an integer:[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.83 (IN) + 0.05 (EV) + 0. 12 (OT) = 1.0 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 +----------------------------------------- -----------+[] [] [74] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 |- --------------------------------------- -----------[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 | +---+ 8 +---+ 4[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 \| (%e ) - 2(%e ) + 1[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 1.85 (EV) + 0.10 (OT) + 0.0 5 (GC) = 2.05 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 3399--3399 []\OT1/cmtt/m/n/10 -- Use a roundabout method---show that expr is a constant eq ual to zero[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 2x + %pi 2 | 2 2x + %pi 2 2x + %pi[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 (tan(--------) + 1)\|tan(x) + 1 - 2tan(--------)tan(x) - 2tan(--------)[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 4 4 4[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 --------------------------------------------------------- ------------------[] [] [75] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.05 (EV) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 3.50 (EV) + 0.03 (OT) + 0.5 2 (GC) = 4.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.83 (IN) + 0.02 (EV) + 0.1 7 (OT) = 1.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.02 (EV) + 0.0 3 (OT) = 0.15 sec[] [] [76] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.03 (EV) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 (14) (2\|r + 1) (4\|r + 4r + 1) - 2\| r - 1[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.05 (EV) + 0.0 2 (OT) = 0.28 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 3399--3399 [] \OT1/cmtt/m/n/10 Time: 1.0 2 (EV) = 1.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.55 (IN) + 0.08 (EV) + 0.20 (OT) + 0.0 8 (GC) = 0.92 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- Solve various nonlinear equations---this cubic polynomial has all real roots[] [] [77] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +----------+2 +----- -----+[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (- 3\|- 3 + 3) |---------- + (6\|- 3 + 6) |----- ----- - 2[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 [x= ----------------------------------------------------- ---------,[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +----------+2 +----- -----+[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (- 3\|- 3 - 3) |---------- + (6\|- 3 - 6) |----- ----- + 2[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 x= ----------------------------------------------------- ---------,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.55 (EV) + 0.15 (OT) + 0.0 8 (GC) = 0.88 sec[] [] [78] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +-+ %pi %pi +-+ +-+ %pi %pi +-+[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 - \|3 sin(---) - cos(---) + 2\|3 \|3 sin(---) - cos(---) + 2\|3[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 18 18 18 18[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 [x= ---------------------------------, x= --------------- ----------------,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 1.62 (EV) + 0.12 (OT) + 0. 02 (GC) = 2.0 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = { [sqrt(5) - 1]/4 +/- 5^(1/4) sqrt(sqrt(5) + 1)/[2 s qrt(2)] i,[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- - [sqrt(5) + 1]/4 +/- 5^(1/4) sqrt(sqrt(5) - 1)/[2 s qrt(2)] i}[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +-------------+2 +------ -------+[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |45 |- - - 25 |45 |- - - 25[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (- 4 3|------------- - 10 3|------ ------- - 40)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +--------------------------------- ----------+[] [] [79] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 | +-------------+2 +-------- -----+[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |4 3|------------- - 5 3|-------- ----- + 40[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |--------------------------------- ----------[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +----------------------------------- --------+[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |4 3|------------- - 5 3|---------- --- + 40[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |----------------------------------- --------[] [] [80] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (- 4 3|------------- - 10 3|--------- ---- - 40)[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +------------------------------------ -------+[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |4 3|------------- - 5 3|----------- -- + 40[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |------------------------------------ -------[] [] [81] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +-------------------------------------- -----+[] [] [82] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +-------------+2 +------ -------+[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |45 |- - - 25 |45 |- - - 25[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (- 4 3|------------- - 10 3|------ ------- - 40)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +--------------------------------- ----------+[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 | +-------------+2 +-------- -----+[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |4 3|------------- - 5 3|-------- ----- + 40[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |--------------------------------- ----------[] [] [83] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +----------------------------------- --------+[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |4 3|------------- - 5 3|---------- --- + 40[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |----------------------------------- --------[] [] [84] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (- 4 3|------------- - 10 3|--------- ---- - 40)[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +------------------------------------ -------+[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |4 3|------------- - 5 3|----------- -- + 40[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 |------------------------------------ -------[] [] [85] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +-------------------------------------- -----+[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.05 (EV) + 0.5 2 (OT) = 0.57 sec[] [] [86] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.47 (IN) + 0.58 (EV) + 0.0 7 (OT) = 1.12 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = {2^(1/3) +- sqrt(3), +- sqrt(3) - 1/2^(2/3) +- i sqrt (3)/2^(2/3)}[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.23 (IN) + 0.08 (EV) + 0.1 3 (OT) = 0.45 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (EV) = 0.05 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = 1 +- sqrt(+-sqrt(+-4 sqrt(3) - 3) - 3)/sqrt(2) [Ric hard Liska][] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 solve(x**8 - 8*x**7 + 34*x**6 - 92*x**5 + 175*x**4 - 236*x** 3 + 226*x**2 _[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (9) [x - 8x + 34x - 92x + 175x - 236x + 226x - 14 0x + 46= 0][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.02 (EV) + 0.0 5 (OT) = 0.12 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- The following equations have an infinite number of soluti ons (let n be an[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = {log(sqrt(z) - 1), log(sqrt(z) + 1) + i pi} [+ n 2 pi i, + n 2 pi i][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.07 (EV) + 0.0 5 (OT) = 0.32 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] [87] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 0.85 (EV) + 0.12 (OT) + 0.3 8 (GC) = 1.67 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = (1 +- sqrt(9 - 8 n pi i))/2. Real solutions correspo nd to n = 0 =>[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.17 (EV) + 0.0 2 (OT) = 0.18 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = -W[n](-1) [e.g., -W[0](-1) = 0.31813 - 1.33724 i] whe re W[n](x) is the[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.07 (EV) + 0.0 2 (OT) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.08 (EV) + 0.0 2 (OT) = 0.13 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- This equation is already factored and so *should* be easy to solve:[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 3 4 3 2 3[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 (15) (x + 1)cos(3x) sin(x) + (2x + 2)cos(3x) sin(x) + (x + 1)cos(3x) = 0[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.03 (EV) + 0.0 3 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 2.88 (EV) + 0.0 2 (GC) = 2.90 sec[] [] [88] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.1 5 (EV) = 0.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (EV) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (EV) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.1 5 (EV) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.68 (EV) + 0.0 2 (OT) = 0.70 sec[] [] [89] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +-----------+ +-----------+ +---------+ +---------+[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 | +-+ | +-+ | +-+ | +-+[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 \|- 2\|5 - 2 \|- 2\|5 - 2 \|2\|5 - 2 \|2\|5 - 2[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 [x= - --------------,x= --------------,x= - ------------, x= ------------][] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 2 2 2 2[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 1.08 (EV) + 0.03 (OT) + 0.3 8 (GC) = 1.52 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.03 (EV) + 0.0 3 (OT) = 0.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 5 (EV) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 3 (EV) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.18 (EV) + 0.0 3 (OT) = 0.25 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 +---------+ +---------+ +-----------+ +-----------+[] [] [90] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 | +-+ | +-+ | +-+ | +-+[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 \|2\|5 - 2 \|2\|5 - 2 \|- 2\|5 - 2 \|- 2\|5 - 2[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 [x= ------------,x= - ------------,x= --------------,x= - --------------][] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 2 2 2 2[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.17 (EV) + 0.0 3 (OT) = 0.27 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- This problem is from a computational biology talk => 1 - log_2[m (m - 1)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.1 2 (EV) = 0.25 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = log(c/a) / log(b/d) for a, b, c, d != 0 and b, d != 1 [Bill Pletsch][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.18 (EV) + 0.0 2 (OT) = 0.35 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.10 (EV) + 0.0 3 (OT) = 0.15 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- Recursive use of inverses, including multiple branches of rational[] [] [91] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.25 (EV) + 0.03 (OT) + 0.0 2 (GC) = 0.35 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- x = {-0.784966, -0.016291, 0.802557} From Metha Kamminga -van Hulsen,[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- ``Hoisting the Sails and Casting Off with Maple'', _Compu ter Algebra[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- Nederland Nieuwsbrief_, Number 13, December 1994, ISSN 13 80-1260, 27--40.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.50 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.53 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 8 (EV) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 3 (EV) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.05 (EV) + 0.0 2 (OT) = 0.08 sec[] [] [92] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.58 (IN) + 0.02 (EV) + 0.1 2 (OT) = 0.72 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- where t = (arctan[sqrt(5)/2] - pi)/3. The third answer i s the root of[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 3 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation Complex E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.47 (IN) + 0.02 (EV) + 0.0 5 (OT) = 0.53 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 conjugate having 1 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] [93] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation Polynomia l Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 3 (OT) = 0.10 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 0.02 (EV) + 0.0 7 (OT) = 0.40 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 8 (IN) = 0.08 sec[] [] [94] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.68 (IN) + 0.05 (EV) + 0.0 8 (OT) = 0.82 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- A linear system arising from the computation of a truncat ed power series[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- solution to a differential equation. There are 189 equat ions to be solved[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- for 49 unknowns. 42 of the equations are repeats of othe r equations; many[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- others are trivial. Solving this system directly by Gaus sian elimination[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- is *not* a good idea. Solving the easy equations first i s probably a better[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- method. The solution is actually rather simple. [Stanl y Steinberg][] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 -- => k1 = ... = k22 = k24 = k25 = k27 = ... = k30 = k32 = k 33 = k35 = ...[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -b*k8/a+c*k8/a = 0, -b*k11/a+c*k11/a = 0, -b*k10/a+c*k10/a+ k2 = 0, _[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -k3-b*k9/a+c*k9/a = 0, -b*k14/a+c*k14/a = 0, -b*k15/a+c*k15 /a = 0, _[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -b*k18/a+c*k18/a-k2 = 0, -b*k17/a+c*k17/a = 0, -b*k16/a+c*k 16/a+k4 = 0, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -b*k13/a+c*k13/a-b*k21/a+c*k21/a+b*k5/a-c*k5/a = 0, b*k44/a -c*k44/a = 0, _[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -b*k45/a+c*k45/a = 0, -b*k20/a+c*k20/a = 0, -b*k44/a+c*k44/ a = 0, _[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 b*k46/a-c*k46/a = 0, b**2*k47/a**2-2*b*c*k47/a**2+c**2*k47 /a**2 = 0, k3 = 0, _[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k4/b-c*k4/b = 0, a*k3/b-c*k3/b+k9 = 0, -k10+a*k2/b-c*k2/ b = 0, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k7/b-c*k7/b = 0, -k9 = 0, k11 = 0, b*k12/a-c*k12/a+a*k6/ b-c*k6/b = 0, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k15/b-c*k15/b = 0, k10+a*k18/b-c*k18/b = 0, -k11+a*k17/b -c*k17/b = 0, _[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k16/b-c*k16/b = 0, -a*k13/b+c*k13/b+a*k21/b-c*k21/b+a*k5 /b-c*k5/b = 0, _[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k19/b-c*k19/b = 0, -a*k45/b+c*k45/b = 0, a*k46/b-c*k46/b = 0, _[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -a*k1/c+b*k1/c = 0, -k16-a*k4/c+b*k4/c = 0, -a*k3/c+b*k3/c = 0, _[] [] [95] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -a*k6/c+b*k6/c = 0, -a*k8/c+b*k8/c = 0, -a*k11/c+b*k11/c+k1 7 = 0, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -a*k13/c+b*k13/c+a*k21/c-b*k21/c-a*k5/c+b*k5/c = 0, a*k44/c -b*k44/c = 0, _[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -a*k45/c+b*k45/c = 0, -a*k44/c+b*k44/c = 0, a*k46/c-b*k46/c = 0, _[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a**2*k49/c**2-2*a*b*k49/c**2+b**2*k49/c**2 = 0, k8 = 0, k1 1 = 0, -k15 = 0, _[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k10-k18 = 0, -k17 = 0, k9 = 0, -k16 = 0, -k29 = 0, k14-k32 = 0, _[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -k21+k23-k31 = 0, -k24-k30 = 0, -k35 = 0, k44 = 0, -k45 = 0 , k36 = 0, _[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k13-k23+k39 = 0, -k20+k38 = 0, k25+k37 = 0, b*k26/a-c*k26/ a-k34+k42 = 0, _[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -2*k44 = 0, k45 = 0, k46 = 0, b*k47/a-c*k47/a = 0, k41 = 0, k44 = 0, _[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -a*k27/b+c*k27/b-k33 = 0, k45 = 0, -k46 = 0, -a*k48/b+c*k48 /b = 0, _[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k28/c-b*k28/c+k40 = 0, -k45 = 0, k46 = 0, a*k48/b-c*k48/ b = 0, _[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k49/c-b*k49/c = 0, -a*k49/c+b*k49/c = 0, -k1 = 0, -k4 = 0, -k3 = 0, _[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k24+k30 = 0, k21+k23-k31 = 0, k28 = 0, -k44 = 0, k45 = 0, -k30-k6 = 0, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k19-k37 = 0, k26-a*k34/b+c*k34/b-k42 = 0, k44 = 0, -2*k45 = 0, k46 = 0, _[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 a*k48/b-c*k48/b = 0, a*k35/c-b*k35/c-k41 = 0, -k44 = 0, k4 6 = 0, _[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 b*k47/a-c*k47/a = 0, -a*k49/c+b*k49/c = 0, -k40 = 0, k45 = 0, -k46 = 0, _[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -a*k48/b+c*k48/b = 0, a*k49/c-b*k49/c = 0, k1 = 0, k4 = 0, k3 = 0, _[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -k8 = 0, -k11 = 0, -k10+k2 = 0, -k9 = 0, k37+k7 = 0, -k14-k 38 = 0, _[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -k28+b*k40/a-c*k40/a = 0, k44 = 0, -k45 = 0, -k27 = 0, -k44 = 0, _[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k46 = 0, b*k47/a-c*k47/a = 0, k29 = 0, k32+k38 = 0, k31-k3 9+k5 = 0, _[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 -b*k47/a+c*k47/a = 0, -a*k48/b+c*k48/b = 0, a*k49/c-b*k49/c = 0, k33 = 0, _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 6.35 (IN) + 0.72 (EV) + 1.33 (OT) + 0.8 7 (GC) = 9.26 sec[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 vars:= [k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k 13, k14, k15, k16, _[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k2 7, k28, k29, k30, _[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k31, k32, k33, k34, k35, k36, k37, k38, k39, k40, k4 1, k42, k43, k44, _[] [] Overfull \hbox (804.73997pt too wide) in paragraph at lines 4359--4359 []\OT1/cmtt/m/n/10 Type: List OrderedVariableList [k1,k2,k3,k4,k5,k6,k7,k8,k9,k 10,k11,k12,k13,k14,k15,k16,k17,k18,k19,k20,k21,k22,k23,k24,k25,k26,k27,k28,k29, k30,k31,k32,k33,k34,k35,k36,k37,k38,k39,k40,k41,k42,k43,k44,k45,k46,k47,k48,k49 ][] [] [96] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 [k1= 0, k2= 0, k3= 0, k4= 0, k5= 0, k6= 0, k7= 0, k8= 0 , k9= 0, k10= 0,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k11= 0, k12= 0, k13= 0, k14= 0, k15= 0, k16= 0, k17= 0 , k18= 0, k19= 0,[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 %DY a[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k20= 0, k21= 0, k22= 0, k23= %DX, k24= 0, k25= 0, k26= -----, k27= 0,[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 %DY b[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k28= 0, k29= 0, k30= 0, k31= %DX, k32= 0, k33= 0, k34= -----, k35= 0,[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 k36= 0, k37= 0, k38= 0, k39= %DX, k40= 0, k41= 0, k42= %DY, k43= %DZ,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.69 (IN) + 1.42 (EV) + 0.1 5 (OT) = 2.25 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: Equation P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] [97] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 4 3 2 2 - 18z + 24z + 2 1z + 12z + 3[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 [12z - 12z - 30z + 7z + 3x = 0, y= ----------------- -------------,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Type: List List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4359--4359 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 1.18 (EV) + 0.03 (OT) + 0.0 3 (GC) = 1.27 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.38 (EV) + 0.18 (OT) + 0.1 5 (GC) = 1.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 T ype: List Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.08 sec[] [] [98] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.23 (IN) + 0.0 2 (OT) = 0.25 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (EV) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.0 3 (OT) = 0.22 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n /10 Type: Boolean[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Type: Lis t Equation Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.0 2 (OT) = 0.15 sec[] [] [99] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] [100] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] [101] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4578--4578 []\OT1/cmtt/m/n/10 -- The next two examples come from Abdubrahim Muhammad Farha t, _Stability[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4578--4578 []\OT1/cmtt/m/n/10 -- Analysis of Finite Difference Schemes_, Ph.D. dissertatio n, University of[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 []\OT1/cmtt/m/n/10 -- New Mexico, Albuquerque, New Mexico, December 1993 => 0 < = A <= 1/2[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4578--4578 []\OT1/cmtt/m/n/10 -- => 125 A^4 + 24 A^2 - 48 < 0 or |A| < 2/5 sqrt([8 sqr t(6) - 3]/5)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 There are 18 exposed and 3 unexposed library operations n amed solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] [102] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4578--4578 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Type: Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.97 (IN) + 0.23 (EV) + 0.33 (OT) + 0.1 7 (GC) = 1.70 sec[] [] [103] Overfull \hbox (43.49661pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- a = (a_r(r, theta, phi), a_theta(r, theta, phi), a_phi(r, theta, phi)).[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- Here, phi is in the x-y plane and theta is the angle with the z-axis.[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- => 1/r^2 d/dr[r^2 a_r] + 1/[r sin(theta)] d/dtheta[sin(th eta) a_theta][] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- => da_r/dr + (2 a_r)/r + 1/r da_theta/dtheta + a_theta/[r tan(theta)][] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- See Keith R. Symon, _Mechanics_, Third Edition, Addison-W esley Publishing[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 --div([a_r(r, theta, phi), a_theta(r, theta, phi), a_phi(r, theta, phi)])[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- Express dR/dt in spherical coordinates (r, theta, phi) wh ere R is the[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- position vector r*Rhat(theta, phi) with Rhat being the un it vector in the[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.0 8 (IN) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 3 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Type: Vector E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.58 (IN) + 0.03 (EV) + 0.1 4 (OT) = 0.75 sec[] [] [104] Overfull \hbox (11.99689pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named D[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 r(t)phi (t)rhat (theta(t),phi(t)) + r(t)theta (t)rha t (theta(t),phi(t))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Type: Vector E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.10 (EV) + 0.0 3 (OT) = 0.15 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- Vector potential => (x y z, x^2 y^2 z^2, y^2 z^3) is one possible solution.[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- See Harry F. Davis and Arthur David Snider, _Introduction to Vector[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 --vectorpotential(vector([2*y*z**3 - 2*x**2*y**2*z, x*y, 2*x *y**2*z**2 - x*z]))[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- Orthogonalize the following vectors (Gram-Schmidt). See Lee W. Johnson and[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- R. Dean Riess, _Introduction to Linear Algebra_, Addison- Wesley Publishing[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 -- Company, 1981, p. 104 => [[0 1 2 1], [0 -1 1 -1], [2 1 0 -1]]^T[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 4742--4742 []\OT1/cmtt/m/n/10 [transpose(matrix([[0, 1, 2, 1]])), transpose(matrix([[0, 1, 3, 1]])), _[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 transpose(matrix([[1, 1, 1, 0]])), transpose(matrix([[1, 3, 6, 2]]))][] [] [105] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Type: Li st Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 3 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Type: List Matrix E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 4742--4742 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.20 (EV) + 0.07 (OT) + 0.0 3 (GC) = 0.40 sec[] [] [106] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.02 (EV) + 0.0 2 (GC) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 T ype: List Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.05 (OT) + 0.0 2 (GC) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Create the 7 x 6 matrix B from rearrangements of the elem ents of the 4 x 4[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- B = [A(1:3,2:4), A([1,2,4],[3,1,4]); A, [A(1:2,3:4); A([4 ,1],[3,2])]][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- [41 42 43 44|13 12]]. See Michael James Wester, _Sym bolic Calculation[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- and Expression Swell Analysis of Matrix Determinants and Eigenstuff_, Ph.D.[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- dissertation, University of New Mexico, Albuquerque, New Mexico, December[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] [107] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 [A(1,3), A(1,2) ]]))))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 3 (OT) = 0.10 sec[] [] Overfull \hbox (232.49496pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 @[matrix({\Tt{}a,\ 1],[0,\ a\nwendquote}), b, matrix({\Tt {}c,\ 1,\ 0],[0,\ c,\ 1],[0,\ 0,\ c\nwendquote})])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/ n/10 Type: Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.22 (OT) + 0.0 2 (GC) = 0.53 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Ma trix PrimeField 2[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.05 (OT) + 0.0 5 (GC) = 0.17 sec[] [] [108] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.23 (EV) + 0.07 (OT) + 0.1 0 (GC) = 0.62 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: SquareMatrix(2,Ex pression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 0.0 7 (EV) = 0.38 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 + matrix({\Tt{}7,\ -9,\ 11],\ [-8,\ 10,\ -12\nwendquote}))[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 @[(2a - 8)y + (a + 7)x (4a + 10)y + (3a - 9)x (6a - 12) y + (5a + 11)x][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 1.58 (IN) + 0.3 5 (OT) = 1.93 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 5 exposed and 6 unexposed library operations na med norm[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named norm[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Frobenius norm => (a^2 + b^2 + c^2)/(|a| |b| |c|) (a, b , c real)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 norm(matrix([[a/(b*c), 1/c, 1/b], [1/c, b/(a*c), 1/a], [1/b, 1/a, c/(a*b)]]), _[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 5 exposed and 6 unexposed library operations na med norm[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] [109] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named norm[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Hermitian (complex conjugate transpose) => [[1, f(4 + 5 i )], [2 - 3 i, 6]][] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- (This assumes f is a real valued function. In general, t he (1, 2) entry[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 7 (IN) = 0.07 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 map('conjugate, transpose(matrix([[1, 2 + 3*%i], [f(4 - 5*%i ), 6]])) _[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot convert from type Matrix Expression Complex Intege r to Matrix[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (OT) = 0.05 sec[] [] [110] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Union(Matrix Fraction Polyno mial Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.38 (IN) + 0.0 7 (OT) = 0.45 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- See Charles G. Cullen, _Matrices and Linear Transformatio ns_, Second[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.0 2 (OT) = 0.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 8 (IN) = 0.08 sec[] [] [111] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- => 2. See Gerald L. Bradley, _A Primer of Linear Algebra _, Prentice-Hall,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.35 (EV) + 0.0 3 (OT) = 0.43 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 [2*(1 - cos(t)**2)*cos(t), (1 - 2*sin(t)**2)*si n(t)]]))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type : PositiveInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.13 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Null space => [[2 4 1 0], [0 -3 0 1]]^T or variant [Bra dley, p. 207][] [] [112] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Li st Vector Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.03 (EV) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Define a Vandermonde matrix (useful for doing polynomial interpolations)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.0 5 (OT) = 0.20 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 2 2 3 3 3 2 2 3 3 2 2 2 3[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 ((x - w )y + (- x + w )y + w x - w x )z + (- w x + w x)y[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 7 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.25 (EV) + 0.0 3 (OT) = 0.35 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Minimum polynomial => (lambda - 1)^2 (lambda + 1) [Cull en, p. 181][] [] [113] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 minimalPolynomial having 1 argument(s) but none was de termined to[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Compute the eigenvalues of a matrix from its characterist ic polynomial[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 3 (OT) = 0.05 sec[] [] [114] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: List Equation Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.47 (IN) + 0.18 (EV) + 0.0 7 (OT) = 0.72 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- In theory, an easy eigenvalue problem! => lambda = {2 - a } for k = 1..100[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (80.24629pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 Type: List Union(Fraction Polynomial Integer,SuchThat(Symbol ,Polynomial Integer))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 31.44 (IN) + 7.85 (EV) + 4.32 (OT) + 5.17 (GC) = 48.77 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- => lambda = {4 sin^2(pi k/[2 (n + 1)])} for k = 1..n for an n x n matrix.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- See J. H. Wilkinson, _The Algebraic Eigenvalue Problem_, Oxford University[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] [115] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.08 (EV) + 0.0 2 (OT) = 0.18 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Eigenvalues of the Rosser matrix. This matrix is notorio us for causing[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- numerical eigenvalue routines to fail. [Wester, p. 146 (Cleve Moler)][] [] Overfull \hbox (190.49533pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 rosser:= matrix({\Tt{}\ 611,\ \ 196,\ -192,\ \ 407,\ \ \ -8, \ \ -52,\ \ -49,\ \ \ 29],\ {\_}\nwnewline[] [] Overfull \hbox (253.49478pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ 196,\ \ 899,\ \ 113,\ - 192,\ \ -71,\ \ -43,\ \ \ -8,\ \ -44],\ {\_}\nwnewline[] [] Overfull \hbox (274.4946pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [-192,\ \ 113,\ \ 899,\ \ 196,\ \ \ 61,\ \ \ 49,\ \ \ \ 8,\ \ \ 52],\ {\_}\nwnewline[] [] Overfull \hbox (269.24464pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ 407,\ -192,\ \ 196,\ \ 611,\ \ \ \ 8,\ \ \ 44,\ \ \ 59,\ \ -23],\ {\_}\nwnewline[] [] Overfull \hbox (269.24464pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ \ -8,\ \ -71,\ \ \ 61,\ \ \ \ 8,\ \ 411,\ -599,\ \ 208,\ \ 208],\ {\_}\nwnewline[] [] Overfull \hbox (258.74474pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ -52,\ \ -43,\ \ \ 49,\ \ \ 44,\ -599,\ \ 411,\ \ 208,\ \ 208],\ {\_}\nwnewline[] [] Overfull \hbox (274.4946pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ -49,\ \ \ -8,\ \ \ \ 8, \ \ \ 59,\ \ 208,\ \ 208,\ \ \ 99,\ -911],\ {\_}\nwnewline[] [] Overfull \hbox (242.99487pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ \ 29,\ \ -44,\ \ \ 52,\ \ -23,\ \ 208,\ \ 208,\ -911,\ \ \ 99\nwendquote});[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 [10\|10405 ,- 10\|10405 ,- 100\|26 + 510,100\|26 + 510, 0,1000,1000,1020][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 1.0 (EV) + 0.0 2 (OT) = 1.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: List Float[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.28 (EV) + 0.05 (OT) + 0.0 2 (GC) = 0.42 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 125 124 123 122[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 ? - 86215.0 ? + 3672643562.0 ? - 10305 25241 36076.0 ?[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 121 120[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 214242065 1760625974.0 ? - 0.3519437981 9139045528 E 23 ?[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 119 118[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.4757930276 0524392937 E 27 ? - 0.5443719612 8759 169508 E 31 ?[] [] [116] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 117 116[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.5379979009 8770356924 E 35 ? - 0.4664749268 2226 816519 E 39 ?[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 115 114[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.3592087692 2534478781 E 43 ? - 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0.9782596656 7436 389234 E 129 ?[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 89 88[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1280860874 3712484582 E 133 ? - 0.1573106414 8242 673085 E 136 ?[] [] [117] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 87 86[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1802439290 923378293 E 139 ? - 0.1909575702 23214 05039 E 142 ?[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 85 84[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1841324046 7558627001 E 145 ? - 0.1565578204 6290 786175 E 148 ?[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 83 82[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1084018298 6945156255 E 151 ? - 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0.2118385504 6752677393 E 175 ? + 0.1812642708 76 94905254 E 178 ?[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 73 72[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 - 0.1449610412 5042294701 E 181 ? + 0.1086839448 89 24848295 E 184 ?[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 71 70[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 - 0.7651391596 9967540208 E 186 ? + 0.5060299956 31 24704326 E 189 ?[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 69 68[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 - 0.3142367184 7713335751 E 192 ? + 0.1829574772 04 15689208 E 195 ?[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 67 66[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 - 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0.1270418736 3 851064032 E 269 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 37 36[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1660218706 9618209188 E 270 %G + 0.2862105879 5 857092645 E 273 %G[] [] [123] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 34 33[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1484448521 8686301081 E 278 %G - 0.2123387008 7 94925024 E 280 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 32 31[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.2506751820 5612670323 E 282 %G - 0.2494329065 6 728197272 E 284 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 30 29[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.2109806712 8889498289 E 286 %G - 0.1521224934 1 012072561 E 288 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 28 27[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.9351456154 4154324412 E 289 %G - 0.4897636603 2 042451012 E 291 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 26 25[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.2184259738 2222779488 E 293 %G - 0.8298614578 7 219241205 E 294 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 24 23[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.2689816827 0170685903 E 296 %G - 0.7455272800 2 234756452 E 297 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 22 21[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1771957532 6653063304 E 299 %G - 0.3622167611 4 512303391 E 300 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 20 19[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.6385537866 7592677628 E 301 %G - 0.9730487915 5 887722779 E 302 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 18 17[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1283818926 2924796953 E 304 %G - 0.1467911675 9 006671118 E 305 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 16 15[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1454586351 2070495541 E 306 %G - 0.1247986846 9 975071194 E 307 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 14 13[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.9251453429 5406258973 E 307 %G - 0.5905679202 8 110037735 E 308 %G[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 12 11[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.3230290678 3860457938 E 309 %G - 0.1503623501 5 158820289 E 310 %G[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 10 9[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.5900666022 0150867207 E 310 %G - 0.1927643191 6 531249396 E 311 %G[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 8 7[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.5152198729 6418385783 E 311 %G - 0.1099680204 06 15001798 E 312 %G[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 6 5[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1809295237 1502506625 E 312 %G - 0.2172461015 83 15085132 E 312 %G[] [] [124] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 4 3[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1733446261 3560586487 E 312 %G - 0.7597264055 30 53863391 E 311 %G[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 0.1050398077 8828775171 E 311 %G - 0.4443971993 29 26345443 E 309 %G[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 Type: List Union(Fraction Polynomial Float,SuchThat(Symbol,P olynomial Float))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 12.73 (EV) + 0.82 (OT) + 1.97 (GC) = 15.83 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.0 3 (OT) = 0.18 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.07 (EV) + 0.0 3 (OT) = 0.27 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Eigenvalues and eigenvectors => lambda = {a, a, a, 1 - i, 1 + i},[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- [0, (1 + i)/2, 0, 0, 1], [0, (1 - i)/2, 0 , 0, 1]]^T[] [] [125] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (190.49533pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 Type: List Record(radval: Expression Integer,radmult: Intege r,radvect: List Matrix Expression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.17 (EV) + 0.0 8 (OT) = 0.28 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Eigenvalues and generalized eigenvectors [Johnson and R iess, p. 193][] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- => lambda = {1, 1, 1}, eigenvectors = [[4 -1 4], [1 -1 2] , [3 -1 3]]^T[] [] [126] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (190.49533pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 Type: List Record(radval: Expression Integer,radmult: Intege r,radvect: List Matrix Expression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Eigenvalues and generalized eigenvectors [Johnson and R iess, p. 199][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] [127] Overfull \hbox (190.49533pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 Type: List Record(radval: Expression Integer,radmult: Intege r,radvect: List Matrix Expression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.02 (EV) + 0.0 5 (OT) = 0.12 sec[] [] Overfull \hbox (153.74565pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Jordan form => diag([[1 1],[0 1]], {\Tt{}1\ 1],[0\ 1\nwen dquote}, -1) [Gantmacher, p. 172][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Smith normal form => [[1, 0], [0, x^4 - x^2 + 1]] [Cull en, p. 230][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 2 exposed and 6 unexposed library operations na med exp[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named exp[] [] [128] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- [[1, 4 sin(w t)/w - 3 t , 6 [w t - sin(w t)], 2/w [1 - co s(w t)] ],[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- [0, 4 cos(w t) - 3 , 6 w [1 - cos(w t)], 2 sin(w t) ],[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- [0, -2/w [1 - cos(w t)], 4 - 3 cos(w t) , sin(w t)/w ],[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- [0, -2 sin(w t) , 3 w sin(w t) , cos(w t) ]][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 2 exposed and 6 unexposed library operations na med exp[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named exp[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Sine of a Jordan matrix => diag([[sin a, cos a],[0, sin a ]], sin b,[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- See F. R. Gantmacher, _The Theory of Matrices_, Volume On e, Chelsea[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Publishing Company, 1977, p. 100 to see how to do a gener al function.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 3 (OT) = 0.07 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 2 exposed and 6 unexposed library operations na med sin[] [] [129] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named sin[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Sine of a matrix => [[1 0 0], [0 1 0], [0 0 1]] [Cullen , p. 261][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/1 0 Type: Matrix Pi[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.0 5 (OT) = 0.35 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 2 exposed and 6 unexposed library operations na med sin[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named sin[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Matrix square root => {+-[[3 1], [1 4]], +-1/sqrt(5) [[-1 7], [7 6]]}[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 2 exposed and 0 unexposed library operations na med sqrt[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] [130] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named sqrt[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- => [[e, (e - n) v w + e/2, (n - e) v], [0, e, 0], [0, (e - n) w, n][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 2 exposed and 0 unexposed library operations na med sqrt[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named sqrt[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 There are 2 exposed and 0 unexposed library operations na med sqrt[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] [131] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named sqrt[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- => [1/sqrt(14) 3/sqrt(10) 1/sqrt(35) ] [2 sqrt(7) 0] [1/ sqrt(2) 1/sqrt(2)][] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- [2/sqrt(14) 0 -sqrt(5/7)] [0 0] [1/ sqrt(2) -1/sqrt(2)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Jacobian of (r cos t, r sin t) => [[cos t, -r sin t], [si n t, r cos t]][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 2 (OT) = 0.08 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Hessian of r^2 sin t => [[2 sin t, 2 r cos t], [2 r cos t , -r^2 sin t]][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Wronskian of (cos t, sin t) => [[cos t, sin t], [-sin t, cos t]][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- How easy is it to define functions to do the last three o perations?[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Jacobian of (r cos t, r sin t) => [[cos t, -r sin t], [si n t, r cos t]][] [] [132] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Compiling function MYjacobian with type (List Expression Integer,[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 List OrderedVariableList [r,t]) -> Matrix Expression I nteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (EV) + 0.0 5 (OT) = 0.15 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Hessian of r^2 sin t => [[2 sin t, 2 r cos t], [2 r cos t , -r^2 sin t]][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Compiling function MYhessian with type (Expression Intege r,List[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.03 (EV) + 0.0 3 (OT) = 0.20 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 []\OT1/cmtt/m/n/10 -- Wronskian of (cos t, sin t) => [[cos t, sin t], [-sin t, cos t]][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Your expression cannot be fully compiled because it conta ins an[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 integer expression (for - ) whose sign cannot be deter mined (in[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 general) and so must be specified by you. Perhaps you can try[] [] [133] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Type: Matrix E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6003--6003 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.0 5 (EV) = 0.20 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 []\OT1/cmtt/m/n/10 -- delta(j, i) delta(h, k) - delta(j, k) delta(h, i). See D avid Lovelock and[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 []\OT1/cmtt/m/n/10 -- Hanno Rund, _Tensors, Differential Forms, & Variational P rinciples_, John[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Type: CartesianTe nsor(1,4,Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.03 (OT) + 0.0 2 (GC) = 0.07 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 There are no exposed library operations named delta but t here is one[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 unexposed operation with that name. Use HyperDoc Brows e or issue[] [] [134] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named delta[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6123--6123 []\OT1/cmtt/m/n/10 -- Levi-Civita symbol: [epsilon(2,1,3), epsilon(1,3,1)] => [ -1, 0][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Type: CartesianTe nsor(1,3,Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 T ype: List Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.0 2 (GC) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.02 (OT) + 0.0 3 (GC) = 0.09 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Typ e: Matrix Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] [135] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Type: CartesianTe nsor(1,2,Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.0 8 (OT) = 0.23 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6123--6123 []\OT1/cmtt/m/n/10 -- Definition of the Christoffel symbol of the first kind (a is the metric[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6123--6123 []\OT1/cmtt/m/n/10 -- Partial covariant derivative of a type (1, 1) tensor fiel d (Chr2 is the[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6123--6123 []\OT1/cmtt/m/n/10 -- Christoffel symbol of the second kind) [Lovelock and Rund , p. 77][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (EV) + 0.0 2 (GC) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Type: Expre ssion List Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6123--6123 [] \OT1/cmtt/m/n/10 Time: 0.65 (IN) + 0.02 (EV) + 0.12 (OT) + 0.0 5 (GC) = 0.83 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6123--6123 []\OT1/cmtt/m/n/10 -- Verify the Bianchi identity for a symmetric connection (K is the Riemann[] [] [136] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- Simplify the sum below to sum(x[i]^2, i = 1..n) - sum(x[i ], i = 1..n)^2/n[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.1 0 (OT) = 0.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.98 (IN) + 0.41 (EV) + 0.32 (OT) + 0.1 5 (GC) = 1.87 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.22 (EV) + 0.07 (OT) + 0.0 2 (GC) = 0.48 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- Derivation of the least squares fitting of data points (x [i], y[i]) to a[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- line y = m x + b. See G. Keady, ``Using Maple's linalg p ackage with Zill[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- and Cullen _Advanced Engineering Mathematics_, Part II: V ectors, Matrices[] [] [137] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (EV) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.15 (EV) + 0.0 2 (OT) = 0.33 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: List List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 1.45 (IN) + 0.30 (EV) + 0.20 (OT) + 0.0 8 (GC) = 2.03 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- Indefinite sum => (-1)^n binomial(2 n, n). See Herbert S , Wilf,[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- ``IDENTITIES and their computer proofs'', University of P ennsylvania.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.90 (EV) + 0.03 (OT) + 0.0 3 (GC) = 1.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] [138] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.92 (EV) + 0.0 2 (OT) = 1.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.40 (EV) + 0.0 3 (OT) = 0.47 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- Dixon's identity (check whether Zeilberger's algorithm is implemented).[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- sum(..., k = -min(a, b, c)..min(a, b, c)) => (a + b + c)! /(a! b! c!)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 6.12 (EV) + 0.05 (OT) + 1.0 2 (GC) = 7.45 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.05 (EV) + 0.0 3 (OT) = 0.33 sec[] [] [139] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.12 (EV) + 0.0 2 (OT) = 0.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Fraction Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.08 (EV) + 0.0 2 (OT) = 0.12 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- See Daniel I. A. Cohen, _Basic Techniques of Combinatoria l Theory_, John[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- Wiley and Sons, 1978, p. 60. The following two sums can be derived directly[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- sum(k^2 * binomial(n, k) * x^k, k = 1..n) = n x (1 + n x) (1 + x)^(n - 2)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.20 (EV) + 0.0 2 (OT) = 0.32 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.20 (EV) + 0.0 2 (OT) = 0.25 sec[] [] [140] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.55 (EV) + 0.0 3 (OT) = 0.67 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 fibonacci having 1 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 fibonacci having 1 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- See Konrad Knopp, _Theory and Application of Infinite Ser ies_, Dover[] [] [141] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.27 (EV) + 0.0 3 (OT) = 0.37 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.20 (EV) + 0.0 3 (OT) = 0.28 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 There are 2 exposed and 0 unexposed library operations na med floor[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named floor[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.45 (IN) + 1.0 (EV) + 0.05 (OT) + 0.5 5 (GC) = 2.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.32 (EV) + 0.0 7 (OT) = 0.48 sec[] [] [142] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 limit(sum(1/((3*k + 1)*(3*k + 2)*(3*k + 3)), k = 0..n), n = %plusInfinity)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.30 (EV) + 0.0 2 (OT) = 0.42 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- => 1/2 (2^(n - 1) + 2^(n/2) cos(n pi/4)) [Gradshteyn an d Ryzhik 0.153(1)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 4.83 (EV) + 0.02 (OT) + 0.5 3 (GC) = 5.52 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 limit(sum(1/(sqrt(k*(k + 1)) * (sqrt(k) + sqrt(k + 1))), k = 1..n), _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.58 (EV) + 0.0 3 (OT) = 0.72 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- => 1/sqrt([1 - x y]^2 - 4 x^2) (| x y | < 1 and -1 <= x < 1).[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 -- From Evangelos A. Coutsias, Michael J. Wester and Alan S. Perelson, ``A[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 limit(sum(sum(binomial(n, k)*binomial(n - k, n - 2*k)*x**n*y **(n - 2*k), _[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 There are 2 exposed and 0 unexposed library operations na med floor[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named floor[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 limit(limit(sum(sum(factorial(n)/(factorial(k)**2*factorial( n - 2*k))* _[] [] [143] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 There are 3 exposed and 0 unexposed library operations na med limit[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named limit[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6474--6474 []\OT1/cmtt/m/n/10 limit(sum(product(k/(2*k - 1), k = 1..m), m = 2..n), n = %pl usInfinity)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6474--6474 [] \OT1/cmtt/m/n/10 Time: 0.37 (IN) + 0.33 (EV) + 0.0 5 (OT) = 0.75 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6579--6579 []\OT1/cmtt/m/n/10 -- => [640 pi^3]/[2187 sqrt(3)] [Gradshteyn and Ryzhik 8.3 38(5)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 1.18 (IN) + 0.25 (EV) + 0.42 (OT) + 0.1 8 (GC) = 2.03 sec[] [] [144] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.45 (IN) + 0.0 7 (OT) = 0.52 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.02 (EV) + 0.0 3 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 0.03 (EV) + 0.0 3 (OT) = 0.33 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.10 sec[] [] [145] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.56 (IN) + 0.07 (EV) + 0.18 (OT) + 0.0 3 (GC) = 0.85 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6579--6579 []\OT1/cmtt/m/n/10 limit(product((k**3 - 1)/(k**3 + 1), k = 2..n), n = %plusInf inity)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.45 (IN) + 0.27 (EV) + 0.09 (OT) + 0.0 3 (GC) = 0.83 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.08 (EV) + 0.0 3 (OT) = 0.22 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 6579--6579 []\OT1/cmtt/m/n/10 limit(product(1 + (-1)**(k + 1)/(2*k - 1), k = 1..n), n = %p lusInfinity)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.1 7 (EV) = 0.25 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6579--6579 []\OT1/cmtt/m/n/10 limit(product((k*(k + 1) + 1 + %i)/(k*(k + 1) + 1 - %i), k = 0..n), _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6579--6579 [] \OT1/cmtt/m/n/10 Time: 0.98 (IN) + 0.50 (EV) + 0.20 (OT) + 0.0 3 (GC) = 1.72 sec[] [] [146] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Union(OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 1.07 (IN) + 0.58 (EV) + 0.28 (OT) + 0.2 5 (GC) = 2.18 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Union(OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.38 (IN) + 0.12 (EV) + 0.0 3 (OT) = 0.53 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6696--6696 []\OT1/cmtt/m/n/10 -- See Dominik Gruntz, _On Computing Limits in a Symbolic Ma nipulation System_,[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6696--6696 []\OT1/cmtt/m/n/10 -- Ph.D. dissertation, Swiss Federal Institute of Technology , Zurich,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.21 (IN) + 0.45 (EV) + 0.02 (OT) + 0.0 2 (GC) = 0.70 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 1.62 (EV) + 0.03 (OT) + 0.0 2 (GC) = 1.72 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6696--6696 []\OT1/cmtt/m/n/10 limit((exp(x*exp(-x)/(exp(-x) + exp(-2*x**2/(x + 1)))) - exp (x))/x, _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 4.52 (EV) + 0.03 (OT) + 0.5 2 (GC) = 5.23 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 2*exp(exp(3*x **3*log(x))))), _[] [] [147] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 2.21 (EV) + 0.0 3 (OT) = 2.42 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 1.45 (EV) + 0.0 7 (OT) = 1.60 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 1.50 (EV) + 0.05 (OT) + 0.0 2 (GC) = 1.68 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 2.22 (EV) + 0.0 8 (OT) = 2.62 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.40 (IN) + 3.75 (EV) + 0.13 (OT) + 0.4 7 (GC) = 4.75 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6696--6696 []\OT1/cmtt/m/n/10 -- See Angus E. Taylor and W. Robert Mann, _Advanced Calculu s_, Second Edition,[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6696--6696 []\OT1/cmtt/m/n/10 limit(x * integrate(exp(-t**2), t = 0..x)/(1 - exp(-x**2)), x = 0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Un ion("failed",...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.65 (IN) + 2.63 (EV) + 0.08 (OT) + 0.0 5 (GC) = 3.42 sec[] [] [148] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: List Union(OrderedCompletion Expression Integer,"failed")[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.23 (IN) + 0.30 (EV) + 0.0 5 (OT) = 0.58 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Type: Union(OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6696--6696 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.7 2 (EV) = 0.75 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- Calculus on a non-smooth (but well defined) function => x /|x| or sign(x)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.30 (EV) + 0.22 (OT) + 0.2 0 (GC) = 0.92 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] [149] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Compiling function a with type Variable x -> Polynomial I nteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.28 (IN) + 0.0 3 (OT) = 0.32 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- Derivative of a piecewise defined function at a point [He rbert Fischer].[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- f(x) = x^2 - 1 for x = 1 otherwise x^3. f(1) = 0 and f'( 1) = 3[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: N onNegativeInteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.0 2 (EV) = 0.12 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Compiling function f with type Variable x -> Polynomial I nteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.0 8 (OT) = 0.27 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.03 (EV) + 0.0 5 (OT) = 0.33 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] [150] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named D[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- Apply the chain rule---this is important for PDEs and man y other[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.42 (IN) + 0.05 (EV) + 0.1 2 (OT) = 0.58 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] [151] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: OutputForm[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named D[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 having 1 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named D[] [] [152] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- Implicit differentiation => dy/dx = [1 - y sin(x y)] / [1 + x sin(x y)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.12 (EV) + 0.05 (OT) + 0.0 2 (GC) = 0.40 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.0 2 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/ n/10 Type: Domain[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] [153] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: List DeRhamComplex (Integer,[x,y,z])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- (2 dx + dz) /\ (3 dx + dy + dz) /\ (dx + dy + 4 dz) => 8 dx /\ dy /\ dz[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Type: DeRhamComplex (Integer,[x,y,z])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (EV) = 0.05 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6976--6976 [] \OT1/cmtt/m/n/10 3*x**5 * dy * dz + 5*x*y**2 * dz * dx + 8*z * dx * dy :: DeRham)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [154] Overfull \hbox (17.24684pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- => min(a - b - c + d, a - b + c - d, a + b - c - d, a + b + c + d)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- Linear programming: minimize the objective function z sub ject to the[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- variables xi being non-negative along with an additional set of constraints.[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- See William R. Smythe, Jr. and Lynwood A. Johnson, _Intro duction to Linear[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- Programming, with Applications_, Prentice Hall, Inc., 196 6, p. 117:[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 -- minimize z = 4 x1 - x2 + 2 x3 - 2 x4 => {x1, x2, x3, x4} = {2, 0, 2, 4}[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 6976--6976 []\OT1/cmtt/m/n/10 --simplex(-(4*x1 - x2 + 2*x3 - 2*x4), [2*x1 + x2 + x3 + x4 < = 10, _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.33 (IN) + 0.62 (EV) + 0.13 (OT) + 0.2 2 (GC) = 1.30 sec[] [] [155] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Compiling function a with type Variable x -> Polynomial I nteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Polynomial Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.33 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- => 2^(1/3)/6 [1/2 log([x + 2^(1/3)]^2/[x^2 - 2^(1/3) x + 2^(2/3)])[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- [2 x - 2^(1/3)]/[2^(1/3) sqrt(3)]})[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Fraction P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 3 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.75 (EV) + 0.07 (OT) + 0.0 7 (GC) = 0.98 sec[] [] [156] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.1 2 (EV) = 0.12 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [157] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.49 (IN) + 0.67 (EV) + 0.20 (OT) + 0.2 0 (GC) = 1.55 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- => 1/[2 m sqrt(10)] log([-5 + e^(m x) sqrt(10)]/[-5 - e^( m x) sqrt(10)])[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.75 (EV) + 0.08 (OT) + 0.0 3 (GC) = 1.02 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- => -3/2 x + 1/4 sinh(2 x) + tanh x [Gradshteyn and Ryzh ik 2.423(24)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.17 (EV) + 0.0 2 (OT) = 0.32 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.05 (EV) + 0.0 2 (OT) = 0.10 sec[] [] [158] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- [sqrt(b^2 - a^2) tan(x/2) - a - b]) (a^2 < b^2)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(List Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.67 (EV) + 0.0 5 (OT) = 0.83 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: List E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.32 (EV) + 0.0 2 (OT) = 0.33 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- The integral of 1/(a + 3 cos x + 4 sin x) can have 4 diff erent forms[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- depending on the value of a ! [Gradshteyn and Ryzhik 2. 558(4)][] [] [159] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.20 (EV) + 0.0 2 (OT) = 0.27 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.27 (EV) + 0.0 2 (OT) = 0.28 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.08 (EV) + 0.0 2 (OT) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.22 (EV) + 0.0 5 (OT) = 0.27 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.20 (EV) + 0.0 2 (OT) = 0.27 sec[] [] [160] Overfull \hbox (64.49643pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- (a x)/2 + 1/2 (x^2 + a^2) arccot(x/a) [Gradshteyn an d Ryzhik 2.853(2)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.80 (EV) + 0.02 (OT) + 0.0 3 (GC) = 0.92 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [161] Overfull \hbox (32.9967pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 -- => 1/2 [f(x) - g(x)]/[f(x) + g(x)] [Gradshteyn and Ryzh ik 2.02(25)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.08 (OT) + 0.0 3 (GC) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 7304--7304 []\OT1/cmtt/m/n/10 integrate((D(f(x), x)*g(x) - f(x)*D(g(x), x))/(f(x)**2 - g(x )**2), x)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7304--7304 [] \OT1/cmtt/m/n/10 Time: 0.72 (IN) + 0.82 (EV) + 0.20 (OT) + 0.0 7 (GC) = 1.80 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- The following two functions have a pole at a. The first integral has a[] [] [162] Overfull \hbox (69.74638pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.63 (IN) + 0.73 (EV) + 0.17 (OT) + 0.2 2 (GC) = 1.75 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Different branches of the square root need to be chosen i n the intervals[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- [0, 1] and [1, 2]. The correct results are 4/3, [4 - sqr t(8)]/3,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] [163] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.13 (EV) + 0.02 (OT) + 0.0 2 (GC) = 0.30 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.83 (EV) + 0.02 (OT) + 0.0 8 (GC) = 1.19 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.20 (EV) + 0.0 3 (OT) = 0.30 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.18 (EV) + 0.0 2 (OT) = 0.25 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.50 (IN) + 0.0 7 (OT) = 0.57 sec[] [] [164] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 2.90 (EV) + 0.02 (OT) + 0.1 0 (GC) = 3.08 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Contour integrals => pi/a e^(-a) for a > 0. See Norman L evinson and[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Raymond M. Redheffer, _Complex Variables_, Holden-Day, In c., 1970, p. 198.[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInf inity)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.23 (IN) + 0.03 (EV) + 0.1 0 (OT) = 0.37 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInf inity, "noPole")[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 1.07 (EV) + 0.6 0 (GC) = 1.73 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.25 (EV) + 0.0 2 (GC) = 0.35 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.62 (EV) + 0.0 3 (GC) = 0.72 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Integrand with a residue at infinity => -2 pi [sin(pi/5) + sin(2 pi/5)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 46.28 (EV) + 0.05 (OT) + 3.97 (GC) = 50.38 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- integrate(1/[1 + x + x^2 + ... + x^(2 n)], x = -infinity. .infinity)[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- [Levinson and Redheffer, p. 255] => 2 pi/5 [1 + cos(pi/5) ] csc(2 pi/5)[] [] [165] Overfull \hbox (17.24684pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(1/(1 + x + x**2 + x**4), x = %minusInfinity..%plus Infinity)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Integrand with a residue at infinity and a branch cut => pi [sqrt(2) - 1][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.55 (IN) + 0.37 (EV) + 0.20 (OT) + 0.1 8 (GC) = 1.30 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 2.62 (EV) + 0.05 (OT) + 0.1 8 (GC) = 3.05 sec[] [] [166] Overfull \hbox (64.49643pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- => q/p sqrt(pi/p) e^(q^2/p) (Re p > 0) [Gradshteyn an d Ryzhik 3.462(6)][] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(x*exp(-p*x**2 + 2*q*x), x = %minusInfinity..%plusI nfinity)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 0.41 (EV) + 0.05 (OT) + 0.0 3 (GC) = 0.82 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.37 (IN) + 0.02 (EV) + 0.0 7 (OT) = 0.45 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(1/log(t) + 1/(1 - t) - log(log(1/t)), t = 0..1, "n oPole")[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.75 (EV) + 0.0 7 (GC) = 0.93 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- This integral comes from atomic collision theory => 0 [ John Prentice][] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(sin(t)/t*exp(2*%i*t), t = %minusInfinity..%plusInf inity)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [167] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.67 (IN) + 0.48 (EV) + 0.32 (OT) + 0.2 0 (GC) = 1.67 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 1.67 (EV) + 0.02 (OT) + 0.1 2 (GC) = 2.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.92 (IN) + 0.40 (EV) + 0.12 (OT) + 0.0 3 (GC) = 1.47 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.37 (IN) + 0.23 (EV) + 0.0 7 (OT) = 0.67 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(exp(-a*x)*besselJ(0, b*x), x = 0..%plusInfinity, " noPole")[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.37 (EV) + 0.0 3 (OT) = 0.45 sec[] [] [168] Overfull \hbox (17.24684pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Integrand contains a special function => 4/(3 pi) [Tom Hagstrom][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(pole: p otentialPole,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.22 (EV) + 0.05 (OT) + 0.0 2 (GC) = 0.40 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.25 (EV) + 0.0 2 (OT) = 0.30 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(real(Ei(%i*x))*besselJ(0, 2*sqrt(7*x)), x = 0..%pl usInfinity)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [169] Overfull \hbox (64.49643pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- This integral comes from doing a two loop Feynman diagram for a QCD problem[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- => - [17/3 + pi^2]/36 + log 2/9 [35/3 - pi^2/2 - 4 log 2 + log(2)^2][] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 --integrate(x**2*polylog(3, 1/(x + 1)), x = 0..1) :: Complex Float[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- - (17/3 + %pi**2)/36 + log(2)/9*(35/3 - %pi**2/2 - 4*log( 2) + log(2)**2)[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Integrate a piecewise defined step function s(t) multipli ed by cos t, where[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- => 0 (u < 1); sin u - sin 1 (1 <= u <= 2); sin 2 - sin 1 (u > 2)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Compiling function s with type Variable t -> NonNegativeI nteger[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.88 (IN) + 0.58 (EV) + 0.37 (OT) + 0.3 3 (GC) = 2.17 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- Integrating first with respect to y and then x is much ea sier than[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(integrate(x/(x**2 + y**2), y = %minusInfinity..%pl usInfinity), _[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 integrate having 2 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (316.49423pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 Union(f1: OrderedCompletion Expression Integer,f2: List Orde redCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] [170] Overfull \hbox (38.24666pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(integrate(x/(x**2 + y**2), y = %minusInfinity..%pl usInfinity, _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union( fail: failed,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.72 (IN) + 1.10 (EV) + 0.12 (OT) + 0.1 2 (GC) = 2.05 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 integrate having 2 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (316.49423pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 Union(f1: OrderedCompletion Expression Integer,f2: List Orde redCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 2.18 (EV) + 0.05 (OT) + 0.0 5 (GC) = 2.38 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 -- => [log(sqrt(2) + 1) + sqrt(2)]/3 [Caviness et all, sec tion 2.10.1][] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 integrate having 2 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (316.49423pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 Union(f1: OrderedCompletion Expression Integer,f2: List Orde redCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] [171] Overfull \hbox (69.74638pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(integrate(sqrt(x**2 + y**2), x = 0..1, "noPole"), y = 0..1, "noPole")[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 +-+ +-+ +-+ +-+ +-+[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 (- 4\|2 + 6)log(- 2\|2 + 3) + (- 2\|2 + 3)log(- 12\|2 + 17) - 24\|2 + 32[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 --------------------------------------------------------- --------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 6.17 (EV) + 0.03 (OT) + 0.0 3 (GC) = 6.33 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(integrate(sin(a)*sin(y)/sqrt(1 - sin(a)**2*sin(x)* *2*sin(y)**2), _[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 integrate having 2 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (316.49423pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 Union(f1: OrderedCompletion Expression Integer,f2: List Orde redCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(integrate(sin(a)*sin(y)/sqrt(1 - sin(a)**2*sin(x)* *2*sin(y)**2), _[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 integrate having 3 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (316.49423pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 Union(f1: OrderedCompletion Expression Integer,f2: List Orde redCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] [172] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 integrate having 2 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (316.49423pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 Union(f1: OrderedCompletion Expression Integer,f2: List Orde redCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 integrate(integrate(abs(y - x**2), y = 0..2, "noPole"), x = -1..1, "noPole")[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 integrate having 3 argument(s) but none was determined to be[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (316.49423pt too wide) in paragraph at lines 7827--7827 []\OT1/cmtt/m/n/10 Union(f1: OrderedCompletion Expression Integer,f2: List Orde redCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Type: Union(f1: OrderedCompletion Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 7827--7827 [] \OT1/cmtt/m/n/10 Time: 1.73 (IN) + 0.55 (EV) + 0.40 (OT) + 0.0 2 (GC) = 2.70 sec[] [] [173] Overfull \hbox (6.74693pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- Taylor series---this first example comes from special rel ativity[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.43 (IN) + 0.18 (EV) + 0.22 (OT) + 0.2 2 (GC) = 1.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,v,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.38 (IN) + 0.27 (EV) + 0.12 (OT) + 0.0 5 (GC) = 0.82 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,v,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 0.1 0 (OT) = 0.37 sec[] [] [174] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.18 (EV) + 0.05 (OT) + 0.0 3 (GC) = 0.38 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 3 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.02 (EV) + 0.0 3 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] [175] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.05 (EV) + 0.0 5 (OT) = 0.12 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.02 (EV) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.0 8 (IN) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: OutputForm[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.57 (IN) + 0.05 (EV) + 0.2 0 (OT) = 0.82 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 There are 3 exposed and 0 unexposed library operations na med series[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] [176] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- Taylor series of nonscalar objects (noncommutative multip lication)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 A is declared as being in SquareMatrix(2,Integer) but has not been[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,t,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.23 (EV) + 0.2 8 (OT) = 0.72 sec[] [] [177] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.05 (EV) + 0.0 5 (OT) = 0.17 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- => 1/sqrt(x - 3/2 pi) + (x - 3/2 pi)^(3/2) / 12 + O([x - 3/2 pi]^(7/2))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expression In teger,x,(3*pi)/2)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.25 (EV) + 0.11 (OT) + 0.0 2 (GC) = 0.58 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- Generalized Taylor series => sum( [x log x]^k/k!, k = 0.. infinity )[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 log(x) 2 log(x) 3 log(x) 4 lo g(x) 5[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 1 + log(x)x + ------- x + ------- x + ------- x + -- ----- x[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: GeneralUnivariatePowerSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.07 (EV) + 0.07 (OT) + 0.0 2 (GC) = 0.18 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- Compare the generalized Taylor series of two different fo rmulations of a[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: GeneralUnivariatePowerSeries(Expres sion Integer,z,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.53 (EV) + 0.0 7 (OT) = 0.68 sec[] [] [178] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: GeneralUnivariatePowerSeries(Expres sion Integer,z,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.53 (EV) + 0.0 7 (OT) = 0.60 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: GeneralUnivariatePowerSeries(Expres sion Integer,z,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 7 (OT) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [179] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 There are 3 exposed and 0 unexposed library operations na med series[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 There are 3 exposed and 0 unexposed library operations na med series[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] [180] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- => 0!/x - 1!/x^2 + 2!/x^3 - 3!/x^4 + O(1/x^5) [Knopp, p . 544][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: OutputForm[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.27 (IN) + 0.12 (EV) + 0.03 (OT) + 0.0 2 (GC) = 0.43 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 There are 3 exposed and 0 unexposed library operations na med series[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- Multivariate Taylor series expansion => 1 - (x^2 + 2 x y + y^2)/2 + O(x^4)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,y,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.32 (IN) + 0.22 (EV) + 0.10 (OT) + 0.1 0 (GC) = 0.73 sec[] [] [181] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 There are 4 exposed and 0 unexposed library operations na med series[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (EV) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: UnivariatePuiseuxSeries(Expres sion Integer,x,0)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.08 (EV) + 0.0 5 (OT) = 0.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- Derive an explicit Taylor series solution of y as a funct ion of x from the[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- y = x - 1 + (x - 1)^2/2 + 2/3 (x - 1)^3 + (x - 1)^4 + 17/ 10 (x - 1)^5 + ...[] [] [182] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.0 8 (IN) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.47 (IN) + 0.02 (EV) + 0.1 4 (OT) = 0.62 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [183] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: Union(Fraction UnivariatePolynomial(x,Express ion Integer),...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.69 (IN) + 0.67 (EV) + 0.28 (OT) + 0. 37 (GC) = 2.0 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- => - (2 p / pi) sum( (-1)^n sin(n pi x / p) / n, n = 1..i nfinity )[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: Variable x[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 8311--8311 []\OT1/cmtt/m/n/10 -- - (2 p / pi^2) sum( [1 - (-1)^n] cos(n pi x / p) / n^2, n = 1..infinity )[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8311--8311 [] \OT1/cmtt/m/n/10 Time: 0.12 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.17 sec[] [] [184] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 0.37 (IN) + 1.22 (EV) + 0.15 (OT) + 0.1 8 (GC) = 1.92 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.08 (EV) + 0.0 2 (OT) = 0.12 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- => w/(s^2 - 4 w^2) (Re s > |Re w|) [Gradshteyn and Ry zhik 17.13(84)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.07 (EV) + 0.0 3 (OT) = 0.32 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- e^(-6 sqrt(s))/s (Re s > 0) [Gradshteyn and Ryzhik 17 .13(102)][] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [185] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Solve y'' + y = 4 [H(t - 1) - H(t - 2)], y(0) = 1, y'(0) = 0 where H is the[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Heaviside (unit step) function (the RHS describes a pulse of magnitude 4 and[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- duration 1). See David A. Sanchez, Richard C. Allen, Jr. and Walter T.[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Kyner, _Differential Equations: An Introduction_, Addison -Wesley Publishing[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Company, 1983, p. 211. First, take the Laplace transform of the ODE[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.10 (OT) + 0.0 2 (GC) = 0.20 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 D(y(t), t, 2) + y(t) = 4*(heaviside(t - 1) - heaviside(t - 2)))[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 4laplace(heaviside(t - 1),t,s) - 4laplace(heaviside(t - 2),t,s)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 1.0 (IN) + 1.17 (EV) + 0.31 (OT) + 0.2 7 (GC) = 2.75 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Now, solve for Y(s) and then take the inverse Laplace tra nsform[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- => Y(s) = s/(s^2 + 1) + 4 [1/s - s/(s^2 + 1)] [e^(-s) - e ^(-2 s)][] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- => y(t) = cos t + 4 {[1 - cos(t - 1)] H(t - 1) - [1 - cos (t - 2)] H(t - 2)}[] [] [186] Overfull \hbox (6.74693pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 There are 31 exposed and 17 unexposed library operations named *[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named *[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 There are 1 exposed and 0 unexposed library operations na med laplace[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Fourier transforms => sqrt(2 pi) delta(z) [Gradshteyn a nd Ryzhik 17.23(1)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Compiling function FourierTransform with type (PositiveIn teger,[] [] [187] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Expression Complex Integer,f2: List OrderedCompletion Expression[] [] Overfull \hbox (458.243pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 Type: List Union(f1: OrderedCompletion Expression Complex In teger,f2: List OrderedCompletion Expression Complex Integer,fail: failed,pole: potentialPole)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 2.50 (IN) + 2.65 (EV) + 0.38 (OT) + 0.6 7 (GC) = 6.20 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- => e^(-z^2/36) / [3 sqrt(2)] [Gradshteyn and Ryzhik 17. 23(13)][] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Compiling function FourierTransform with type (Expression Integer,[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Expression Complex Integer,f2: List OrderedCompletion Expression[] [] Overfull \hbox (458.243pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 Type: List Union(f1: OrderedCompletion Expression Complex In teger,f2: List OrderedCompletion Expression Complex Integer,fail: failed,pole: potentialPole)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 0.37 (IN) + 1.42 (EV) + 0.18 (OT) + 0.0 2 (GC) = 1.99 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- => sqrt(2 / pi) (9 - z^2)/(9 + z^2)^2 [Gradshteyn and R yzhik 17.23(11)][] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] [188] Overfull \hbox (22.4968pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- => pi cot(pi s) (0 < Re s < 1) [Gradshteyn and Ryzhik 17.43(5)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Compiling function MellinTransform with type (Fraction Po lynomial[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 OrderedCompletion Expression Integer,f2: List OrderedC ompletion[] [] Overfull \hbox (374.24373pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 Type: List Union(f1: OrderedCompletion Expression Integer,f2 : List OrderedCompletion Expression Integer,fail: failed,pole: potentialPole)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Time: 1.10 (IN) + 1.95 (EV) + 0.38 (OT) + 0.3 7 (GC) = 3.80 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Compiling function MellinTransform with type (Expression Integer,[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 8586--8586 [] \OT1/cmtt/m/n/10 Expression Integer,f2: List OrderedCompletion Expressi on Integer,[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [189] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Z transforms. See _CRC Standard Mathematical Tables_, Tw enty-first Edition,[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 8586--8586 []\OT1/cmtt/m/n/10 -- Z[H(t - m T)] => z/[z^m (z - 1)] (H is the Heaviside (u nit step) function)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- ---------- Ordinary Difference and Differential Equations ----------[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- Second order linear recurrence equation: r(n) = (n - 1)^2 + m n[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.05 (OT) + 0.0 2 (GC) = 0.13 sec[] [] [190] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 1.17 (IN) + 0.05 (EV) + 0.24 (OT) + 0.0 7 (GC) = 1.52 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.10 (IN) + 0.0 5 (OT) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- => [c^(n+1) [c^(n+1) - 2 c - 2] + (n+1) c^2 + 2 c - n] / [(c-1)^3 (c+1)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 n - 1 n - 2 n n - 1 2[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 (c - c r(n - 2)c + c r(n - 2) - 1)c + r(n - 1)(c )[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 ((- c - 2)r(n - 1) - 1)c + c r(n - 2)c + (c + 1)r(n - 1)[] [] [191] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.48 (IN) + 0.13 (EV) + 0.13 (OT) + 0.0 3 (GC) = 0.78 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- Second order ODE with initial conditions---solve first us ing Laplace[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.15 (EV) + 0.02 (OT) + 0.0 2 (GC) = 0.35 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.92 (EV) + 0.02 (OT) + 0. 07 (GC) = 1.0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.47 (IN) + 0.02 (EV) + 0.0 7 (OT) = 0.55 sec[] [] [192] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation Union(Expression Integer,"failed")[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.10 (EV) + 0.0 3 (OT) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.87 (EV) + 0.0 7 (OT) = 1.23 sec[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- Separable equation => y(x)^2 = 2 log(x + 1) + (4 x + 3)/( x + 1)^2 + 2 A[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (EV) + 0.0 7 (OT) = 0.17 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] [193] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.82 (EV) + 0.02 (OT) + 0.4 2 (GC) = 1.27 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- Homogeneous equation. See Emilio O. Roxin, _Ordinary Dif ferential[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.02 (EV) + 0.0 2 (OT) = 0.20 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.1 5 (EV) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.0 8 (IN) = 0.08 sec[] [] Overfull \hbox (106.49606pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 Type: Union(Record(particular: Expression Integer,basis: Lis t Expression Integer),...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.33 (EV) + 0.02 (OT) + 0.0 2 (GC) = 0.37 sec[] [] [194] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 5 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.08 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 3 (EV) = 0.08 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [195] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- ---------- Ordinary Difference and Differential Equations ----------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.08 (OT) + 0.0 2 (GC) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.60 (IN) + 0.22 (EV) + 0.18 (OT) + 0.0 8 (GC) = 1.08 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- => y(x) = [3 x + sqrt(1 + 9 x^2)]^(1/3) - 1/[3 x + sqrt(1 + 9 x^2)]^(1/3)[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [196] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- ---------- Ordinary Difference and Differential Equations ----------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.08 (OT) + 0.0 2 (GC) = 0.15 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.47 (IN) + 0.15 (EV) + 0.18 (OT) + 0.0 7 (GC) = 0.86 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] [197] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- ---------- Ordinary Difference and Differential Equations ----------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 8 (OT) = 0.13 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- ODE with boundary conditions. This problem has nontrivia l solutions[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 1.15 (IN) + 0.97 (EV) + 0.17 (OT) + 0.1 7 (GC) = 2.45 sec[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- => y(x) = Z_v[sqrt(x)] where Z_v is an arbitrary Bessel f unction of order v[] [] [198] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.35 (IN) + 0.03 (EV) + 0.0 8 (OT) = 0.47 sec[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 WARNING (genufact): No known algorithm to factor ? - --, trying square-free.[] [] Overfull \hbox (106.49606pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 Type: Union(Record(particular: Expression Integer,basis: Lis t Expression Integer),...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 81.03 (EV) + 0.02 (OT) + 17.42 (GC) = 98.48 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- Delay (or mixed differential-difference) equation. See D aniel Zwillinger,[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- _Handbook of Differential Equations_, Second Edition, Aca demic Press, Inc.,[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- 1992, p. 210 => y(t) = y0 sum((-a)^n (t - n + 1)^n/n!, n = 0..floor(t) + 1)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.0 7 (OT) = 0.28 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.30 (EV) + 0.02 (OT) + 0.0 3 (GC) = 0.37 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] [199] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Union(Expres sion Integer,...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.13 (EV) + 0.0 3 (OT) = 0.32 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 There are 31 exposed and 17 unexposed library operations named *[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named *[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- Integro-differential equation. See A. E. Fitzgerald, Dav id E. Higginbotham[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- and Arvin Grabel, _Basic Electrical Engineering_, Fourth Edition,[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 eqn:= D(i(t), t) + 2*i(t) + 5*'integrate(i(tau), tau = 0..t) = 10*%e**(-4*t)[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 , - 4t[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Eq uation OutputForm[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.05 (EV) + 0.0 3 (OT) = 0.25 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 There are 6 exposed and 1 unexposed library operations na med solve[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] [200] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named solve[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 There are 1 exposed and 0 unexposed library operations na med laplace[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 having 3 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Anonymous user functions created with +-> that are proces sed in[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- x(t) = e^t [A cos(t) - B sin(t)], y(t) = e^t [A sin(t) + B cos(t)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] [201] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 ans:= [x(t) = %e^t*(A*cos(t) - B*sin(t)), y(t) = %e^t*(A*sin (t) + B*cos(t))][] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 t t t t[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 (13) [x(t)= - B %e sin(t) + A cos(t)%e ,y(t)= A %e sin(t ) + B cos(t)%e ][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.07 (EV) + 0.0 2 (OT) = 0.33 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.07 (EV) + 0.0 2 (OT) = 0.10 sec[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 t t t t[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 (- B + A)%e sin(t) + (B + A)cos(t)%e = (- B + A)%e sin(t ) + (B + A)cos(t)%e[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.03 (EV) + 0.0 3 (OT) = 0.08 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- See Nicolas Robidoux, ``Does Axiom Solve Systems of O.D.E .'s Like[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- Mathematica?'', LA-UR-93-2235, Los Alamos National Labora tory, Los Alamos,[] [] [202] Overfull \hbox (22.4968pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 (16) [x (t)= -------------------------------,y (t)= - y( t) + x(t)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.03 (EV) + 0.0 3 (OT) = 0.15 sec[] [] Overfull \hbox (106.49606pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 Type: Union(Record(particular: Expression Integer,basis: Lis t Expression Integer),...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.70 (EV) + 0.02 (OT) + 0.0 3 (GC) = 0.75 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.0 2 (OT) = 0.18 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 - t t 2 - t t 2[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 2C1 %e (%e ) sin(t) + (- C1 cos(t) + 5C1)% e (%e )[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 [particular= -------------------------------------------- ----------,[] [] Overfull \hbox (106.49606pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 Type: Union(Record(particular: Expression Integer,basis: Lis t Expression Integer),...)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 2.0 (EV) + 0.02 (OT) + 0.0 5 (GC) = 2.10 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.23 (EV) + 0.0 3 (OT) = 0.35 sec[] [] [203] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- (1) real distinct characteristic roots (= 2, 1, 3) [Rox in, p. 109][] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 (24) [x (t)= 2x(t),y (t)= - 2z(t) + y(t) - 2x(t),z (t)= 3z(t) + x(t)][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.0 3 (OT) = 0.17 sec[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- (2) complex characteristic roots (= 0, -1 +- sqrt(2) i) [Roxin, p. 111][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (EV) + 0.0 3 (OT) = 0.13 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- (3) multiple characteristic roots (= 2, 2, 2) [Roxin, p . 113][] [] [204] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.57 (IN) + 0.03 (EV) + 0.03 (OT) + 0.4 7 (GC) = 1.10 sec[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 9273--9273 []\OT1/cmtt/m/n/10 -- y(t) = -2/w [1 - cos(w t)] x0' + [4 - 3 cos(w t)] y0 + si n(w t)/w y0'[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Type: List Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9273--9273 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.03 (EV) + 0.0 2 (OT) = 0.18 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- A very simple PDE => g(x) + h(y) for arbitrary functions g and h[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.10 (OT) + 0.0 5 (GC) = 0.22 sec[] [] [205] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Time: 0.65 (IN) + 0.27 (EV) + 0.27 (OT) + 0.1 5 (GC) = 1.33 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- Heat equation: the fundamental solution is 1/sqrt(4 pi t) exp(-x^2/[4 t]).[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- If f(x, t) and a(x, t) are solutions, the most general so lution obtainable[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- from f(x, t) by group transformations is of the form u(x, t) = a(x, t)[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- + 1/sqrt(1 + 4 e6 t) exp(e3 - [e5 x + e6 x^2 - e5^2 t]/[ 1 + 4 e6 t])[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- f([e^(-e4) (x - 2 e5 t)]/[1 + 4 e6 t] - e1, [e^(-2 e4) t] /[1 + 4 e6 t] - e2)[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- See Peter J. Olver, _Applications of Lie Groups to Differ ential Equations_,[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- Second Edition, Springer Verlag, 1993, p. 120 (an excelle nt book). See also[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.05 (EV) + 0.0 3 (OT) = 0.15 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- => v(r, theta) = a[0] + sum(a[n] r^n cos(n theta), n = 1. .infinity)[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 9344--9344 []\OT1/cmtt/m/n/10 -- + sum(b[n] r^n sin(n theta), n = 1. .infinity)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] [206] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9344--9344 [] \OT1/cmtt/m/n/10 Time: 0.63 (IN) + 0.15 (EV) + 0.1 0 (OT) = 0.88 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 There are 31 exposed and 17 unexposed library operations named *[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named *[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 There are 31 exposed and 17 unexposed library operations named *[] [] [207] Overfull \hbox (11.99689pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named *[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: LinearOrdinaryDifferentialOperator(Expression Integer ,theMap("NIL",1))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.02 (EV) + 0.15 (OT) + 0.0 7 (GC) = 0.32 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: LinearOrdinaryDifferentialOperator(Expression Integer ,theMap("NIL",1))[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.10 (EV) + 0.0 3 (GC) = 0.27 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 2 (OT) = 0.08 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.0 5 (IN) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] [208] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.53 (IN) + 0.22 (EV) + 0.13 (OT) + 0.0 7 (GC) = 0.95 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.54 (IN) + 0.08 (EV) + 0.1 0 (OT) = 0.72 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.13 (IN) + 0.20 (EV) + 0.07 (OT) + 0.0 2 (GC) = 0.42 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 []\OT1/cmtt/m/n/10 T:= (f, xx, a) +-> subst((DD**0)(f(x)), x = a)/factorial(0) * (xx - a)**0 + _[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 subst((DD**1)(f(x)), x = a)/factorial(1) * (xx - a)**1 + _[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 subst((DD**2)(f(x)), x = a)/factorial(2) * (xx - a)**2[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 subst(DD (f(x)),x= a) 0 subst(DD (f(x)),x= a) 1[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 --------------------- (xx - a) + ------------------- -- (xx - a)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: AnonymousFunction[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] [209] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.50 (IN) + 0.13 (EV) + 0.1 0 (OT) = 0.73 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.12 (EV) + 0.0 7 (OT) = 0.37 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 9505--9505 [] \OT1/cmtt/m/n/10 Time: 0.18 (IN) + 0.07 (EV) + 0.0 5 (OT) = 0.30 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 9505--9505 []\OT1/cmtt/m/n/10 -- Define the binary infix operator ~ so that x ~ y => sqrt( x^2 + y^2)[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 9505--9505 []\OT1/cmtt/m/n/10 -- Define the matchfix pair of operators | and | so that | x | => abs(x)[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- How easy is it to substitute x for a + b in the following expression?[] [] [210] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.23 (IN) + 0.02 (EV) + 0.18 (OT) + 0.1 0 (GC) = 0.53 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 ------------------------------------------------------------ -----------------[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- How easy is it to substitute x for a + b in the following expression?[] [] [211] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.25 (IN) + 0.03 (EV) + 0.15 (OT) + 0.0 7 (GC) = 0.50 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.38 (IN) + 0.05 (EV) + 0.17 (OT) + 0.1 2 (GC) = 0.72 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- How easy is it to substitute r for sqrt(x^2 + y^2) in the following[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.30 (IN) + 0.07 (EV) + 0.1 2 (OT) = 0.48 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.0 2 (EV) = 0.17 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- Change variables so that the following transcendental exp ression is[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- => (r - 1)^4 (u^4 - r u^3 - r^3 u + r u + r^4)/[u^4 (2 r - 1)^2][] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 - 2*(r - cos(t))/(r**2 * (r**2 - 2*r*cos(t) + 1)* *(3/2))) / _[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (1/r**4 + 1/(r - 1)**4 - 2*(r - 1)/(r**2 * (r**2 - 2*r + 1)**(3/2)))[] [] [212] Overfull \hbox (53.99652pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 7 6 5 4 3 2 8 7[] [] Overfull \hbox (48.74657pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (- 4r + 16r - 28r + 32r - 28r + 16r - 4r)co s(t) + 2r - 8r[] [] Overfull \hbox (43.49661pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 8 7 6 5 4 3 2 9 8[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (6r - 24r + 38r - 32r + 18r - 8r + 2r )cos( t) - 2r + 8r[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 7 6 5 4 3 2 8 7[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (- 8r + 16r - 32r + 32r - 28r + 16r - 4r) cos(t) + 2r - 4r[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 8 7 6 5 4 3 9 8 7 6[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (8r - 24r + 32r - 32r + 24r - 8r )cos(t) - 2r + 6r - 10r + 14r[] [] [213] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.61 (IN) + 0.28 (EV) + 0.28 (OT) + 0.0 7 (GC) = 1.25 sec[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 +-----------+[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 4 3 2 4 8 7 6 5 4 | 2[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 ((r - 4r + 6r - 4r + 1)u + r - 4r + 6r - 4r + r )\|r - 2r + 1[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 5 4 3 2 4 7 6 5 3 2 2[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 ((- r + 4r - 6r + 4r - r)u + (- r + 4r - 5r + 5r - 4r + r)u )[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.15 (IN) + 0.17 (EV) + 0.1 2 (OT) = 0.43 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 4 3 2 4 5 4 3 2 3[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (r - 4r + 6r - 4r + 1)u + (- r + 4r - 6r + 4 r - r)u[] [] Overfull \hbox (32.9967pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 7 6 5 3 2 8 7 6 5 4[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (- r + 4r - 5r + 5r - 4r + r)u + r - 4r + 6r - 4r + r[] [] [214] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 4 3 2 4 | 2 5 4 3 2 4[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (2r - 4r + 6r - 4r + 1)u \|r - 2r + 1 + (- 2r + 6 r - 6r + 2r )u[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.93 (EV) + 0.1 2 (OT) = 1.12 sec[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 4 3 2 4 5 4 3 2 3[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (r - 4r + 6r - 4r + 1)u + (- r + 4r - 6r + 4r - r)u[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 7 6 5 3 2 8 7 6 5 4[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (- r + 4r - 5r + 5r - 4r + r)u + r - 4r + 6r - 4r + r[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.47 (EV) + 0.0 7 (OT) = 0.57 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: Fraction Factored P olynomial Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.17 (IN) + 0.25 (EV) + 0.03 (OT) + 0.0 2 (GC) = 0.47 sec[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- Establish a rule to symmetrize a differential operator: [Stanly Steinberg][] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Ty pe: BasicOperator[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.0 3 (IN) = 0.03 sec[] [] Overfull \hbox (22.4968pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 f(x)*D(g(x), x, 2) + D(f(x), x)*D(g(x), x) == D(f(x)*D(g( x), x), x)[] [] [215] Overfull \hbox (11.99689pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 (12) f(x)g (x) + f (x)g (x) + %B == 'D('f(x)'D('g(x),x) ,x) + %B[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: RewriteRule(Integer,Integer,Ex pression Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.62 (IN) + 0.05 (EV) + 0.0 7 (OT) = 0.73 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.03 (EV) + 0.0 5 (OT) = 0.12 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 to learn if there is any operation containing " %diff " in its[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named %diff[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.05 (IN) + 0.0 2 (OT) = 0.07 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: Strea m PositiveInteger[] [] [216] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 3 (OT) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Typ e: Stream Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.03 (IN) + 0.0 2 (EV) = 0.05 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Typ e: Stream Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.02 (IN) + 0.0 2 (OT) = 0.03 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Compiling function p with type (NonNegativeInteger,Variab le x) ->[] [] [217] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.08 (EV) + 0.1 2 (OT) = 0.40 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: Polynomial Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.63 (IN) + 0.02 (EV) + 0.1 2 (OT) = 0.77 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (OT) = 0.02 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Compiling function pp with type (Integer,Variable x) -> P olynomial[] [] [218] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.33 (IN) + 0.03 (EV) + 0.0 5 (OT) = 0.42 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: Fraction Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 5 (OT) = 0.13 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.0 2 (IN) = 0.02 sec[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 outputAsFortran having 1 argument(s) but none was dete rmined to[] [] [219] Overfull \hbox (27.74675pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/ 10 Type: List Any[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.0 7 (OT) = 0.28 sec[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- Define the function p(x) = x^2 - 4 x + 7 such that p(lamb da) = 0 for[] [] Overfull \hbox (53.99652pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- lambda = 2 +- i sqrt(3) and p(A) = [[0 0], [0 0]] for A = [[1 -2], [2 3]][] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- (the lambda are the eigenvalues and p(x) is the character istic polynomial of[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: Expressio n Complex Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.43 (IN) + 0.08 (EV) + 0.12 (OT) + 0.0 3 (GC) = 0.67 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 There are 11 exposed and 5 unexposed library operations n amed +[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 having 2 argument(s) but none was determined to be app licable.[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 package-calling the operation or using coercions on th e arguments[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Cannot find a definition or applicable library operation named +[] [] [220] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: Square Matrix(2,Integer)[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.22 (IN) + 0.03 (EV) + 0.03 (OT) + 0.0 5 (GC) = 0.33 sec[] [] Overfull \hbox (38.24666pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 + atan((2*x - 2**(1/3))/(2**(1/3) * sqrt(3))) / (2**(2/3) * sqrt(3)) _[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/ n/10 3+-+2 +-+[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 +-+ 3+-+2 3+-+ 2 +-+ 3+-+ (x \|2 - 1)\|3[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 - \|3 log(\|2 - x\|2 + x ) + 2\|3 log(\|2 + x) + 6ata n(-----------------)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 10066--10066 [] \OT1/cm tt/m/n/10 3[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 --------------------------------------------------------- --------------------[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.65 (IN) + 0.55 (EV) + 0.1 3 (OT) = 1.33 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/ n/10 Type: Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.08 (IN) + 0.0 3 (EV) = 0.12 sec[] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Compiling function f with type Variable y -> Expression I nteger[] [] Overfull \hbox (69.74638pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/ n/10 3+-+2 +-+[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 +-+ 3+-+2 3+-+ 2 +-+ 3+-+ (y \|2 - 1)\|3[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 - \|3 log(\|2 - y\|2 + y ) + 2\|3 log(\|2 + y) + 6ata n(-----------------)[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 10066--10066 [] \OT1/cm tt/m/n/10 3[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 --------------------------------------------------------- --------------------[] [] [221] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.23 (IN) + 0.22 (EV) + 0.1 7 (OT) = 0.62 sec[] [] Overfull \hbox (11.99689pt too wide) in paragraph at lines 10066--10066 []\OT1/cmtt/m/n/10 -- Display the top-level structure of a nasty expression, hi ding the[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/ n/10 Type: Symbol[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m /n/10 Time: 0 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Type: Equation E xpression Integer[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.20 (IN) + 0.07 (EV) + 0.0 5 (OT) = 0.32 sec[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/ m/n/10 Type: Void[] [] Overfull \hbox (59.24648pt too wide) in paragraph at lines 10066--10066 [] \OT1/cmtt/m/n/10 Time: 0.07 (IN) + 0.0 3 (EV) = 0.10 sec[] [] [222] [223] No file WesterProblemSet.ind. [224] (./WesterProblemSet.aux) ) Here is how much of TeX's memory you used: 533 strings out of 94075 6311 string characters out of 1165177 110152 words of memory out of 1500000 3878 multiletter control sequences out of 10000+50000 8709 words of font info for 31 fonts, out of 1200000 for 2000 645 hyphenation exceptions out of 8191 25i,6n,17p,242b,245s stack positions out of 5000i,500n,6000p,200000b,5000s Output written on WesterProblemSet.dvi (224 pages, 356456 bytes).