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Edit detail for SandBoxFriCAS revision 43 of 43

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Editor: test int
Time: 2018/06/10 12:52:12 GMT+0
Note: integrate(exp(x-x^2), x)

added:

From testint Sun Jun 10 12:52:12 +0000 2018
From: test  int
Date: Sun, 10 Jun 2018 12:52:12 +0000
Subject: integrate(exp(x-x^2), x)
Message-ID: <20180610125212+0000@axiom-wiki.newsynthesis.org>

\begin{fricas}
integrate((x+sin(x))^(1/2), x)
\end{fricas}

This page is set to execute \begin{axiom}... \end{axiom}
commands using FriCAS.  See also FriCASIntegration.
fricas
)version
Value = "FriCAS 1.3.3 compiled at Fri Mar 16 16:15:43 UTC 2018"

Any comments added here use this version of FriCAS.

fricas
solve(s=v*t+a*t^2/2,t)
\begin{equation*} \label{eq1}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
radicalSolve(s=v*t+a*t^2/2,t)
\begin{equation*} \label{eq2}\left[{t ={{-{\sqrt{{4 \ {{v}^{2}}}+{8 \ a \ s}}}-{2 \ v}}\over{2 \ a}}}, \:{t ={{{\sqrt{{4 \ {{v}^{2}}}+{8 \ a \ s}}}-{2 \ v}}\over{2 \ a}}}\right]?\end{equation*}
Type: List(Equation(Expression(Integer)))

fricas
solve(v*t+a*t^2/2-s=0,t)
\begin{equation*} \label{eq3}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(v*t+a*t/2-s=0,t)
\begin{equation*} \label{eq4}\left[{t ={{2 \ s}\over{{2 \ v}+ a}}}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(v*t+a*t^2/2-s=0,t)
\begin{equation*} \label{eq5}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
radicalSolve(p^3 - p + 1/10=0,p)
\begin{equation*} \label{eq6}\begin{array}{@{}l} \displaystyle \left[{p ={{{{\left(-{3 \ {\sqrt{- 3}}}+ 3 \right)}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}- 2}\over{{\left({3 \ {\sqrt{- 3}}}+ 3 \right)}\ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}, \: \right. \ \ \displaystyle \left.{p ={{{{\left(-{3 \ {\sqrt{- 3}}}- 3 \right)}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}+ 2}\over{{\left({3 \ {\sqrt{- 3}}}- 3 \right)}\ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}, \: \right. \ \ \displaystyle \left.{p ={{{3 \ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{37 3}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}+ 1}\over{3 \ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}\right] \end{array} \end{equation*}
Type: List(Equation(Expression(Integer)))

fricas
R1 ==> Record(foo1: String, remLexs: List Integer)
Type: Void
fricas
R2 ==> Record(foo2: String, remLexs: List Integer)
Type: Void
fricas
r1: R1 := ["a", [1,2,3]]
\begin{equation*} \label{eq7}\left[{foo 1 = \verb#"a"#}, \:{remLexs ={\left[ 1, \: 2, \: 3 \right]?}}\right]\end{equation*}
Type: Record(foo1: String,remLexs: List(Integer))
fricas
r2: R2 := ["b", [5]]
\begin{equation*} \label{eq8}\left[{foo 2 = \verb#"b"#}, \:{remLexs ={\left[ 5 \right]?}}\right]\end{equation*}
Type: Record(foo2: String,remLexs: List(Integer))
fricas
r1.remLexs
\begin{equation*} \label{eq9}\left[ 1, \: 2, \: 3 \right]?\end{equation*}
Type: List(Integer)
fricas
r2.remLexs
\begin{equation*} \label{eq10}\left[ 5 \right]?\end{equation*}
Type: List(Integer)

fricas
)set output tex off
 
fricas
)set output algebra on
guessPRec [1, 0, 1, 1, 4, 10, 35, 120, 455, 1792, 7413, 31780, 140833, 641928, 3000361, 14338702, 69902535, 346939792, 1750071307, 8958993507, 46484716684, 244187539270, 1297395375129, 6965930587924]
(13) [ [ f(n): 2 2 (- n - 17 n - 72)f(n + 3) + (4 n + 30 n + 44)f(n + 2) + 2 2 (19 n + 113 n + 150)f(n + 1) + (14 n + 42 n + 28)f(n) = 0 , f(0) = 1, f(1) = 0, f(2) = 1] ]
Type: List(Expression(Integer))

fricas
guessRec([1,1,0,1,- 1,2,- 1,5,- 4,29,- 13,854,- 685])
2 (14) [[f(n): f(n + 2) + f(n + 1) - f(n) = 0, f(0) = 1, f(1) = 1]]
Type: List(Expression(Integer))

integrate(exp(x-x^2), x) --mariuszi28cg, Mon, 25 Sep 2017 20:14:29 +0000 reply
fricas
integrate(exp(x-x^2), x)
1 - 4 2 x - 1 +---+ %e erf(-------)\|%pi 2 (15) --------------------- 2
Type: Union(Expression(Integer),...)

fricas
1+1
(16) 2
Type: PositiveInteger?

2^3-2**3

2^3

fricas
2^3
(17) 8
Type: PositiveInteger?

fricas
2**3
There are no library operations named ** Use HyperDoc Browse or issue )what op ** to learn if there is any operation containing " ** " in its name.
Cannot find a definition or applicable library operation named ** with argument type(s) PositiveInteger PositiveInteger
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

fricas
sqrt(2)^2-2
(18) 0
Type: AlgebraicNumber?

fricas
a:=sqrt(2)
+-+ (19) \|2
Type: AlgebraicNumber?
fricas
b:=sqrt(a)
+----+ | +-+ (20) \|\|2
Type: AlgebraicNumber?
fricas
b^2-a
(21) 0
Type: AlgebraicNumber?

fricas
f(a) == { local b=sqrt(a); b^2-a}
Line 1: f(a) == { local b=sqrt(a); b^2-a} ........A........B Error A: Missing mate. Error B: syntax error at top level Error B: Possibly missing a } 3 error(s) parsing

fricas
f(a) == { local b:=sqrt(a); b^2-a}
Line 1: f(a) == { local b:=sqrt(a); b^2-a} ..........A Error A: syntax error at top level Error A: Improper syntax. 2 error(s) parsing

fricas
[q,r]
(22) [q, r]
Type: List(OrderedVariableList?([q,r]))

fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Type: Void
fricas
f(2)
fricas
Compiling function f with type PositiveInteger -> AlgebraicNumber 
(24) 0
Type: AlgebraicNumber?
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
(25) 0
Type: AlgebraicNumber?

fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(2)
fricas
Compiling function f with type PositiveInteger -> AlgebraicNumber 
(27) 0
Type: AlgebraicNumber?
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
(28) 0
Type: AlgebraicNumber?
fricas
f(z)
fricas
Compiling function f with type Variable(z) -> Expression(Integer) 
(29) 0
Type: Expression(Integer)
fricas
f(%i)
fricas
Compiling function f with type Complex(Integer) -> Expression(
      Complex(Integer)) 
(30) 0
Type: Expression(Complex(Integer))

)display properties --aUser, Thu, 01 Feb 2018 15:08:53 +0000 reply
fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(2)
fricas
Compiling function f with type PositiveInteger -> AlgebraicNumber 
(32) 0
Type: AlgebraicNumber?
fricas
c:=f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
(33) 0
Type: AlgebraicNumber?
fricas
)display properties c
Properties of c : Value (has type AlgebraicNumber): 0

fricas
f(a) == ( local b; b:=sqrt(a); b^2 = a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void

\begin{AxiomCode?} f(a) == ( local b; b:=sqrt(a); b^2-a) f(2) \end{AxiomCode?}

fricas
f(a) == ( local b; b:=sqrt(a); b^2 = a)
1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(2)
fricas
Compiling function f with type PositiveInteger -> Equation(
      AlgebraicNumber) 
(36) 2 = 2
Type: Equation(AlgebraicNumber?)
fricas
f(%i)
fricas
Compiling function f with type Complex(Integer) -> Equation(
      Expression(Complex(Integer))) 
(37) %i = %i
Type: Equation(Expression(Complex(Integer)))
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> Equation(
      AlgebraicNumber) 
+-+ +-+ (38) \|2 = \|2
Type: Equation(AlgebraicNumber?)
fricas
f(2^(1/2))
+-+ +-+ (39) \|2 = \|2
Type: Equation(AlgebraicNumber?)
fricas
f(2^(1/3))
3+-+ 3+-+ (40) \|2 = \|2
Type: Equation(AlgebraicNumber?)

fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
(42) 0
Type: AlgebraicNumber?
fricas
)set output fortran
--------------------------- The fortran Option ----------------------------
Description: create output in FORTRAN format
)set output fortran is used to tell FriCAS to turn FORTRAN-style output printing on and off, and where to place the output. By default, the destination for the output is the screen but printing is turned off.
Also See: )set fortran
Syntax: )set output fortran <arg> where arg can be one of on turn FORTRAN printing on off turn FORTRAN printing off (default state) console send FORTRAN output to screen (default state) fp<.fe> send FORTRAN output to file with file prefix fp and file extension .fe. If not given, .fe defaults to .sfort.
If you wish to send the output to a file, you must issue this command twice: once with on and once with the file name. For example, to send FORTRAN output to the file polymer.sfort, issue the two commands
)set output fortran on )set output fortran polymer
The output is placed in the directory from which you invoked FriCAS or the one you set with the )cd system command. The current setting is: Off:CONSOLE f(sqrt(2))
(43) 0
Type: AlgebraicNumber?
fricas
)set output tex
----------------------------- The tex Option ------------------------------
Description: create output in TeX style
)set output tex is used to tell FriCAS to turn TeX-style output printing on and off, and where to place the output. By default, the destination for the output is the screen but printing is turned off.
Syntax: )set output tex <arg> where arg can be one of on turn TeX printing on off turn TeX printing off (default state) console send TeX output to screen (default state) fp<.fe> send TeX output to file with file prefix fp and file extension .fe. If not given, .fe defaults to .stex.
If you wish to send the output to a file, you must issue this command twice: once with on and once with the file name. For example, to send TeX output to the file polymer.stex, issue the two commands
)set output tex on )set output tex polymer
The output is placed in the directory from which you invoked FriCAS or the one you set with the )cd system command. The current setting is: Off:CONSOLE f(sqrt(2))
(44) 0
Type: AlgebraicNumber?
fricas
)set output script
---------------------------- The script Option ----------------------------
Description: display output in SCRIPT formula format
)set output script is used to tell FriCAS to turn IBM Script formula-style output printing on and off, and where to place the output. By default, the destination for the output is the screen but printing is turned off.
Syntax: )set output script <arg> where arg can be one of on turn IBM Script formula printing on off turn IBM Script formula printing off (default state) console send IBM Script formula output to screen (default state) fp<.fe> send IBM Script formula output to file with file prefix fp and file extension .fe. If not given, .fe defaults to .sform.
If you wish to send the output to a file, you must issue this command twice: once with on and once with the file name. For example, to send IBM Script formula output to the file polymer.sform, issue the two commands
)set output script on )set output script polymer
The output is placed in the directory from which you invoked FriCAS or the one you set with the )cd system command. The current setting is: Off:CONSOLE f(sqrt(2))
(45) 0
Type: AlgebraicNumber?

fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
(47) 0
Type: AlgebraicNumber?
fricas
)set output fortran on
f(sqrt(2))
R48=0
(48) 0
Type: AlgebraicNumber?
fricas
)set output tex on 
f(sqrt(2))
R49=0
(49) 0
\begin{equation} \label{eq11}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output script on
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R50=0
(50) 0
\begin{equation} \label{eq12}0\end{equation}
Type: AlgebraicNumber?

fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
.eq set blank @ :df. 0 :edf.
R52=0
(52) 0
\begin{equation} \label{eq13}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output fortran console
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R53=0
(53) 0
\begin{equation} \label{eq14}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output tex console
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R54=0
(54) 0
\begin{equation} \label{eq15}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output script console
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R55=0
(55) 0
\begin{equation} \label{eq16}0\end{equation}
Type: AlgebraicNumber?

fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
.eq set blank @ :df. 0 :edf.
R57=0
(57) 0
\begin{equation} \label{eq17}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output fortran on
 
fricas
)set output fortran console
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R58=0
(58) 0
\begin{equation} \label{eq18}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output tex on 
 
fricas
)set output tex console
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R59=0
(59) 0
\begin{equation} \label{eq19}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output script on
 
fricas
)set output script console
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R60=0
(60) 0
\begin{equation} \label{eq20}0\end{equation}
Type: AlgebraicNumber?

fricas
f(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared. 1 old definition(s) deleted for function or rule f
Type: Void
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> AlgebraicNumber 
.eq set blank @ :df. 0 :edf.
R62=0
(62) 0
\begin{equation} \label{eq21}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output fortran on
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
R63=0
(63) 0
\begin{equation} \label{eq22}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output fortran off
 
fricas
)set output tex on 
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
(64) 0
\begin{equation} \label{eq23}0\end{equation}
Type: AlgebraicNumber?
fricas
)set output tex off
 
fricas
)set output script on
f(sqrt(2))
.eq set blank @ :df. 0 :edf.
(65) 0
Type: AlgebraicNumber?
fricas
)set output script off

((1+2)/3)::SquareMatrix?(3,Integer)

fricas
((1+2)/3)::SquareMatrix(3,Integer)
+1 0 0+ | | (66) |0 1 0| | | +0 0 1+
Type: SquareMatrix?(3,Integer)

fricas
((1+2)/3)::SquareMatrix(3,Integer)
+1 0 0+ | | (67) |0 1 0| | | +0 0 1+
Type: SquareMatrix?(3,Integer)

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integrate(exp(x-x^2), x) --test int, Sun, 10 Jun 2018 12:51:40 +0000 reply
fricas
integrate((x+sin(x))^(1/2), x)
>> Error detected within library code: integrate: implementation incomplete (constant residues)

integrate(exp(x-x^2), x) --test int, Sun, 10 Jun 2018 12:52:12 +0000 reply
\begin{fricas} integrate((x+sin(x))^(1/2), x) \end{fricas}

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