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SandBoxFriCAS

last edited 4 months ago by test1

Edit detail for SandBoxFriCAS revision 35 of 62

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Editor: aUser Time: 2018/02/01 15:30:47 GMT+0
Note:

added:

From aUser Thu Feb 1 15:30:46 +0000 2018
From: aUser
Date: Thu, 01 Feb 2018 15:30:46 +0000
Subject: 
Message-ID: <20180201153046+0000@axiom-wiki.newsynthesis.org>

\begin{axiom}
f(a) == ( local b; b:=sqrt(a); b^2-a)
f(sqrt(2))
)set output fortran on
f(sqrt(2))
)set output tex on 
f(sqrt(2))
)set output script on
f(sqrt(2))
\end{axiom}

This page is set to execute \begin{axiom}... \end{axiom} commands using FriCAS?. See also FriCASIntegration?.

fricas

)version

Value = "FriCAS 1.3.1 compiled at Thu Feb 16 03:24:08 UTC 2017"

Any comments added here use this version of FriCAS?.

... --meliusja, Tue, 08 Apr 2008 10:38:33 -0700 reply

fricas

solve(s=v*t+a*t^2/2,t)

$\label{eq1}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]$

(1)

Type: List(Equation(Fraction(Polynomial(Integer))))

... --meliusja, Tue, 08 Apr 2008 10:39:28 -0700 reply

fricas

radicalSolve(s=v*t+a*t^2/2,t)

$\label{eq2}\left[{t ={{-{\sqrt{{4 \ {{v}^{2}}}+{8 \ a \ s}}}-{2 \ v}}\over{2 \ a}}}, \:{t ={{{\sqrt{{4 \ {{v}^{2}}}+{8 \ a \ s}}}-{2 \ v}}\over{2 \ a}}}\right]$

(2)

Type: List(Equation(Expression(Integer)))

... --meliusja, Tue, 08 Apr 2008 10:40:28 -0700 reply

fricas

solve(v*t+a*t^2/2-s=0,t)

$\label{eq3}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]$

(3)

Type: List(Equation(Fraction(Polynomial(Integer))))

... --meliusja, Tue, 08 Apr 2008 10:41:13 -0700 reply

fricas

solve(v*t+a*t/2-s=0,t)

$\label{eq4}\left[{t ={{2 \ s}\over{{2 \ v}+ a}}}\right]$

(4)

Type: List(Equation(Fraction(Polynomial(Integer))))

... --meliusja, Tue, 08 Apr 2008 10:42:37 -0700 reply

fricas

solve(v*t+a*t^2/2-s=0,t)

$\label{eq5}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]$

(5)

Type: List(Equation(Fraction(Polynomial(Integer))))

fricas

radicalSolve(p^3 - p + 1/10=0,p)

$\label{eq6}\begin{array}{@{}l} \displaystyle \left[{p ={{{{\left(-{3 \ {\sqrt{- 3}}}+ 3 \right)}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}- 2}\over{{\left({3 \ {\sqrt{- 3}}}+ 3 \right)}\ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}, \: \right. \ \ \displaystyle \left.{p ={{{{\left(-{3 \ {\sqrt{- 3}}}- 3 \right)}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}+ 2}\over{{\left({3 \ {\sqrt{- 3}}}- 3 \right)}\ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}, \: \right. \ \ \displaystyle \left.{p ={{{3 \ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{37 3}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}+ 1}\over{3 \ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}\right]$

(6)

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]]

$\label{eq7}\left[{foo 1 = \verb#"a"#}, \:{remLexs ={\left[ 1, \: 2, \: 3 \right]}}\right]$

(7)

Type: Record(foo1: String,remLexs: List(Integer))

fricas

r2: R2 := ["b", [5]]

$\label{eq8}\left[{foo 2 = \verb#"b"#}, \:{remLexs ={\left[ 5 \right]}}\right]$

(8)

Type: Record(foo2: String,remLexs: List(Integer))

fricas

r1.remLexs

$\label{eq9}\left[ 1, \: 2, \: 3 \right]$

(9)

Type: List(Integer)

fricas

r2.remLexs

$\label{eq10}\left[ 5 \right]$

(10)

Type: List(Integer)

... --jib jabber, Fri, 07 Mar 2014 07:04:39 +0000 reply

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  - 17n - 72)f(n + 3) + (4n  + 30n + 44)f(n + 2)
           + 
                 2                             2
             (19n  + 113n + 150)f(n + 1) + (14n  + 42n + 28)f(n)
         = 
           0
       ,
      f(0) = 1, f(1) = 0, f(2) = 1]
     ]

Type: List(Expression(Integer))

... --panacea, Fri, 21 Nov 2014 18:25:05 +0000 reply

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    2x - 1  +---+
         %e erf(------)\|%pi
                   2
   (15)  --------------------
                   2

Type: Union(Expression(Integer),...)

test 1+1 --aUser, Thu, 01 Feb 2018 14:32:47 +0000 reply

fricas

1+1

$\label{eq1}2$

(1)

Type: PositiveInteger?

^ or **? --aUser, Thu, 01 Feb 2018 14:34:22 +0000 reply

2^3-2**3

2^3 --aUser, Thu, 01 Feb 2018 14:34:46 +0000 reply

2^3

^ or **? --aUser, Thu, 01 Feb 2018 14:35:09 +0000 reply

fricas

2^3

$\label{eq1}8$

(1)

Type: PositiveInteger?

^ or **? --aUser, Thu, 01 Feb 2018 14:35:49 +0000 reply

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.

bug? --aUser, Thu, 01 Feb 2018 14:37:03 +0000 reply

fricas

sqrt(2)^2-2

$\label{eq1}0$

(1)

Type: AlgebraicNumber?

bug? --aUser, Thu, 01 Feb 2018 14:38:36 +0000 reply

fricas

a:=sqrt(2)

$\label{eq1}\sqrt{2}$

(1)

Type: AlgebraicNumber?

fricas

b:=sqrt(a)

$\label{eq2}\root{4}\of{2}$

(2)

Type: AlgebraicNumber?

fricas

b^2-a

$\label{eq3}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(3)

Type: AlgebraicNumber?

bug? --aUser, Thu, 01 Feb 2018 14:41:20 +0000 reply

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

... --aUser, Thu, 01 Feb 2018 14:41:44 +0000 reply

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

[q,r]? type --aUser, Thu, 01 Feb 2018 15:00:38 +0000 reply

fricas

[q,r]

$\label{eq1}\left[ q , \: r \right]$

(1)

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

... --aUser, Thu, 01 Feb 2018 15:03:11 +0000 reply

fricas

f(a) == ( local b; b:=sqrt(a); b^2-a)

Type: Void

fricas

f(2)

fricas

Compiling function f with type PositiveInteger -> AlgebraicNumber

$\label{eq1}0$

(1)

Type: AlgebraicNumber?

fricas

f(sqrt(2))

fricas

Compiling function f with type AlgebraicNumber -> AlgebraicNumber

$\label{eq2}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(2)

Type: AlgebraicNumber?

bug --aUser, Thu, 01 Feb 2018 15:03:46 +0000 reply

fricas

f(a) == ( local b; b:=sqrt(a); b^2-a)

Type: Void

fricas

f(2)

fricas

Compiling function f with type PositiveInteger -> AlgebraicNumber

$\label{eq1}0$

(1)

Type: AlgebraicNumber?

fricas

f(sqrt(2))

fricas

Compiling function f with type AlgebraicNumber -> AlgebraicNumber

$\label{eq2}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(2)

Type: AlgebraicNumber?

fricas

f(z)

fricas

Compiling function f with type Variable(z) -> Expression(Integer)

$\label{eq3}0$

(3)

Type: Expression(Integer)

fricas

f(%i)

fricas

Compiling function f with type Complex(Integer) -> Expression(
      Complex(Integer))

$\label{eq4}0$

(4)

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)

Type: Void

fricas

f(2)

fricas

Compiling function f with type PositiveInteger -> AlgebraicNumber

$\label{eq1}0$

(1)

Type: AlgebraicNumber?

fricas

c:=f(sqrt(2))

fricas

Compiling function f with type AlgebraicNumber -> AlgebraicNumber

$\label{eq2}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(2)

Type: AlgebraicNumber?

fricas

)display properties c

Properties of c :
                                      4+-+2    +-+
   Value (has type AlgebraicNumber):  \|2   - \|2

... --aUser, Thu, 01 Feb 2018 15:21:08 +0000 reply

fricas

f(a) == ( local b; b:=sqrt(a); b^2 = a)

Type: Void

... --aUser,  Thu, 01 Feb 2018 15:21:23 +0000 reply
\begin{AxiomCode}
f(a) == ( local b; b:=sqrt(a); b^2-a)
f(2)
\end{AxiomCode}

Some or all expressions may not have rendered properly, because Latex returned the following error:

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(/usr/share/texmf-texlive/tex/latex/geometry/geometry.sty
(/usr/share/texmf-texlive/tex/xelatex/xetexconfig/geometry.cfg)
Package geometry Warning: `lmargin' and `rmargin' result in NEGATIVE (-108.405p
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) (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `? option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
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Package: `setspace 6.7 <2000/12/01>
) (/usr/share/texmf-texlive/tex/generic/xypic/xy.sty
(/usr/share/texmf-texlive/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes,
docmode, (/usr/share/texmf-texlive/tex/generic/xypic/xyrecat.tex)
(/usr/share/texmf-texlive/tex/generic/xypic/xyidioms.tex)
 Xy-pic version 3.7 <1999/02/16>
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 Xy-pic is free software: see the User's Guide for details.

Loading kernel: messages; fonts; allocations: state, direction,
utility macros; pictures: \xy, positions, objects, decorations;
kernel objects: directionals, circles, text; options; algorithms: directions,
edges, connections;  Xy-pic loaded))
(/usr/share/texmf-texlive/tex/generic/xypic/xyall.tex
 Xy-pic option: All features v.3.3
(/usr/share/texmf-texlive/tex/generic/xypic/xycurve.tex
 Xy-pic option: Curve and Spline extension v.3.7 curve, circles, loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyframe.tex
 Xy-pic option: Frame and Bracket extension v.3.7 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xycmtip.tex
 Xy-pic option: Computer Modern tip extension v.3.3
(/usr/share/texmf-texlive/tex/generic/xypic/xytips.tex
 Xy-pic option: More Tips extension v.3.3 loaded) loaded)
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 Xy-pic option: Line styles extension v.3.6 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyrotate.tex
 Xy-pic option: Rotate and Scale extension v.3.3 loaded)
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 Xy-pic option: Colour extension v.3.3 loaded)
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 Xy-pic option: Matrix feature v.3.4 loaded)
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 Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded)
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(/usr/share/texmf/tex/latex/graphviz/graphviz.sty
(/usr/share/texmf-texlive/tex/latex/psfrag/psfrag.sty))
(/usr/share/texmf/tex/latex/sagetex.sty
Writing sage input file 6576055087707332466-16.0px.sage
) (/usr/share/texmf-texlive/tex/latex/gnuplottex/gnuplottex.sty
(/usr/share/texmf-texlive/tex/latex/base/latexsym.sty)
(/usr/share/texmf-texlive/tex/latex/moreverb/moreverb.sty)
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(./6576055087707332466-16.0px.aux)
(/usr/share/texmf-texlive/tex/latex/ucs/ucsencs.def)
 LaTeX Error: Environment AxiomCode undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
l.121 \begin{AxiomCode}
 Missing $ inserted.
<inserted text> 
                $
l.122 f(a) == ( local b; b:=sqrt(a); b^
                                       2-a)
(/usr/share/texmf-texlive/tex/latex/jknapltx/ursfs.fd)
(/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd)
(/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd)
(/usr/share/texmf-texlive/tex/latex/base/ulasy.fd)
 LaTeX Error: \begin{document} ended by \end{AxiomCode}.
See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
l.124 \end{AxiomCode}
 Missing $ inserted.
<inserted text> 
                $
l.124 \end{AxiomCode}
[1] (./6576055087707332466-16.0px.aux) )
(see the transcript file for additional information)
Output written on 6576055087707332466-16.0px.dvi (1 page, 644 bytes).
Transcript written on 6576055087707332466-16.0px.log.

... --aUser, Thu, 01 Feb 2018 15:22:39 +0000 reply

fricas

f(a) == ( local b; b:=sqrt(a); b^2 = a)

Type: Void

fricas

f(2)

fricas

Compiling function f with type PositiveInteger -> Equation(
      AlgebraicNumber)

$\label{eq1}2 = 2$

(1)

Type: Equation(AlgebraicNumber?)

fricas

f(%i)

fricas

Compiling function f with type Complex(Integer) -> Equation(
      Expression(Complex(Integer)))

$\label{eq2}i = i$

(2)

Type: Equation(Expression(Complex(Integer)))

fricas

f(sqrt(2))

fricas

Compiling function f with type AlgebraicNumber -> Equation(
      AlgebraicNumber)

$\label{eq3}{{\root{4}\of{2}}^{2}}={\sqrt{2}}$

(3)

Type: Equation(AlgebraicNumber?)

fricas

f(2^(1/2))

$\label{eq4}{{\root{4}\of{2}}^{2}}={\sqrt{2}}$

(4)

Type: Equation(AlgebraicNumber?)

fricas

f(2^(1/3))

$\label{eq5}{{\root{6}\of{2}}^{2}}={\root{3}\of{2}}$

(5)

Type: Equation(AlgebraicNumber?)

)set output --aUser, Thu, 01 Feb 2018 15:29:41 +0000 reply

fricas

f(a) == ( local b; b:=sqrt(a); b^2-a)

Type: Void

fricas

f(sqrt(2))

fricas

Compiling function f with type AlgebraicNumber -> AlgebraicNumber

$\label{eq1}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(1)

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))

$\label{eq2}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(2)

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:  On:CONSOLE 
f(sqrt(2))

$\label{eq3}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(3)

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))

$\label{eq4}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(4)

Type: AlgebraicNumber?

... --aUser, Thu, 01 Feb 2018 15:30:46 +0000 reply

fricas

f(a) == ( local b; b:=sqrt(a); b^2-a)

Type: Void

fricas

f(sqrt(2))

fricas

Compiling function f with type AlgebraicNumber -> AlgebraicNumber

$\label{eq1}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(1)

Type: AlgebraicNumber?

fricas

)set output fortran on

f(sqrt(2))

      R3=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)

$\label{eq2}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(2)

Type: AlgebraicNumber?

fricas

)set output tex on 

f(sqrt(2))

      R4=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)

$\label{eq3}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(3)

Type: AlgebraicNumber?

fricas

)set output script on

f(sqrt(2))

.eq set blank @
:df.
<<<midsup adjust(u 1.5 r 9) 4 sqrt 2> sup 2> -<sqrt 2>> 
:edf.

      R5=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)

$\label{eq4}{{\root{4}\of{2}}^{2}}-{\sqrt{2}}$

(4)

Type: AlgebraicNumber?