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# Edit detail for SandBoxFriCAS revision 39 of 50

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Editor: jr Time: 2018/02/03 13:20:20 GMT+0 Note: test

added:

From jr Sat Feb 3 13:20:20 +0000 2018
From: jr
Date: Sat, 03 Feb 2018 13:20:20 +0000
Subject: test
Message-ID: <20180203132020+0000@axiom-wiki.newsynthesis.org>

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


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

fricas
solve(s=v*t+a*t^2/2,t)
 (1)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
radicalSolve(s=v*t+a*t^2/2,t)
 (2)
Type: List(Equation(Expression(Integer)))

fricas
solve(v*t+a*t^2/2-s=0,t)
 (3)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(v*t+a*t/2-s=0,t)
 (4)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(v*t+a*t^2/2-s=0,t)
 (5)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
radicalSolve(p^3 - p + 1/10=0,p)
 (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]]
 (7)
Type: Record(foo1: String,remLexs: List(Integer))
fricas
r2: R2 := ["b", [5]]
 (8)
Type: Record(foo2: String,remLexs: List(Integer))
fricas
r1.remLexs
 (9)
Type: List(Integer)
fricas
r2.remLexs
 (10)
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  - 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))

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),...)

fricas
1+1
 (1)
Type: PositiveInteger?

2^3-2**3

fricas
2^3
 (1)
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  (1) Type: AlgebraicNumber? fricas a:=sqrt(2)  (1) Type: AlgebraicNumber? fricas b:=sqrt(a)  (2) Type: AlgebraicNumber? fricas b^2-a  (3) 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]  (1) 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  (1) Type: AlgebraicNumber? fricas f(sqrt(2)) fricas Compiling function f with type AlgebraicNumber -> AlgebraicNumber  (2) Type: AlgebraicNumber? fricas f(a) == ( local b; b:=sqrt(a); b^2-a) Type: Void fricas f(2) fricas Compiling function f with type PositiveInteger -> AlgebraicNumber  (1) Type: AlgebraicNumber? fricas f(sqrt(2)) fricas Compiling function f with type AlgebraicNumber -> AlgebraicNumber  (2) Type: AlgebraicNumber? fricas f(z) fricas Compiling function f with type Variable(z) -> Expression(Integer)  (3) Type: Expression(Integer) fricas f(%i) fricas Compiling function f with type Complex(Integer) -> Expression( Complex(Integer))  (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  (1) Type: AlgebraicNumber? fricas c:=f(sqrt(2)) fricas Compiling function f with type AlgebraicNumber -> AlgebraicNumber  (2) Type: AlgebraicNumber? fricas )display properties c Properties of c : 4+-+2 +-+ Value (has type AlgebraicNumber): \|2 - \|2 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: This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) \write18 enabled. %&-line parsing enabled. entering extended mode (./6576055087707332466-16.0px.tex LaTeX2e <2005/12/01> Babel <v3.8h> 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. (/usr/share/texmf-texlive/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size12.clo)) (/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty (/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf-texlive/tex/latex/base/inputenc.sty (/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def)) (/usr/share/texmf-texlive/tex/latex/bbm/bbm.sty) (/usr/share/texmf-texlive/tex/latex/jknapltx/mathrsfs.sty) (/usr/share/texmf-texlive/tex/latex/base/fontenc.sty (/usr/share/texmf-texlive/tex/latex/base/t1enc.def)) (/usr/share/texmf-texlive/tex/latex/pstricks/pstricks.sty (/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.tex PSTricks' v1.15 <2006/12/22> (tvz) (/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.con)) (/usr/share/texmf/tex/latex/xcolor/xcolor.sty (/etc/texmf/tex/latex/config/color.cfg) (/usr/share/texmf-texlive/tex/latex/graphics/dvips.def) (/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))) (/usr/share/texmf-texlive/tex/latex/graphics/epsfig.sty (/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty (/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty) (/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty (/usr/share/texmf-texlive/tex/latex/graphics/trig.sty) (/etc/texmf/tex/latex/config/graphics.cfg)))) (/usr/share/texmf-texlive/tex/latex/pst-grad/pst-grad.sty (/usr/share/texmf-texlive/tex/generic/pst-grad/pst-grad.tex (/usr/share/texmf-texlive/tex/latex/xkeyval/pst-xkey.tex (/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.sty (/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.tex))) pst-plot' v1.05, 2006/11/04 (tvz,dg,hv))) (/usr/share/texmf-texlive/tex/latex/pstricks/pst-plot.sty (/usr/share/texmf-texlive/tex/generic/pstricks/pst-plot.tex v97 patch 2, 1999/12/12 (/usr/share/texmf-texlive/tex/generic/multido/multido.tex v1.41, 2004/05/18 <tvz>))) (/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 t). width' should be shortened in length. ) (/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)) (/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty) (/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty) (/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty) (/usr/share/texmf-texlive/tex/latex/setspace/setspace.sty 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> Copyright (c) 1991-1998 by Kristoffer H. Rose <krisrose@ens-lyon.fr> 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) (/usr/share/texmf-texlive/tex/generic/xypic/xyline.tex 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) (/usr/share/texmf-texlive/tex/generic/xypic/xycolor.tex Xy-pic option: Colour extension v.3.3 loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xymatrix.tex Xy-pic option: Matrix feature v.3.4 loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xyarrow.tex Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xygraph.tex Xy-pic option: Graph feature v.3.7 loaded) loaded) (/usr/share/texmf-texlive/tex/latex/tools/verbatim.sty) (/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) (/usr/share/texmf-texlive/tex/latex/base/ifthen.sty)) (./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.


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)
 (1)
Type: Equation(AlgebraicNumber?)
fricas
f(%i)
fricas
Compiling function f with type Complex(Integer) -> Equation(
Expression(Complex(Integer)))
 (2)
Type: Equation(Expression(Complex(Integer)))
fricas
f(sqrt(2))
fricas
Compiling function f with type AlgebraicNumber -> Equation(
AlgebraicNumber)
 (3)
Type: Equation(AlgebraicNumber?)
fricas
f(2^(1/2))
 (4)
Type: Equation(AlgebraicNumber?)
fricas
f(2^(1/3))
 (5)
Type: Equation(AlgebraicNumber?)

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
 (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))
 (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))
 (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))
 (4)
Type: AlgebraicNumber?

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
 (1)
Type: AlgebraicNumber?
fricas
)set output fortran on
f(sqrt(2))
R3=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)
 (2)
Type: AlgebraicNumber?
fricas
)set output tex on
f(sqrt(2))
R4=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)
 (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)
 (4)
Type: AlgebraicNumber?

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
 (1)
Type: AlgebraicNumber?
fricas
)set output fortran console
f(sqrt(2))
 (2)
Type: AlgebraicNumber?
fricas
)set output tex console
f(sqrt(2))
 (3)
Type: AlgebraicNumber?
fricas
)set output script console
f(sqrt(2))
 (4)
Type: AlgebraicNumber?

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
 (1)
Type: AlgebraicNumber?
fricas
)set output fortran on

fricas
)set output fortran console
f(sqrt(2))
R3=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)
 (2)
Type: AlgebraicNumber?
fricas
)set output tex on

fricas
)set output tex console
f(sqrt(2))
R4=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)
 (3)
Type: AlgebraicNumber?
fricas
)set output script on

fricas
)set output script console
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)
 (4)
Type: AlgebraicNumber?

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
 (1)
Type: AlgebraicNumber?
fricas
)set output fortran on
f(sqrt(2))
R3=(2.0D0**(1/4.0D0))**2-DSQRT(2.0D0)
 (2)
Type: AlgebraicNumber?
fricas
)set output fortran off

fricas
)set output tex on
f(sqrt(2))
 (3)
Type: AlgebraicNumber?
fricas
)set output tex off

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.
Type: AlgebraicNumber?
fricas
)set output script off`

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