login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit

Edit detail for SandBoxFriCAS revision 32 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: aUser
Time: 2018/02/01 15:21:24 GMT+0
Note:

added:

From aUser Thu Feb 1 15:21:23 +0000 2018
From: aUser
Date: Thu, 01 Feb 2018 15:21:23 +0000
Subject: 
Message-ID: <20180201152123+0000@axiom-wiki.newsynthesis.org>


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

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?.

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))))

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)))

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))))

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))))

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)

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

\label{eq1}2(1)
Type: PositiveInteger?

2^3-2**3

fricas
2^3

\label{eq1}8(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

\label{eq1}0(1)
Type: AlgebraicNumber?

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?

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]

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

\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(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

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


\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.