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SandBoxFriCAS

last edited 11 months ago by test1

Edit detail for SandBoxFriCAS revision 33 of 62

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Editor: aUser Time: 2018/02/01 15:22:40 GMT+0
Note:

added:

From aUser Thu Feb 1 15:22:39 +0000 2018
From: aUser
Date: Thu, 01 Feb 2018 15:22:39 +0000
Subject: 
Message-ID: <20180201152239+0000@axiom-wiki.newsynthesis.org>

\begin{axiom}
f(a) == ( local b; b:=sqrt(a); b^2 = a)
f(2)
f(%i)
f(sqrt(2))
f(2^(1/2))
f(2^(1/3))
\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}

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Loading kernel: messages; fonts; allocations: state, direction,
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(/usr/share/texmf-texlive/tex/generic/xypic/xyall.tex
 Xy-pic option: All features v.3.3
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 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)
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 Xy-pic option: Computer Modern tip extension v.3.3
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Writing sage input file 6576055087707332466-16.0px.sage
) (/usr/share/texmf-texlive/tex/latex/gnuplottex/gnuplottex.sty
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 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)
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 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?)