This page is set to execute \begin{axiom}... \end{axiom}
commands using FriCAS?. See also FriCASIntegration?.
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)version
Value = "FriCAS 1.2.7 compiled at Tue Sep 29 13:45:04 UTC 2015"
Any comments added here use this version of FriCAS?.
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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))))
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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)))
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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))))
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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))))
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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))))
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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)))
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R1 ==> Record(foo1: String, remLexs: List Integer)
Type: Void
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R2 ==> Record(foo2: String, remLexs: List Integer)
Type: Void
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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))
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r2: R2 := ["b", [5]]
\label{eq8}\left[{foo 2 = \verb#"b"#}, \:{remLexs ={\left[ 5 \right]}}\right]
(8) Type: Record(foo2: String,remLexs: List(Integer))
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r1.remLexs
\label{eq9}\left[ 1, \: 2, \: 3 \right]
(9) Type: List(Integer)
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r2.remLexs
\label{eq10}\left[ 5 \right]
(10) Type: List(Integer)
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)set output tex off
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)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))
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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))