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ExampleGroebner ←	↑	→ ExpressionInteger

ExampleIntegration

Edit detail for ExampleIntegration revision 2 of 6

	1 2 3 4 5 6
Editor: Bill Page Time: 2015/03/10 19:54:37 GMT+0
Note: a little more

added:
i0 := integrate(f, x=1..2)
s:=radicalSolve(23*f0^3+f0+1,f0)
eval(i0,%%F0=rhs(s(1)));
complexNumeric %
eval(i0,%%F0=rhs(s(2)));
complexNumeric %
eval(i0,%%F0=rhs(s(3)));
complexNumeric %

fricas

f := x/(x^3-x+1)

$\label{eq1}x \over{{{x}^{3}}- x + 1}$

(1)

Type: Fraction(Polynomial(Integer))

fricas

i := integrate(f, x)

$\label{eq2}{\left( \begin{array}{@{}l} \displaystyle { \begin{array}{@{}l} \displaystyle 4 \ {\sqrt{{{69}\ {{\%\%F 0}^{2}}}+ 4}}\ \cdot \ \ \displaystyle {\arctan{\left({{{\left({9 \ {\sqrt{23}}\ \%\%F 0}+{\sqrt{23}}\right)}\ {\sqrt{{{6 9}\ {{\%\%F 0}^{2}}}+ 4}}}\over{{{10}\ {\sqrt{{{\left(-{{207}\ x}+{46}\right)}\ {{\%\%F 0}^{2}}}+{{\left({{23}\ x}-{69}\right)}\ \%\%F 0}+{{25}\ {{x}^{2}}}-{6 \ x}- 7}}}-{{207}\ {{\%\%F 0}^{2}}}+{{23}\ \%\%F 0}+{{50}\ x}- 6}}\right)}}$

(2)

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

fricas

D(i, x)

$\label{eq3}x \over{{{x}^{3}}- x + 1}$

(3)

Type: Expression(Integer)

fricas

23*%%F0^3 + %%F0 + 1

$\label{eq4}0$

(4)

Type: Expression(Integer)

fricas

i0 := integrate(f, x=1..2)

$\label{eq5}{\left( \begin{array}{@{}l} \displaystyle { \begin{array}{@{}l} \displaystyle 8 \ {\sqrt{{{69}\ {{\%\%F 0}^{2}}}+ 4}}\ \cdot \ \ \displaystyle {\arctan{\left({{{\left({9 \ {\sqrt{23}}\ \%\%F 0}+{\sqrt{23}}\right)}\ {\sqrt{{{6 9}\ {{\%\%F 0}^{2}}}+ 4}}}\over{{{10}\ {\sqrt{-{{368}\ {{\%\%F 0}^{2}}}-{{23}\ \%\%F 0}+{81}}}}-{{207}\ {{\%\%F 0}^{2}}}+{{2 3}\ \%\%F 0}+{94}}}\right)}}$

(5)

Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

fricas

s:=radicalSolve(23*f0^3+f0+1,f0)

$\label{eq6}\begin{array}{@{}l} \displaystyle \left[{f 0 ={{{{\left(-{{69}\ {\sqrt{- 3}}}+{69}\right)}\ {{\root{3}\of{{-{3 \ {\sqrt{69}}}+{25}}\over{{138}\ {\sqrt{69}}}}}^{2}}}+ 2}\over{{\left({{6 9}\ {\sqrt{- 3}}}+{69}\right)}\ {\root{3}\of{{-{3 \ {\sqrt{69}}}+{25}}\over{{138}\ {\sqrt{69}}}}}}}}, \: \right. \ \ \displaystyle \left.{f 0 ={{{{\left(-{{69}\ {\sqrt{- 3}}}-{69}\right)}\ {{\root{3}\of{{-{3 \ {\sqrt{69}}}+{25}}\over{{138}\ {\sqrt{69}}}}}^{2}}}- 2}\over{{\left({{6 9}\ {\sqrt{- 3}}}-{69}\right)}\ {\root{3}\of{{-{3 \ {\sqrt{69}}}+{25}}\over{{138}\ {\sqrt{69}}}}}}}}, \: \right. \ \ \displaystyle \left.{f 0 ={{{{69}\ {{\root{3}\of{{-{3 \ {\sqrt{69}}}+{25}}\over{{1 38}\ {\sqrt{69}}}}}^{2}}}- 1}\over{{69}\ {\root{3}\of{{-{3 \ {\sqrt{6 9}}}+{25}}\over{{138}\ {\sqrt{69}}}}}}}}\right]$