fricas digits 20
Type: PositiveInteger?
fricas -- n:=x^3+a1*x^2+a2*x+a3 ::Polynomial Fraction Integer
Type: Polynomial(Fraction(Integer))
fricas R:=(9*a1*a2-27*a3-2*a1^3)/54
Type: Polynomial(Fraction(Integer))
fricas S:=(R+(Q^3+R^2)^(1/2))^(1/3)
Type: Expression(Integer)
fricas T:=(R-(Q^3+R^2)^(1/2))^(1/3)
Type: Expression(Integer)
fricas x1:=S+T-a1/3
Type: Expression(Integer)
fricas x2:=-(S+T)/2-a1/3 + %i*sqrt(3)*(S-T)/2
Type: Expression(Complex(Integer))
fricas x3:=-(S+T)/2-a1/3 - %i*sqrt(3)*(S-T)/2
Type: Expression(Complex(Integer))
fricas a5:=x^3+a1*x^2+a2*x+a3 ::Polynomial AlgebraicNumber
Type: Polynomial(AlgebraicNumber?)
fricas a6:=(x-x11) ::Polynomial AlgebraicNumber; Type: Polynomial(AlgebraicNumber?)
fricas a7:=monicDivide(a5, fricas a77:=a7.quotient; Type: Polynomial(AlgebraicNumber?)
fricas a78:=a7.remainder; Type: Polynomial(AlgebraicNumber?)
fricas qu1 :=eval(a77,
Type: Expression(Integer)
fricas rem1:=eval(a78,
Type: Expression(Integer)
fricas eval(rem1,
Type: Expression(Float)
... --wyscc, Mon, 14 Nov 2005 02:53:03 -0600 reply How about this:
fricas pkg:= SOLVEFOR(UP('x,
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last edited 16 years ago |
![\label{eq6}{\left(
\begin{array}{@{}l}
\displaystyle
{3 \ {\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{1
8}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{3 \ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}-
\
\
\displaystyle
a 1](images/4639049191377970483-16.0px.png "\label{eq6}{\left(
\begin{array}{@{}l}
\displaystyle
{3 \ {\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{1
8}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{3 \ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}-
\
\
\displaystyle
a 1")
![\label{eq7}{\left(
\begin{array}{@{}l}
\displaystyle
{{\left({3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{{9 \ {\sqrt{{{2
7}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{{\left(-{3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}}-
\
\
\displaystyle
{2 \ a 1}](images/2280024898385730472-16.0px.png "\label{eq7}{\left(
\begin{array}{@{}l}
\displaystyle
{{\left({3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{{9 \ {\sqrt{{{2
7}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{{\left(-{3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}}-
\
\
\displaystyle
{2 \ a 1}")
![\label{eq8}{\left(
\begin{array}{@{}l}
\displaystyle
{{\left(-{3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{{\left({3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}}-
\
\
\displaystyle
{2 \ a 1}](images/8297630147332314623-16.0px.png "\label{eq8}{\left(
\begin{array}{@{}l}
\displaystyle
{{\left(-{3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{{\left({3 \ i \ {\sqrt{3}}}- 3 \right)}\ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}}-
\
\
\displaystyle
{2 \ a 1}")
![\label{eq10}{\left(
\begin{array}{@{}l}
\displaystyle
{9 \ {{\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}^{2}}}+
\
\
\displaystyle
{{\left({
\begin{array}{@{}l}
\displaystyle
{{18}\ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{9 \ x}+{3 \ a 1}](images/3887557069164108647-16.0px.png "\label{eq10}{\left(
\begin{array}{@{}l}
\displaystyle
{9 \ {{\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}^{2}}}+
\
\
\displaystyle
{{\left({
\begin{array}{@{}l}
\displaystyle
{{18}\ {\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{5
4}\ {\sqrt{3}}}}}}+
\
\
\displaystyle
{9 \ x}+{3 \ a 1}")
![\label{eq11}{\left(
\begin{array}{@{}l}
\displaystyle
{
\begin{array}{@{}l}
\displaystyle
9 \ \cdot
\
\
\displaystyle
{\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}\ \cdot
\
\
\displaystyle
{{\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}^{2}}](images/5654703226383662064-16.0px.png "\label{eq11}{\left(
\begin{array}{@{}l}
\displaystyle
{
\begin{array}{@{}l}
\displaystyle
9 \ \cdot
\
\
\displaystyle
{\root{3}\of{{-{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}\ \cdot
\
\
\displaystyle
{{\root{3}\of{{{9 \ {\sqrt{{{27}\ {{a 3}^{2}}}+{{\left(-{{18}\ a 1 \ a 2}+{4 \ {{a 1}^{3}}}\right)}\ a 3}+{4 \ {{a 2}^{3}}}-{{{a 1}^{2}}\ {{a 2}^{2}}}}}}+{{\left(-{{27}\ a 3}+{9 \ a 1 \ a 2}-{2 \ {{a 1}^{3}}}\right)}\ {\sqrt{3}}}}\over{{54}\ {\sqrt{3}}}}}^{2}}")
