fricas (1) -> c(x, Type: Void
fricas eqns := [x^2 - y + z,
Type: List(Polynomial(Integer))
fricas solve(eqns,
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas c:=[2*a^2+x=8,
Type: List(Equation(Polynomial(Integer)))
fricas solve(c,
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas radicalSolve(c)
Type: List(List(Equation(Expression(Integer))))
fricas radicalSolve(c,
Type: List(List(Equation(Expression(Integer))))
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last edited 12 years ago by test1 |
![\label{eq1}\left[{z - y +{{x}^{2}}}, \:{{{{x}^{2}}\ z}-{b \ y}+{{x}^{4}}}, \:{{{{y}^{2}}\ z}-{b \ x}- a}\right]](images/7309316272200029144-16.0px.png "\label{eq1}\left[{z - y +{{x}^{2}}}, \:{{{{x}^{2}}\ z}-{b \ y}+{{x}^{4}}}, \:{{{{y}^{2}}\ z}-{b \ x}- a}\right]")
![\label{eq2}\begin{array}{@{}l}
\displaystyle
\left[{\left[{x = -{\frac{a}{b}}}, \:{y = 0}, \:{z = -{\frac{{a}^{2}}{{b}^{2}}}}\right]}, \: \right.
\
\
\displaystyle
\left.{
\begin{array}{@{}l}
\displaystyle
\left[{x ={\frac{{{z}^{3}}+{2 \ b \ {{z}^{2}}}+{{{b}^{2}}\ z}- a}{b}}}, \:{y ={z + b}}, \: \right.
\
\
\displaystyle
\left.{
\begin{array}{@{}l}
\displaystyle
{{{z}^{6}}+{4 \ b \ {{z}^{5}}}+{6 \ {{b}^{2}}\ {{z}^{4}}}+{{\left({4 \ {{b}^{3}}}-{2 \ a}\right)}\ {{z}^{3}}}+{{\left({{b}^{4}}-{4 \ a \ b}\right)}\ {{z}^{2}}}-{2 \ a \ {{b}^{2}}\ z}-{{b}^{3}}+{{a}^{2}}}=
\
\
\displaystyle
0](images/179327189571473195-16.0px.png "\label{eq2}\begin{array}{@{}l}
\displaystyle
\left[{\left[{x = -{\frac{a}{b}}}, \:{y = 0}, \:{z = -{\frac{{a}^{2}}{{b}^{2}}}}\right]}, \: \right.
\
\
\displaystyle
\left.{
\begin{array}{@{}l}
\displaystyle
\left[{x ={\frac{{{z}^{3}}+{2 \ b \ {{z}^{2}}}+{{{b}^{2}}\ z}- a}{b}}}, \:{y ={z + b}}, \: \right.
\
\
\displaystyle
\left.{
\begin{array}{@{}l}
\displaystyle
{{{z}^{6}}+{4 \ b \ {{z}^{5}}}+{6 \ {{b}^{2}}\ {{z}^{4}}}+{{\left({4 \ {{b}^{3}}}-{2 \ a}\right)}\ {{z}^{3}}}+{{\left({{b}^{4}}-{4 \ a \ b}\right)}\ {{z}^{2}}}-{2 \ a \ {{b}^{2}}\ z}-{{b}^{3}}+{{a}^{2}}}=
\
\
\displaystyle
0")
![\label{eq3}\left[{{x +{2 \ {{a}^{2}}}}= 8}, \:{{{4 \ a \ x}+ 2}= 4}\right]](images/2438885250724754975-16.0px.png "\label{eq3}\left[{{x +{2 \ {{a}^{2}}}}= 8}, \:{{{4 \ a \ x}+ 2}= 4}\right]")
![\label{eq4}\left[{\left[{a ={-{{x}^{2}}+{8 \ x}}}, \:{{{2 \ {{x}^{3}}}-{{16}\ {{x}^{2}}}+ 1}= 0}\right]}\right]](images/1621534868728867607-16.0px.png "\label{eq4}\left[{\left[{a ={-{{x}^{2}}+{8 \ x}}}, \:{{{2 \ {{x}^{3}}}-{{16}\ {{x}^{2}}}+ 1}= 0}\right]}\right]")
![\label{eq5}\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
x =
\
\
\displaystyle
{\frac{{{\left({{48}\ {\sqrt{- 3}}}-{48}\right)}\ {{\root{3}\of{\frac{{\sqrt{-{\frac{4069}{3}}}}- 3}{3}}}^{2}}}+{{\left({{\left({3 \ {\sqrt{-{\frac{4069}{3}}}}}- 9 \right)}\ {\sqrt{- 3}}}+{3 \ {\sqrt{-{\frac{4
069}{3}}}}}- 9 \right)}\ {\root{3}\of{\frac{{\sqrt{-{\frac{40
69}{3}}}}- 3}{3}}}}-{512}}{{\left({{18}\ {\sqrt{- 3}}}-{18}\right)}\ {{\root{3}\of{\frac{{\sqrt{-{\frac{4069}{3}}}}- 3}{3}}}^{2}}}}](images/3753425259340196304-16.0px.png "\label{eq5}\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
x =
\
\
\displaystyle
{\frac{{{\left({{48}\ {\sqrt{- 3}}}-{48}\right)}\ {{\root{3}\of{\frac{{\sqrt{-{\frac{4069}{3}}}}- 3}{3}}}^{2}}}+{{\left({{\left({3 \ {\sqrt{-{\frac{4069}{3}}}}}- 9 \right)}\ {\sqrt{- 3}}}+{3 \ {\sqrt{-{\frac{4
069}{3}}}}}- 9 \right)}\ {\root{3}\of{\frac{{\sqrt{-{\frac{40
69}{3}}}}- 3}{3}}}}-{512}}{{\left({{18}\ {\sqrt{- 3}}}-{18}\right)}\ {{\root{3}\of{\frac{{\sqrt{-{\frac{4069}{3}}}}- 3}{3}}}^{2}}}}")
![\label{eq6}\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
a =
\
\
\displaystyle
{\frac{{{\left({{\left(-{\sqrt{-{\frac{4069}{3}}}}+ 3 \right)}\ {\sqrt{- 3}}}+{\sqrt{-{\frac{4069}{3}}}}- 3 \right)}\ {\root{3}\of{\frac{{9 \ {\sqrt{-{\frac{4069}{3}}}}}+{2021}}{4}}}}+{{\left(-{8 \ {\sqrt{-{\frac{4069}{3}}}}}+{24}\right)}\ {\sqrt{- 3}}}-{8 \ {\sqrt{-{\frac{4069}{3}}}}}+{24}}{8 \ {{\root{3}\of{\frac{{9 \ {\sqrt{-{\frac{4069}{3}}}}}+{2021}}{4}}}^{2}}}}](images/4027962308593541631-16.0px.png "\label{eq6}\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
a =
\
\
\displaystyle
{\frac{{{\left({{\left(-{\sqrt{-{\frac{4069}{3}}}}+ 3 \right)}\ {\sqrt{- 3}}}+{\sqrt{-{\frac{4069}{3}}}}- 3 \right)}\ {\root{3}\of{\frac{{9 \ {\sqrt{-{\frac{4069}{3}}}}}+{2021}}{4}}}}+{{\left(-{8 \ {\sqrt{-{\frac{4069}{3}}}}}+{24}\right)}\ {\sqrt{- 3}}}-{8 \ {\sqrt{-{\frac{4069}{3}}}}}+{24}}{8 \ {{\root{3}\of{\frac{{9 \ {\sqrt{-{\frac{4069}{3}}}}}+{2021}}{4}}}^{2}}}}")