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fricas
c(x,y,z)==  x^2 - y + z
Type: Void
fricas
eqns := [x^2 - y + z, x^2*z + x^4 - b*y, y^2 *z - a - b*x]

\label{eq1}\left[{z - y +{{x}^{2}}}, \:{{{{x}^{2}}\  z}-{b \  y}+{{x}^{4}}}, \:{{{{y}^{2}}\  z}-{b \  x}- a}\right](1)
Type: List(Polynomial(Integer))
fricas
solve(eqns,[x,y,z])

\label{eq2}\begin{array}{@{}l}
\displaystyle
\left[{\left[{x = -{a \over b}}, \:{y = 0}, \:{z = -{{{a}^{2}}\over{{b}^{2}}}}\right]}, \: \right.
\
\
\displaystyle
\left.{
\begin{array}{@{}l}
\displaystyle
\left[{x ={{{{z}^{3}}+{2 \  b \ {{z}^{2}}}+{{{b}^{2}}\  z}- a}\over 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 
(2)
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
c:=[2*a^2+x=8,2+4*a*x=4]
Function definition for c is being overwritten.

\label{eq3}\left[{{x +{2 \ {{a}^{2}}}}= 8}, \:{{{4 \  a \  x}+ 2}= 4}\right](3)
Type: List(Equation(Polynomial(Integer)))
fricas
solve(c,[a,x])

\label{eq4}\left[{\left[{a ={-{{x}^{2}}+{8 \  x}}}, \:{{{2 \ {{x}^{3}}}-{{16}\ {{x}^{2}}}+ 1}= 0}\right]}\right](4)
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
radicalSolve(c)

\label{eq5}\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
x ={{{{\left({{96}\ {\sqrt{- 3}}}-{96}\right)}\ {\sqrt{3}}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{4069}}}}\over{{24}\ {\sqrt{3}}}}}^{2}}}+{{\left({{\left(-{9 \ {\sqrt{- 3}}}- 9 \right)}\ {\sqrt{3}}}+{3 \ {\sqrt{-{4069}}}\ {\sqrt{- 3}}}+{3 \ {\sqrt{-{4069}}}}\right)}\ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{4069}}}}\over{{24}\ {\sqrt{3}}}}}}-{{256}\ {\sqrt{3}}}}\over{{\left({{36}\ {\sqrt{- 3}}}-{36}\right)}\ {\sqrt{3}}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{4069}}}}\over{{24}\ {\sqrt{3}}}}}^{2}}}}
(5)
Type: List(List(Equation(Expression(Integer))))
fricas
radicalSolve(c,[a,x])

\label{eq6}\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
\left[{
\begin{array}{@{}l}
\displaystyle
a ={{{{\left({{\left({9 \ {\sqrt{- 3}}}- 9 \right)}\ {\sqrt{3}}}-{3 \ {\sqrt{-{4069}}}\ {\sqrt{- 3}}}+{3 \ {\sqrt{-{4069}}}}\right)}\ {\root{3}\of{{{{2
021}\ {\sqrt{3}}}+{9 \ {\sqrt{-{4069}}}}}\over{{108}\ {\sqrt{3}}}}}}+{{\left({{24}\ {\sqrt{- 3}}}+{24}\right)}\ {\sqrt{3}}}-{8 \ {\sqrt{-{4069}}}\ {\sqrt{- 3}}}-{8 \ {\sqrt{-{4069}}}}}\over{{72}\ {\sqrt{3}}\ {{\root{3}\of{{{{2
021}\ {\sqrt{3}}}+{9 \ {\sqrt{-{4069}}}}}\over{{108}\ {\sqrt{3}}}}}^{2}}}}
(6)
Type: List(List(Equation(Expression(Integer))))




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