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SandBox Experimenting

Edit detail for SandBox Experimenting revision 2 of 2

	1 2
Editor: test1 Time: 2013/04/25 18:38:27 GMT+0
Note:

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

eqns := [x^2 - y + z, x^2*z + x^4 - b*y, y^2 *z - a - b*x]

fricas

(1) -> 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])

$\label{eq2}\begin{array}{@{}l} \displaystyle \left[{\left[{x = -{\frac{a}{b}}}, \:{y = 0}, \:{z = -{\frac{{a}^{2}}{{b}^{2}}}}\right]}, \: \right. \ \ \displaystyle \left.{ \begin{array}{@{}l} \displaystyle \left[{x ={\frac{{{z}^{3}}+{2 \ b \ {{z}^{2}}}+{{{b}^{2}}\ z}- a}{b}}}, \:{y ={z + b}}, \: \right. \ \ \displaystyle \left.{ \begin{array}{@{}l} \displaystyle {{{z}^{6}}+{4 \ b \ {{z}^{5}}}+{6 \ {{b}^{2}}\ {{z}^{4}}}+{{\left({4 \ {{b}^{3}}}-{2 \ a}\right)}\ {{z}^{3}}}+{{\left({{b}^{4}}-{4 \ a \ b}\right)}\ {{z}^{2}}}-{2 \ a \ {{b}^{2}}\ z}-{{b}^{3}}+{{a}^{2}}}= \ \ \displaystyle 0$

(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)

$\label{eq5}\begin{array}{@{}l} \displaystyle \left[{ \begin{array}{@{}l} \displaystyle \left[{ \begin{array}{@{}l} \displaystyle x = \ \ \displaystyle {\frac{{{\left({{48}\ {\sqrt{- 3}}}-{48}\right)}\ {{\root{3}\of{\frac{{\sqrt{-{\frac{4069}{3}}}}- 3}{3}}}^{2}}}+{{\left({{\left({3 \ {\sqrt{-{\frac{4069}{3}}}}}- 9 \right)}\ {\sqrt{- 3}}}+{3 \ {\sqrt{-{\frac{4 069}{3}}}}}- 9 \right)}\ {\root{3}\of{\frac{{\sqrt{-{\frac{40 69}{3}}}}- 3}{3}}}}-{512}}{{\left({{18}\ {\sqrt{- 3}}}-{18}\right)}\ {{\root{3}\of{\frac{{\sqrt{-{\frac{4069}{3}}}}- 3}{3}}}^{2}}}}$

(5)

Type: List(List(Equation(Expression(Integer))))

fricas

radicalSolve(c,[a,x])

$\label{eq6}\begin{array}{@{}l} \displaystyle \left[{ \begin{array}{@{}l} \displaystyle \left[{ \begin{array}{@{}l} \displaystyle a = \ \ \displaystyle {\frac{{{\left({{\left(-{\sqrt{-{\frac{4069}{3}}}}+ 3 \right)}\ {\sqrt{- 3}}}+{\sqrt{-{\frac{4069}{3}}}}- 3 \right)}\ {\root{3}\of{\frac{{9 \ {\sqrt{-{\frac{4069}{3}}}}}+{2021}}{4}}}}+{{\left(-{8 \ {\sqrt{-{\frac{4069}{3}}}}}+{24}\right)}\ {\sqrt{- 3}}}-{8 \ {\sqrt{-{\frac{4069}{3}}}}}+{24}}{8 \ {{\root{3}\of{\frac{{9 \ {\sqrt{-{\frac{4069}{3}}}}}+{2021}}{4}}}^{2}}}}$

(6)

Type: List(List(Equation(Expression(Integer))))