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last edited 11 years ago by test1 |
Edit detail for SandBox Experimenting revision 1 of 2
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Editor: xlma
Time: 2010/04/18 20:19:58 GMT-7 |
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changed: - \begin{axiom} 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] solve(eqns,[x,y,z]) c:=[2*a^2+x=8,2+4*a*x=4] solve(c,[a,x]) radicalSolve(c) radicalSolve(c,[a,x]) \end{axiom}
axiom
c(x,y, z)== x**2 - y + z
Type: Void
axiom
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]](images/2689273322634518-16.0px.png "\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))
axiom
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](images/7200161769001710576-16.0px.png "\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)))))
axiom
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]](images/8169584270090826151-16.0px.png "\label{eq3}\left[{{x +{2 \ {a^2}}}= 8}, \:{{{4 \ a \ x}+ 2}= 4}\right]") | (3) |
Type: List(Equation(Polynomial(Integer)))
axiom
solve(c,[a, x])
![\label{eq4}\left[{\left[{a ={-{x^2}+{8 \ x}}}, \:{{{2 \ {x^3}}-{{16}\ {x^2}}+ 1}= 0}\right]}\right]](images/6210954247010940943-16.0px.png "\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)))))
axiom
radicalSolve(c)
 | (5) |
Type: List(List(Equation(Expression(Integer))))
axiom
radicalSolve(c,[a, x])
 | (6) |
Type: List(List(Equation(Expression(Integer))))