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last edited 11 years ago by test1 |
Edit detail for SandBox DoOps revision 1 of 2
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Editor:
Time: 2007/11/18 17:58:45 GMT-8 |
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changed: - \begin{axiom} zerosOf(7-5*x+5*x**2-x**3,x) \end{axiom} \begin{axiom} simplify((6+(-1+x)**2*(-2+(-3+x)*(-1+x))-6*x)/(-1+x)) \end{axiom} \begin{axiom} factor(-(-x**2+y**2)*(z-x)+(-x**2+z**2)*(y-x)) simplify(((-(-w+y)*(-w**2+x**2)+(-w**2+y**2)*(x-w))*(-(-w**3+x**3)*(z-w)+(-w**3+z**3)*(x-w))-((-w**3+y**3)*(x-w)-(-w+y)*(-w**3+x**3))*((-w**2+z**2)*(x-w)-(-w**2+x**2)*(z-w)))/(x-w)) expand((z-y)*(z-x)*(z-w)*(y-x)*(y-w)*(x-w)) \end{axiom}
axiom
zerosOf(7-5*x+5*x**2-x**3,x)
![\label{eq1}\begin{array}{@{}l}
\displaystyle
\left[ \%x 0, \:{{-{\sqrt{-{3 \ {\%x 0^2}}+{{10}\ \%x 0}+ 5}}- \%x 0 + 5}\over 2}, \: \right.
\
\
\displaystyle
\left.{{{\sqrt{-{3 \ {\%x 0^2}}+{{10}\ \%x 0}+ 5}}- \%x 0 + 5}\over 2}\right]](images/68387026944142786-16.0px.png "\label{eq1}\begin{array}{@{}l}
\displaystyle
\left[ \%x 0, \:{{-{\sqrt{-{3 \ {\%x 0^2}}+{{10}\ \%x 0}+ 5}}- \%x 0 + 5}\over 2}, \: \right.
\
\
\displaystyle
\left.{{{\sqrt{-{3 \ {\%x 0^2}}+{{10}\ \%x 0}+ 5}}- \%x 0 + 5}\over 2}\right]") | (1) |
Type: List(Expression(Integer))
axiom
simplify((6+(-1+x)**2*(-2+(-3+x)*(-1+x))-6*x)/(-1+x))
 | (2) |
Type: Expression(Integer)
axiom
factor(-(-x**2+y**2)*(z-x)+(-x**2+z**2)*(y-x))
 | (3) |
Type: Factored(Polynomial(Integer))
axiom
simplify(((-(-w+y)*(-w**2+x**2)+(-w**2+y**2)*(x-w))* ;(-(-w**3+x**3)*(z-w)+(-w**3+z**3)*(x-w))-((-w** ;3+y**3)*(x-w)-(-w+y)*(-w**3+x**3))*((-w**2+z*& #42;2)*(x-w)-(-w**2+x**2)*(z-w)))/(x-w))
![\label{eq4}\begin{array}{@{}l}
\displaystyle
{{\left({{\left(x - w \right)}\ {y^2}}+{{\left(-{x^2}+{w^2}\right)}\ y}+{w \ {x^2}}-{{w^2}\ x}\right)}\ {z^3}}+
\
\
\displaystyle
{{\left({{\left(- x + w \right)}\ {y^3}}+{{\left({x^3}-{w^3}\right)}\ y}-{w \ {x^3}}+{{w^3}\ x}\right)}\ {z^2}}+
\
\
\displaystyle
{{\left({{\left({x^2}-{w^2}\right)}\ {y^3}}+{{\left(-{x^3}+{w^3}\right)}\ {y^2}}+{{w^2}\ {x^3}}-{{w^3}\ {x^2}}\right)}\ z}+
\
\
\displaystyle
{{\left(-{w \ {x^2}}+{{w^2}\ x}\right)}\ {y^3}}+{{\left({w \ {x^3}}-{{w^3}\ x}\right)}\ {y^2}}+
\
\
\displaystyle
{{\left(-{{w^2}\ {x^3}}+{{w^3}\ {x^2}}\right)}\ y}](images/3813108500810951764-16.0px.png "\label{eq4}\begin{array}{@{}l}
\displaystyle
{{\left({{\left(x - w \right)}\ {y^2}}+{{\left(-{x^2}+{w^2}\right)}\ y}+{w \ {x^2}}-{{w^2}\ x}\right)}\ {z^3}}+
\
\
\displaystyle
{{\left({{\left(- x + w \right)}\ {y^3}}+{{\left({x^3}-{w^3}\right)}\ y}-{w \ {x^3}}+{{w^3}\ x}\right)}\ {z^2}}+
\
\
\displaystyle
{{\left({{\left({x^2}-{w^2}\right)}\ {y^3}}+{{\left(-{x^3}+{w^3}\right)}\ {y^2}}+{{w^2}\ {x^3}}-{{w^3}\ {x^2}}\right)}\ z}+
\
\
\displaystyle
{{\left(-{w \ {x^2}}+{{w^2}\ x}\right)}\ {y^3}}+{{\left({w \ {x^3}}-{{w^3}\ x}\right)}\ {y^2}}+
\
\
\displaystyle
{{\left(-{{w^2}\ {x^3}}+{{w^3}\ {x^2}}\right)}\ y}") | (4) |
Type: Expression(Integer)
axiom
expand((z-y)*(z-x)*(z-w)*(y-x)*(y-w)*(x-w))
![\label{eq5}\begin{array}{@{}l}
\displaystyle
{{\left({{\left(x - w \right)}\ {y^2}}+{{\left(-{x^2}+{w^2}\right)}\ y}+{w \ {x^2}}-{{w^2}\ x}\right)}\ {z^3}}+
\
\
\displaystyle
{{\left({{\left(- x + w \right)}\ {y^3}}+{{\left({x^3}-{w^3}\right)}\ y}-{w \ {x^3}}+{{w^3}\ x}\right)}\ {z^2}}+
\
\
\displaystyle
{{\left({{\left({x^2}-{w^2}\right)}\ {y^3}}+{{\left(-{x^3}+{w^3}\right)}\ {y^2}}+{{w^2}\ {x^3}}-{{w^3}\ {x^2}}\right)}\ z}+
\
\
\displaystyle
{{\left(-{w \ {x^2}}+{{w^2}\ x}\right)}\ {y^3}}+{{\left({w \ {x^3}}-{{w^3}\ x}\right)}\ {y^2}}+
\
\
\displaystyle
{{\left(-{{w^2}\ {x^3}}+{{w^3}\ {x^2}}\right)}\ y}](images/1114979366668281245-16.0px.png "\label{eq5}\begin{array}{@{}l}
\displaystyle
{{\left({{\left(x - w \right)}\ {y^2}}+{{\left(-{x^2}+{w^2}\right)}\ y}+{w \ {x^2}}-{{w^2}\ x}\right)}\ {z^3}}+
\
\
\displaystyle
{{\left({{\left(- x + w \right)}\ {y^3}}+{{\left({x^3}-{w^3}\right)}\ y}-{w \ {x^3}}+{{w^3}\ x}\right)}\ {z^2}}+
\
\
\displaystyle
{{\left({{\left({x^2}-{w^2}\right)}\ {y^3}}+{{\left(-{x^3}+{w^3}\right)}\ {y^2}}+{{w^2}\ {x^3}}-{{w^3}\ {x^2}}\right)}\ z}+
\
\
\displaystyle
{{\left(-{w \ {x^2}}+{{w^2}\ x}\right)}\ {y^3}}+{{\left({w \ {x^3}}-{{w^3}\ x}\right)}\ {y^2}}+
\
\
\displaystyle
{{\left(-{{w^2}\ {x^3}}+{{w^3}\ {x^2}}\right)}\ y}") | (5) |
Type: Polynomial(Integer)