MathAction SandBox DoOps

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SandBox DoOps
last edited 12 years ago by test1

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fricas

(1) -> zerosOf(7-5*x+5*x^2-x^3,x)

\label{eq1}\begin{array}{@{}l} \displaystyle \left[ \%x 0, \:{\frac{-{\sqrt{-{3 \ {{\%x 0}^{2}}}+{{10}\ \%x 0}+ 5}}- \%x 0 + 5}{2}}, \: \right. \ \ \displaystyle \left.{\frac{{\sqrt{-{3 \ {{\%x 0}^{2}}}+{{10}\ \%x 0}+ 5}}- \%x 0 + 5}{2}}\right] (1)

Type: List(Expression(Integer))

fricas

simplify((6+(-1+x)^2*(-2+(-3+x)*(-1+x))-6*x)/(-1+x))

\label{eq2}{{x}^{3}}-{5 \ {{x}^{2}}}+{5 \ x}- 7 (2)

Type: Expression(Integer)

fricas

factor(-(-x^2+y^2)*(z-x)+(-x^2+z^2)*(y-x))

\label{eq3}{\left(y - x \right)}\ {\left(z - y \right)}\ {\left(z - x \right)} (3)

Type: Factored(Polynomial(Integer))

fricas

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))

\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)

fricas

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} (5)

Type: Polynomial(Integer)