fricas (1) -> zerosOf(7-5*x+5*x^2-x^3,
Type: List(Expression(Integer))
fricas simplify((6+(-1+x)^2*(-2+(-3+x)*(-1+x))-6*x)/(-1+x))
Type: Expression(Integer)
fricas factor(-(-x^2+y^2)*(z-x)+(-x^2+z^2)*(y-x))
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))
Type: Expression(Integer)
fricas expand((z-y)*(z-x)*(z-w)*(y-x)*(y-w)*(x-w))
Type: Polynomial(Integer)
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last edited 12 years ago by test1 |
![\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]](images/1827333320239515350-16.0px.png "\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]")
![\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/7717934642346786631-16.0px.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}")
![\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/5198125564200214064-16.0px.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}")