using SymPy
@syms x, y, z
eq1 = x + y + z
eq2 = x + 3y + 4z
sympy.resultant(eq1, eq2, z)
\(- 3 x - y\)
factor(x^2 + 1)
\(x^{2} + 1\)
factor(x^2 + 1, gaussian=true)
\(\left(x - i\right) \left(x + i\right)\)
factor(x^2 -2, extension=√Sym(2))
\(\left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right)\)
eq = 2^(x^2 + 2*x + 1)
\(2^{x^{2} + 2 x + 1}\)
factor(eq, deep=true)
\(2^{\left(x + 1\right)^{2}}\)
factor(5*x + 3*exp(2 - 7*x), deep=true, fraction=false)
\(5 x + 3 e^{2} e^{- 7 x}\)
factor(5*x + 3*exp(2 - 7*x), deep=true)
\(\left(5 x e^{7 x} + 3 e^{2}\right) e^{- 7 x}\)
sympy.all_roots(x^3 + x + 1)
\(\left[\begin{smallmatrix}\operatorname{CRootOf} {\left(x^{3} + x + 1, 0\right)}\\\operatorname{CRootOf} {\left(x^{3} + x + 1, 1\right)}\\\operatorname{CRootOf} {\left(x^{3} + x + 1, 2\right)}\end{smallmatrix}\right]\)
real_roots(2x^3 - 7x^2 + 4x + 4)
\(\displaystyle \left[\begin{smallmatrix}- \frac{1}{2}\\2\\2\end{smallmatrix}\right]\)
nroots(x^2 - 3, n=30)
\(\left[\begin{smallmatrix}-1.73205080756887729352744634151\\1.73205080756887729352744634151\end{smallmatrix}\right]\)
@syms A
cancel( (sqrt(Sym(3)) + sqrt(Sym(15))*A)/(sqrt(Sym(2)) + sqrt(Sym(10))*A))
\(\displaystyle \frac{\sqrt{6}}{2}\)
