Important: The polytools package has been deprecated. Use the superseding command PolynomialTools[Split] instead.

The split function computes the complete factorization of a univariate polynomial.

The univariate polynomial a in x, with rational or algebraic number coefficients or polynomial coefficients, is factored into linear factors.

In the case of three arguments, the third argument b is assigned the extensions of Q on output, where Q is the set of rational numbers.

The command with(polytools,split) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{polytools}\right)\:$

$\mathrm{split}\left(x^2+x+1\,x\right)$

$\left(x-\mathrm{RootOf}\left({\mathrm{\_Z}}^2+\mathrm{\_Z}+1\right)\right)\left(x+1+\mathrm{RootOf}\left({\mathrm{\_Z}}^2+\mathrm{\_Z}+1\right)\right)$

$\mathrm{split}\left(x^2+yx+1+y^2\,x\,'b'\right)$

$\left(x+y+\mathrm{RootOf}\left({\mathrm{\_Z}}^2+y\mathrm{\_Z}+y^2+1\right)\right)\left(x-\mathrm{RootOf}\left({\mathrm{\_Z}}^2+y\mathrm{\_Z}+y^2+1\right)\right)$

$b$

$\left\{\mathrm{RootOf}\left({\mathrm{\_Z}}^2+y\mathrm{\_Z}+y^2+1\right)\right\}$