Online Help

The AFactors function is a placeholder for representing an absolute factorization of the polynomial p, that is a factorization over an algebraic closure of its coefficient field. It is used in conjunction with evala.

The construct AFactors(p) produces a data structure of the form $\left[u\,\left[\left[f_1\,e_1\right]\,\mathrm{...}\,\left[f_n\,e_n\right]\right]\right]$ such that $p\=u{f}_1^{e_1}\cdots f_n^{e_n}$, where each $f_i$ is a monic (for the ordering chosen by Maple) irreducible polynomial.

The call evala(AFactors(p)) computes the factorization of the polynomial p over the field of complex numbers. The polynomial p must have algebraic number coefficients.

In the case of a univariate polynomial, the absolute factorization is just the decomposition into linear factors.

$\mathrm{evala}\left(\mathrm{AFactors}\left(x^2-2y^2\right)\right)$

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