 AFactors - Maple Help

AFactors

inert absolute factorization Calling Sequence AFactors(p) Parameters

 p - multivariate polynomial Description

 • 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. Examples

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