AFactors - Maple Programming 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 $[u,[[{f}_{1},{ⅇ}_{1}],...,[{f}_{n},{ⅇ}_{n}]]]$ such that $p=u{{f}_{1}}^{{ⅇ}_{1}}...{{f}_{n}}^{{ⅇ}_{n}}$, 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)