polytools(deprecated)/splits - Maple Help

polytools

 splits
 complete Factorization of a Polynomial

 Calling Sequence splits(a, x) splits(a, x, b)

Parameters

 a - polynomial x - variable b - variable

Description

 • Important: The polytools package has been deprecated. Use the superseding command PolynomialTools[Splits] instead.
 • The splits 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.
 • The factorization is returned in the form $\left[u,\left[\left[{f}_{1},{m}_{1}\right],..,\left[{f}_{n},{m}_{n}\right]\right]\right]$ where $a=u{{f}_{1}}^{{m}_{1}}\mathrm{...}{{f}_{n}}^{{m}_{n}}$ where each ${f}_{k}$ (the factor) is a unit normal irreducible polynomial and each ${m}_{k}$ (its multiplicity) is a positive integer.
 • 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,splits) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{polytools}\right):$
 > $\mathrm{splits}\left({x}^{2}+x+1,x\right)$
 $\left[{1}{,}\left[\left[{x}{+}{1}{+}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{\mathrm{_Z}}{+}{1}\right){,}{1}\right]{,}\left[{x}{-}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{\mathrm{_Z}}{+}{1}\right){,}{1}\right]\right]\right]$ (1)
 > $\mathrm{splits}\left({x}^{2}+yx+1+{y}^{2},x,'b'\right)$
 $\left[{1}{,}\left[\left[{x}{+}{y}{+}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{y}{}{\mathrm{_Z}}{+}{{y}}^{{2}}{+}{1}\right){,}{1}\right]{,}\left[{x}{-}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{y}{}{\mathrm{_Z}}{+}{{y}}^{{2}}{+}{1}\right){,}{1}\right]\right]\right]$ (2)
 > $b$
 $\left\{{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{y}{}{\mathrm{_Z}}{+}{{y}}^{{2}}{+}{1}\right)\right\}$ (3)