zppoly - Maple Help

type/zppoly

check for a modp1 or modp2 polynomial

 Calling Sequence type(a, zppoly)

Parameters

 a - expression

Description

 • The  type(a, zppoly) calling sequence checks that a is a modp1 or a modp2 polynomial.
 • The modp1 function provides efficient arithmetic and other operations for univariate polynomials modulo a prime.  The modp2 function provides similar efficiency for bivariate polynomials modulo a prime. They achieve this efficiency by using a dedicated data structure.

Supertypes

 •

Examples

 > $a≔\mathrm{modp1}\left(\mathrm{ConvertIn}\left({x}^{4}-{x}^{2}+2,x\right),11\right)$
 ${a}{≔}\left({{x}}^{{4}}{+}{10}{}{{x}}^{{2}}{+}{2}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{11}$ (1)
 > $\mathrm{type}\left(a,\mathrm{zppoly}\right)$
 ${\mathrm{true}}$ (2)
 > $b≔\mathrm{modp2}\left(\mathrm{ConvertIn}\left({x}^{4}{y}^{2}-1,x,y\right),17\right)$
 ${b}{≔}\left({{x}}^{{4}}{}{{y}}^{{2}}{+}{16}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{mod}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{17}$ (3)
 > $\mathrm{type}\left(b,\mathrm{zppoly}\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{type}\left(\mathrm{modp2}\left(\mathrm{Diff}\left(b,1\right),17\right),\mathrm{zppoly}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{type}\left({x}^{2}+2y,\mathrm{zppoly}\right)$
 ${\mathrm{false}}$ (6)