OreTools[Modular] - Maple Programming Help

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OreTools[Modular]

 ModularOrePoly
 compute the normal form of an Ore polynomial modulo a prime
 Content
 compute the content of an Ore polynomial modulo a prime
 Primitive
 compute the primitive part of an Ore polynomial modulo a prime
 MonicAssociate
 compute the left associate of an Ore polynomial modulo a prime

 Calling Sequence Modular[ModularOrePoly](Ore, p) Modular[Content](Ore, p, 'pp') Modular[Primitive](Ore, p, 'c') Modular[MonicAssociate](Ore, p)

Parameters

 Ore - Ore polynomial; to define an Ore polynomial, use the OrePoly structure p - prime c, pp - unevaluated names

Description

 • The Modular[ModularOrePoly](Ore, p) calling sequence computes the normal form of the Ore polynomial Ore modulo the prime p
 • The Modular[Content](Ore, p) calling sequence computes the content of the Ore polynomial Ore modulo the prime p. If the third (optional) argument is present, it is assigned the primitive part of Ore.
 • The Modular[Primitive](Ore, p) calling sequence computes the primitive part of Ore modulo the prime p. If the third (optional) argument is present, it is assigned the content of Ore.
 • The Modular[MonicAssociate](Ore, p) calling sequence computes the left monic associate of the Ore polynomial Ore modulo the prime p.

Examples

 > $\mathrm{with}\left(\mathrm{OreTools}\right):$
 > $\mathrm{Ore}≔'\mathrm{OrePoly}'\left(-\frac{n}{n-1},-\frac{-5n+{n}^{2}+3}{n-1},n-3,\frac{38}{n-3}\right)$
 ${\mathrm{Ore}}{:=}{\mathrm{OrePoly}}{}\left({-}\frac{{n}}{{n}{-}{1}}{,}{-}\frac{{{n}}^{{2}}{-}{5}{}{n}{+}{3}}{{n}{-}{1}}{,}{n}{-}{3}{,}\frac{{38}}{{n}{-}{3}}\right)$ (1)
 > $\mathrm{Modular}[\mathrm{ModularOrePoly}]\left(\mathrm{Ore},19\right)$
 ${\mathrm{OrePoly}}{}\left(\frac{{18}{}{n}}{{n}{+}{18}}{,}\frac{{18}{}\left({{n}}^{{2}}{+}{14}{}{n}{+}{3}\right)}{{n}{+}{18}}{,}{n}{+}{16}\right)$ (2)
 > $\mathrm{Modular}[\mathrm{ModularOrePoly}]\left(\mathrm{Ore},11\right)$
 ${\mathrm{OrePoly}}{}\left(\frac{{10}{}{n}}{{n}{+}{10}}{,}\frac{{10}{}\left({{n}}^{{2}}{+}{6}{}{n}{+}{3}\right)}{{n}{+}{10}}{,}{n}{+}{8}{,}\frac{{5}}{{n}{+}{8}}\right)$ (3)
 > $\mathrm{Ore}≔'\mathrm{OrePoly}'\left(-n,3n-{n}^{2}-1,{\left(n-1\right)}^{2}\right)$
 ${\mathrm{Ore}}{:=}{\mathrm{OrePoly}}{}\left({-}{n}{,}{-}{{n}}^{{2}}{+}{3}{}{n}{-}{1}{,}{\left({n}{-}{1}\right)}^{{2}}\right)$ (4)
 > $\mathrm{Modular}[\mathrm{Primitive}]\left(\mathrm{Ore},7,'c'\right)$
 ${\mathrm{OrePoly}}{}\left({6}{}{n}{,}{6}{}{{n}}^{{2}}{+}{3}{}{n}{+}{6}{,}{{n}}^{{2}}{+}{5}{}{n}{+}{1}\right)$ (5)
 > $c$
 ${1}$ (6)
 > $\mathrm{Modular}[\mathrm{Content}]\left('\mathrm{OrePoly}'\left({n}^{2}-1,n+10\right),11,'\mathrm{pp}'\right)$
 ${n}{+}{10}$ (7)
 > $\mathrm{pp}$
 ${\mathrm{OrePoly}}{}\left({n}{+}{1}{,}{1}\right)$ (8)
 > $\mathrm{Ore}≔'\mathrm{OrePoly}'\left({n}^{2},3n-{n}^{2}-1,{\left(n-17\right)}^{2}\right)$
 ${\mathrm{Ore}}{:=}{\mathrm{OrePoly}}{}\left({{n}}^{{2}}{,}{-}{{n}}^{{2}}{+}{3}{}{n}{-}{1}{,}{\left({n}{-}{17}\right)}^{{2}}\right)$ (9)
 > $\mathrm{Modular}[\mathrm{MonicAssociate}]\left(\mathrm{Ore},17\right)$
 ${\mathrm{OrePoly}}{}\left({1}{,}\frac{{16}{}{{n}}^{{2}}{+}{3}{}{n}{+}{16}}{{{n}}^{{2}}}{,}{1}\right)$ (10)