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.

type/algebraic

$a≔\mathrm{modp1}\left(\mathrm{ConvertIn}\left(x^4-x^2+2\,x\right)\,11\right)$

$a≔\left(x^4+10x^2+2\right)\mathbf{mod}11$

$\mathrm{type}\left(a\,\mathrm{zppoly}\right)$

$\mathrm{true}$

$b≔\mathrm{modp2}\left(\mathrm{ConvertIn}\left(x^4{y}^2-1\,x\,y\right)\,17\right)$

$b≔\left(x^4{y}^2+16\right)\mathbf{mod}17$

$\mathrm{type}\left(b\,\mathrm{zppoly}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{modp2}\left(\mathrm{Diff}\left(b\,1\right)\,17\right)\,\mathrm{zppoly}\right)$

$\mathrm{true}$

$\mathrm{type}\left(x^2+2y\,\mathrm{zppoly}\right)$

$\mathrm{false}$