The Powmod function is a placeholder for representing $\mathrm{Rem}\left(a^n\,b\right)$ or $\mathrm{Rem}\left(a^n\,b\,x\right)$.  Powmod is more efficient than computing Power(a, n) separately.  It is used in conjunction with either mod or modp1.

The call Powmod(a, n, b, x) mod p computes $\mathrm{Rem}\left(a^n\,b\,x\right)\mathbf{mod}p$. The polynomials a and b must have rational coefficients or coefficients over a finite field specified by RootOfs.

The call modp1(Powmod(a, n, b), p) computes $\mathrm{Rem}\left(a^n\,b\right)\mathbf{mod}p$. The polynomials a and b must be in the modp1 representation and p must be a positive integer.

$\mathrm{Powmod}\left(x\,16\,x^4+x+1\,x\right)\mathbf{mod}2$

$x$

$\mathrm{Powmod}\left(x\,-5\,x^4+x+1\,x\right)\mathbf{mod}2$

$x^2+x+1$