Module elements (internally module polynomials) are constructed in general by giving a sequence or vector of elements from the coefficient ring P.

M ! Q : ModMPol, [ RngElt ] -> ModMPolElt

Suppose M is a module over the multivariate polynomial ring or quotient ring P of degree r. Given a sequence Q = [a_1, ..., a_r] of ring elements such that the a_i are coercible into P, construct the element of M corresponding to Q.

M ! v : ModMPol, ModTupRngElt -> ModMPolElt

Suppose M is a module over the multivariate polynomial ring or quotient ring P of degree r. Given a vector v from the R-space P^r, construct the element of M corresponding to v.

M ! 0 : ModMPol, RngIntElt -> ModMPolElt

Zero(M) : ModMPol -> ModMPolElt

Create the zero element of the module M.

Suppose M is a module over the multivariate polynomial ring or quotient ring P of degree r. Given an integer i in the range [1 .. r], construct the i-th unit vector of M (the vector with 1 in the i-th column and 0 elsewhere) whose parent is the generic module of M (since it may not lie in M itself). Note that this not the same as the function BasisElement (see below).