RSpace(R, n) : Rng, RngIntElt -> ModTupRng
RModule(R, n) : Rng, RngIntElt -> ModRng
Given a ring R and a non-negative integer n, create the free right
R-module R(n), consisting of all n-tuples over R. The module
is created with the standard basis, e1, ..., en, where ei (i
= 1, ..., n) is the vector containing a 1 in the i-th position
and zeros elsewhere. The function RModule creates a module
in reduced mode while RSpace creates a module in embedded mode.
Given a ring R, a non-negative integer n and a square n x n
symmetric matrix F, create the free right R-module R(n)
(in embedded form), with inner product matrix F.
This is the same as RSpace(R, n), except that the
functions Norm and InnerProduct (see below) will
be with respect to the inner product matrix F.
We construct the module consisting of 6-tuples over the integers.
> Z := IntegerRing();
> M := RModule(Z, 6);
> M;
RModule M of dimension 6 with base ring Integer Ring
The module comprising all m x n matrices over the ring R.
RSpaceWithBasis(Q) : [ModTupRngElt] -> ModTupRng
RSpaceWithBasis(a) : AlgMatElt -> ModTupRng
RSpaceWithBasis(a) : ModMatRngElt -> ModTupRng
Given a sequence Q (or matrix a) of k independent vectors each
lying in a module M, construct the submodule of M of dimension k
whose basis is Q (or the rows of a).
The basis is echelonized internally but all functions which depend
on the basis of the space (e.g. Coordinates)
will use the given basis.
The module of m x n matrices whose basis is given by the
linearly independent matrices of the sequence Q.
V2.28, 13 July 2023