Matrix ** Module -- tensor product

Matrix ** Module -- tensor product

Synopsis:

Operator: ** -- a binary operator, usually used for tensor product

Input:

an instance of class Matrix.

an instance of class Module.

Output:

an instance of class Matrix.

f ** N -- tensor product of a matrix f and a module N.

This is the same as tensoring f with the identity map of N.

When N is a free module of rank 1 the net effect of the operation is to shift the degrees of f.

i1 : R = ZZ/101[t]



o1 = R



o1 : PolynomialRing

i2 : f = matrix {{t}}



o2 = | t |



             1       1

o2 : Matrix R  <--- R

i3 : degrees source f



o3 = {{1}}



o3 : List

i4 : degrees source (f ** R^{-3})



o4 = {{4}}



o4 : List

See also:

Matrix -- the class of all matrices

Module -- the class of all modules

Code:

     -- ../../../Macaulay2/m2/modules2.m2:53-60
     Matrix ** Module := Matrix => (f,M) -> (
          P := youngest(f,M);
          key := (f,M,symbol **);
          if P#?key then P#key
          else f**M = (
               f ** id_M
               )
          )