RingMap ** Module -- a binary operator, usually used for tensor product

RingMap ** Module -- a binary operator, usually used for tensor product

Synopsis:

Usage: N = f ** M

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

Input:

f, an instance of class RingMap: a ring map from R to S.

M, an instance of class Module: an R-module

Output:

N, an instance of class Module: the tensor product of M with S over R.

i1 : R = QQ[x,y];

i2 : S = QQ[t];

i3 : f = map(S,R,{t^2,t^3})



               2   3

o3 = map(S,R,{t , t })



o3 : RingMap S <--- R

i4 : f ** coker vars R



o4 = cokernel | t2 t3 |



                            1

o4 : S-module, quotient of S

i5 : f ** image vars R



o5 = cokernel {1} | -t3 |

              {1} | t2  |



                            2

o5 : S-module, quotient of S

See also:

RingMap Module -- blank operator for adjacent expressions

Code:

     -- ../../../Macaulay2/m2/ringmap.m2:298-302
     RingMap ** Module := Module => (f,M) -> (
          R := source f;
          S := target f;
          if R =!= ring M then error "expected module over source ring";
          cokernel f(presentation M));