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tensor(RingMap,Matrix) -- tensor product via a ring map

Synopsis

Function: tensor
Usage:

f ** M

tensor(f, M)
Inputs:
- f, a ring map, from $R \to S$
- M, a matrix, a matrix or a module, over the source ring $R$ of f
Outputs:
- a matrix, a matrix or a module, the same type as M, but over the target ring $S$ of f

Description

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing

i2 : S = QQ[s,t]

o2 = S

o2 : PolynomialRing

i3 : F = map(S,R,{s^4,s^3*t,s*t^3,t^4})

                  4   3      3   4
o3 = map (S, R, {s , s t, s*t , t })

o3 : RingMap S <--- R

i4 : m = matrix{{a,b,c,d}}

o4 = | a b c d |

             1       4
o4 : Matrix R  <--- R

i5 : F ** m

o5 = | s4 s3t st3 t4 |

             1       4
o5 : Matrix S  <--- S

i6 : F ** image m

o6 = cokernel {1} | -s3t 0    -st3 0   0   -t4 |
              {1} | s4   -st3 0    0   -t4 0   |
              {1} | 0    s3t  s4   -t4 0   0   |
              {1} | 0    0    0    st3 s3t s4  |

                            4
o6 : S-module, quotient of S

See also

RingMap Module -- apply a ring map
RingMap Module -- apply a ring map

Ways to use this method:

tensor(RingMap,Matrix) -- tensor product via a ring map
"tensor(RingMap,Module)"