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 = image | s4 s3t st3 t4 |

                             1
o6 : S-module, submodule of S

See also

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