RingMap RingElement -- apply a ring map

Synopsis

• Operator: SPACE

• Usage:

  f X

• Inputs:
  • f, a ring map, a ring map from R to S.
  • X, a ring element, an ideal, a matrix, a vector, a module, or a chain complex
• Outputs:
  • a ring element, the image of X under the ring map f. The result has the same type as X, except that its ring will be S.

Description

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 (x+y^2)

      6    2
o4 = t  + t

o4 : S

i5 : f image vars R

o5 = image | t2 t3 |

                             1
o5 : S-module, submodule of S

i6 : f ideal (x^2,y^2)

             4   6
o6 = ideal (t , t )

o6 : Ideal of S

i7 : f resolution coker vars R

      1      2      1
o7 = S  <-- S  <-- S  <-- 0
                           
     0      1      2      3

o7 : ChainComplex

Caveat

See also

• RingElement Sequence -- evaluation of polynomials