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Macaulay2Doc :: RingMap RingElement

RingMap RingElement -- apply a ring map

Synopsis

Description

If X is a module then it must be either free or a submodule of a free module. If X is a chain complex, then every module of X must be free or a submodule of a free module.
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

If the rings R and S have different degree monoids, then the degrees of the image might need to be changed, since Macaulay2 sometimes doesn't have enough information to determine the image degrees of elements of a free module.