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map > map(Module,Module,RingElement)

map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators

Synopsis

Description

If r is not zero, then either M and N should be equal, or they should have the same number of generators. This gives the same map as r * map(M,N,1). map(M,N,1) is the map induced by the identity on the generators of M and N.
i1 : R = QQ[x];
i2 : map(R^2,R^3,0)

o2 = 0

             2       3
o2 : Matrix R  <--- R
i3 : f = map(R^2,R^2,x)

o3 = | x 0 |
     | 0 x |

             2       2
o3 : Matrix R  <--- R
i4 : f == x *map(R^2,R^2,1)

o4 = true

Caveat

If M or N is not free, then we don't check that the the result is a well defined homomorphism.

See also