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

Synopsis

• Function: map

• Usage:

  map(M,N,r)

• Inputs:
  • M, a module
  • N, a module, over the same ring R as M. An integer here stands for the free module of that rank.
  • r, a ring element, in the ring R
• Optional inputs:
  • Degree => ..., default value null, specify the degree of a map
  • DegreeLift => ..., default value null, make a ring map
  • DegreeMap => ..., default value null, make a ring map
• Outputs:
  • a matrix, The map induced by multiplication by r on the generators

Description

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

See also

• inducedMap -- compute an induced map