map(Module,Nothing,Matrix) -- recast a matrix to have a new target, and a free module as source

• Function: map

• Usage:

  map(M,,f)

• Inputs:
  • M, a module
  • f, a matrix, whose target has the same number of generators as M
• 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, A map with a free source module, and target M, whose entries are those of f.

i1 : R = ZZ/101[x,y];

i2 : p = matrix{{x,y}}

o2 = | x y |

             1      2
o2 : Matrix R  <-- R

i3 : q = map(R^{3},,p)

o3 = {-3} | x y |

             1      2
o3 : Matrix R  <-- R

i4 : degrees target q

o4 = {{-3}}

o4 : List

i5 : degrees source q

o5 = {{-2}, {-2}}

o5 : List