map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry

Synopsis

• Function: map

• Usage:

  map(M,n,f)

• Inputs:
  • M, a module
  • n, an integer
  • f, a function
• 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 from a graded free module of rank n to the module M whose matrix entry h_(i,j) is obtained from the function f by evaluating f(i,j).

Description

i1 : R = GF(9,Variable=>a)[x,y,z];

i2 : f = map(R^1, 3, (i,j) -> (a^j * x - y)^(j+1))

o2 = | x-y (a+1)x2+axy+y2 (-a-1)x3-y3 |

             1       3
o2 : Matrix R  <--- R

i3 : source f

      3
o3 = R

o3 : R-module, free, degrees {1..3}

i4 : isHomogeneous f

o4 = true

See also

• map(Module,Module,Function) -- create a matrix by specifying a function that gives each entry
• source(Matrix) -- find the source module of matrix
• isHomogeneous(Matrix) -- whether something is homogeneous (graded)