cover(Module) -- get the covering free module

Synopsis

• Function: cover

• Usage:

  F = cover M

• Inputs:
  • M, a module
• Outputs:
  • F, a module, the free module whose basis elements correspond to the generators of M.

Description

i1 : R = QQ[a..f];

i2 : g = matrix{{a,b},{c,d},{e,f}}

o2 = | a b |
     | c d |
     | e f |

             3      2
o2 : Matrix R  <-- R

i3 : M = subquotient(g,matrix{{b},{c},{d}})

o3 = subquotient (| a b |, | b |)
                  | c d |  | c |
                  | e f |  | d |

                               3
o3 : R-module, subquotient of R

i4 : cover M

      2
o4 = R

o4 : R-module, free, degrees {2:1}

i5 : cover M == source generators M

o5 = true

See also

• ambient(Module) -- ambient free module
• super(Module) -- get the ambient module