cover Module -- get the covering free module

cover Module -- get the covering free module

Synopsis:

Usage: F = cover M

Function: cover -- get the covering free module

Input:

M, an instance of class Module.

Output:

F, an instance of class Module: the free module whose basis elements correspond to the generators of M.

The free module F is the source of the generator matrix of M.

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 {1, 1}

i5 : cover M == source generators M



o5 = true

See also:

ambient Module -- ambient free module of a subquotient, or ambient ring

super Module -- get the ambient module

Code:

     -- ../../../Macaulay2/m2/modules.m2:424-427
     cover(Module) := Module => (M) -> (
          if M.?generators then M.generators.source
          else if M.?relations then M.relations.target
          else M)