declareGenerators -- builds a free module and names its generators

Synopsis

• Usage:

  declareGenerators(R,genList)

• Inputs:
  • R, a ring, the coefficients
  • genList, a list, of the form { ... , x => deg, ... } where x is a symbol and deg is a degree
• Outputs:
  • a module, free on the generating set of variables in their various degrees, and with coefficients drawn from R
• Consequences:

  • The symbols in the list variableNames bind to the generators of the output module.

Description

i1 : declareGenerators(ZZ[x],{a => 1,b => 2,c => 3})

            3
o1 = (ZZ[x])

o1 : ZZ[x]-module, free, degrees {3, 1..2}

i2 : cospan(x*a-2*b,x*b-2*c)

o2 = cokernel {3} | 0  -2 |
              {1} | x  0  |
              {2} | -2 x  |

                                      3
o2 : ZZ[x]-module, quotient of (ZZ[x])

Caveat

See also

• cospan -- mods out by a collection of module elements