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ExactCouples :: cospan

cospan -- mods out by a collection of module elements

Synopsis

Usage:

cospan(elements)
Inputs:
- elements, a sequence, all members of the same module M
Outputs:
- a module, the quotient of M by the listed elements

Description

Useful for building modules by generators and relations.

Here, we build a $\ZZ[x]$-module by placing generators in degrees 1, 2, and 3, and imposing two relations.

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

In M2, multiplication of ring elements by module elements happens on the left, so use x*a, not a*x.

See also

declareGenerators -- builds a free module and names its generators

Ways to use `cospan`:

cospan(Sequence)
cospan(Thing)

For the programmer

The object cospan is a method function with a single argument.