decomposeGradedModule -- decompose a graded module over a ring of graded module maps

Synopsis

• Usage:

  (x',y',f) = decomposeGradedModule(x,y)

• Inputs:
  • x, a graded module map, a graded module map of degree 1
  • y, a graded module map, a graded module map of degree 1
• Outputs:
  • x', a graded module map
  • y', a graded module map
  • f, a graded module map, an isomorphism

Description

Given maps x and y of degree 1 from a graded module M over a field k to M, we can think of M as a module over k[x,y]. If x^2=0, y^2=0, and x*y+y*x=0, we can decompose M into a direct sum of simple modules.