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Macaulay2 web site
Kronecker
::
decomposeGradedModule
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 isormophism
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.
Ways to use
decomposeGradedModule
:
decomposeGradedModule(GradedModuleMap,GradedModuleMap)