degreeGroup -- the degree group of a ring or monoid

Usage:

degreeGroup A
Inputs:
- A, a ring or a monoid,
Outputs:
- a module, over integers, representing a group;

Description

i1 : degreeGroup ZZ

o1 = 0

i2 : degreeGroup(ZZ[])

       1
o2 = ZZ

o2 : ZZ-module, free

i3 : degreeGroup(ZZ[x])

       1
o3 = ZZ

o3 : ZZ-module, free

i4 : degreeGroup(ZZ[x, Degrees => {{1,2,3}}])

       3
o4 = ZZ

o4 : ZZ-module, free

i5 : degreeGroup(ZZ[x,y,z, DegreeRank => 3])

       3
o5 = ZZ

o5 : ZZ-module, free

i6 : degreeGroup(ZZ[x,y,z, DegreeGroup => ZZ^3])

       3
o6 = ZZ

o6 : ZZ-module, free

i7 : degreeGroup(ZZ[x,y,z, DegreeGroup => ZZ^2 ++ coker(2 * id_(ZZ^3))])

o7 = cokernel | 0 0 0 |
              | 0 0 0 |
              | 2 0 0 |
              | 0 2 0 |
              | 0 0 2 |

                              5
o7 : ZZ-module, quotient of ZZ

Ways to use degreeGroup:

degreeGroup(Monoid)
degreeGroup(PolynomialRing)
degreeGroup(QuotientRing)
degreeGroup(Ring)

For the programmer

The object degreeGroup is a method function.

The source of this document is in Macaulay2Doc/functions/degreeGroup-doc.m2:36:0.

degreeGroup -- the degree group of a ring or monoid

Description

See also

Ways to use degreeGroup:

For the programmer