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# 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

## See also

- degree
- degreeLength -- the length of the degree vector
- degreesRing -- the ring or monoid of degrees
- degreesMonoid -- the ring or monoid of degrees
- monoid(...,DegreeGroup=>...) -- specify the degrees of the variables

## 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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/degreeGroup-doc.m2:36:0.