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degreeGroup -- the degree group of a ring or monoid

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

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.