generatorDegrees -- The hom-degrees (and optional internal degrees) of the DG generators

Usage:

degs = generatorDegrees A

degs = generatorDegrees M
Inputs:
- A, an instance of the type DGAlgebra,
- M, an instance of the type DGModule,
Outputs:
- degs, a list, A list of degree vectors, one per DG generator (for a DG algebra) or one per natural generator (for a DG module).

Description

generatorDegrees returns the degree data that was supplied at construction. Each entry is a list whose first coordinate is the homological degree and whose remaining coordinates record the internal (multi-)grading of the base ring.

i1 : R = QQ[x, y] / ideal(x^2, y^2)

o1 = R

o1 : QuotientRing

i2 : A = koszulComplexDGA R

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o2 : DGAlgebra

i3 : generatorDegrees A

o3 = {{1, 1}, {1, 1}}

o3 : List

i4 : M = freeDGModule(A, {0, 1, 3})

o4 = {Base ring => R                               }
      DG algebra => R[T   ..T   ]
                       1,1   1,2
                                       3
      Natural module => (R[T   ..T   ])
                            1,1   1,2
      Generator degrees => {{0, 0}, {1, 0}, {3, 0}}
      Differentials on gens => {0, 0, 0}

o4 : DGModule

i5 : generatorDegrees M

o5 = {{0, 0}, {1, 0}, {3, 0}}

o5 : List

Ways to use generatorDegrees:

generatorDegrees(DGAlgebra)
generatorDegrees(DGModule)

For the programmer

The object generatorDegrees is a method function.

The source of this document is in DGAlgebras/doc.m2:7414:0.

generatorDegrees -- The hom-degrees (and optional internal degrees) of the DG generators

Description

See also

Ways to use generatorDegrees:

For the programmer