maxDegree -- Computes the maximum homological degree of a DGAlgebra

Usage:

mDegree = maxDegree(A)
Inputs:
- A, an instance of the type DGAlgebra,
Outputs:
- mDegree, an integer, The maximum degree of the DGAlgebra A (this can be infinite).

Description

Note that if the DGAlgebra A has any generators of even degree, then maxDegree returns infinity.

i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3}

o1 = R

o1 : QuotientRing

i2 : A = koszulComplexDGA(R)

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,4
      Differential => {a, b, c, d}

o2 : DGAlgebra

i3 : B = acyclicClosure(A,EndDegree=>3)

o3 = {Ring => R                                                   }
      Underlying algebra => R[T   ..T   ]
                               1,1   2,4
                                    2       2       2       2
      Differential => {a, b, c, d, a T   , b T   , c T   , d T   }
                                      1,1     1,2     1,3     1,4

o3 : DGAlgebra

i4 : maxDegree(A)

o4 = 4

i5 : maxDegree(B)

o5 = infinity

o5 : InfiniteNumber

Ways to use maxDegree:

maxDegree(DGAlgebra)
maxDegree(DGModule) -- Largest hom-degree present in a DG module
maxDegree(DGQuotientModule) -- Largest hom-degree present in a DG quotient module

For the programmer

The object maxDegree is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:8242:0.