maxDegree -- Computes the maximum homological degree of a DGAlgebra

Synopsis

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   4
      Differential => {a, b, c, d}

o2 : DGAlgebra

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

o3 = {Ring => R                                           }
      Underlying algebra => R[T ..T ]
                               1   8
                                    2     2     2     2
      Differential => {a, b, c, d, a T , b T , c T , d T }
                                      1     2     3     4

o3 : DGAlgebra

i4 : maxDegree(A)

o4 = 4

i5 : maxDegree(B)

o5 = infinity

o5 : InfiniteNumber

Ways to use maxDegree :

maxDegree(DGAlgebra)

For the programmer

The object maxDegree is a method function.