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

Description

Passing a DG quotient module to maxDegree returns the max hom-degree of its ambient DG module. Because taking a quotient cannot introduce elements of higher hom-degree than are already in the ambient, the ambient's bound is valid for the quotient. The value is what toComplex(DGQuotientModule) and toComplexMap(DGModuleMap) use to decide where to truncate when no EndDegree is supplied.

i1 : R = ZZ/101[x]

o1 = R

o1 : PolynomialRing
 
i2 : A = koszulComplexDGA R

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

o2 : DGAlgebra
 
i3 : M = freeDGModule(A, {0, 1})

o3 = {Base ring => R                       }
      DG algebra => R[T   ]
                       1,1
                                 2
      Natural module => (R[T   ])
                            1,1
      Generator degrees => {{0, 0}, {1, 0}}
      Differentials on gens => {0, 0}

o3 : DGModule
 
i4 : z = zeroDGModuleMap(M, M)

                         2
o4 = {Source => (R[T   ]) }
                    1,1
                         2
      Target => (R[T   ])
                    1,1
      Natural => 0

o4 : DGModuleMap
 
i5 : Q = cokernel z

o5 = DGQuotientModule Q = M / S
                          2
     Q.natural = (R[T   ])
                     1,1
     Degrees   = {{0, 0}, {1, 0}}

o5 : DGQuotientModule
 
i6 : assert(maxDegree Q == maxDegree M)

See also

Ways to use this method:

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:7687:0.