DGAlgebra -- The class of all DGAlgebras

Functions and methods returning an object of class DGAlgebra:

• acyclicClosure -- Tate's construction of a semifree acyclic DG algebra extension
• adjoinVariables -- Extend a DG algebra by a user-chosen list of cycles to be killed
• baseChange -- Transport a DG algebra along a ring map on its base
• ensureDGAlgebraCaches -- Guarantee that the standard cache sub-tables are present
• freeDGAlgebra -- Construct a free DG algebra with given generator degrees
• invalidateDGAlgebraCache -- Discard cached derived data so that it is recomputed from scratch
• killCycles -- Adjoin variables to kill non-bounding cycles in the lowest positive degree
• killHomologyAtDegree -- Adjoin variables killing the homology of a DG algebra at a prescribed degree
• koszulComplexDGA -- The Koszul complex on the variables of a ring, as a DG algebra
• minimalModel -- Build the minimal DG algebra resolution of a quotient ring
• restrictDifferential -- Synonym for subDGAlgebra, named to match the restricted-differential vocabulary
• setDiff -- Install or replace the differential on a DG algebra
• subDGAlgebra -- The sub-DG algebra generated by a chosen subset of DG generators
• truncateGenerators -- Restrict a DG algebra to its generators of hom-degree strictly above a bound

Methods that use an object of class DGAlgebra:

• acyclicClosure(DGAlgebra) -- see acyclicClosure -- Tate's construction of a semifree acyclic DG algebra extension
• adjoinVariables(DGAlgebra,List) -- see adjoinVariables -- Extend a DG algebra by a user-chosen list of cycles to be killed
• baseChange(DGAlgebra,Ring) -- see baseChange -- Transport a DG algebra along a ring map on its base
• baseChange(DGAlgebra,RingMap) -- see baseChange -- Transport a DG algebra along a ring map on its base
• blockDiff(DGAlgebra,ZZ) -- see blockDiff -- prepares a map for display
• DGAlgebra ** DGAlgebra -- Exterior tensor product of DG algebras over a common ground ring
• tensorFactors(DGAlgebra) -- see DGAlgebra ** DGAlgebra -- Exterior tensor product of DG algebras over a common ground ring
• tensorInclusions(DGAlgebra) -- see DGAlgebra ** DGAlgebra -- Exterior tensor product of DG algebras over a common ground ring
• DGAlgebra ** Ring -- Base change of a DG algebra to another ring
• DGAlgebra / DGIdeal -- Quotient DG algebra by a DG ideal
• dgAlgebraMap(DGAlgebra,DGAlgebra,Matrix) -- see dgAlgebraMap -- Define a DG algebra map between DG algebras.
• dgAlgebraMultMap(DGAlgebra,RingElement) -- see dgAlgebraMultMap -- Returns the chain map corresponding to multiplication by a cycle.
• dgComplex(DGAlgebra) -- see dgComplex -- Package a DG algebra or DG module as a Complex of free base-ring modules
• dgIdeal(DGAlgebra,Ideal) -- see dgIdeal -- Construct a DG ideal from a list, matrix, or ideal of generators
• dgIdeal(DGAlgebra,List) -- see dgIdeal -- Construct a DG ideal from a list, matrix, or ideal of generators
• dgIdeal(DGAlgebra,Matrix) -- see dgIdeal -- Construct a DG ideal from a list, matrix, or ideal of generators
• diff(DGAlgebra,RingElement) -- Apply the differential of a DGAlgebra to a ring element
• differential(DGAlgebra) -- see differential -- The list of generator differentials stored in a DG algebra or DG module
• displayBlockDiff(DGAlgebra,Array,Array) -- see displayBlockDiff -- Shows natural decomposition of a map in the Tate resolution
• displayBlockDiff(DGAlgebra,List,List) -- see displayBlockDiff -- Shows natural decomposition of a map in the Tate resolution
• displayBlockDiff(DGAlgebra,VisibleList) -- see displayBlockDiff -- Shows natural decomposition of a map in the Tate resolution
• displayBlockDiff(DGAlgebra,ZZ) -- see displayBlockDiff -- Shows natural decomposition of a map in the Tate resolution
• ensureDGAlgebraCaches(DGAlgebra) -- see ensureDGAlgebraCaches -- Guarantee that the standard cache sub-tables are present
• findNaryTrivialMasseyOperation(DGAlgebra,List,HashTable,ZZ) -- see findTrivialMasseyOperation -- Finds a trivial Massey operation on a set of generators of H(A)
• findTrivialMasseyOperation(DGAlgebra) -- see findTrivialMasseyOperation -- Finds a trivial Massey operation on a set of generators of H(A)
• freeDGModule(DGAlgebra,List) -- see freeDGModule -- Construct a free DG module over a DG algebra
• generatorDegrees(DGAlgebra) -- see generatorDegrees -- The hom-degrees (and optional internal degrees) of the DG generators
• generators(DGAlgebra) (missing documentation)
• getBasis(ZZ,DGAlgebra) -- see getBasis -- Get a basis for a particular homological degree of a DG algebra.
• getBoundaryPreimage(DGAlgebra,List) -- see getBoundaryPreimage -- Attempt to find a preimage of a boundary under the differential of a DGAlgebra.
• getBoundaryPreimage(DGAlgebra,RingElement) -- see getBoundaryPreimage -- Attempt to find a preimage of a boundary under the differential of a DGAlgebra.
• getGenerators(DGAlgebra) -- see getGenerators -- Cycles whose classes generate the homology algebra of a DG algebra
• HH DGAlgebra -- The homology algebra of a DG algebra
• HH_ZZ DGAlgebra -- Computes the homology of a DG algebra as a module
• homologyAlgebra(DGAlgebra) -- see homologyAlgebra -- Compute the homology algebra of a DGAlgebra.
• homologyClass(DGAlgebra,RingElement) -- see homologyClass -- Computes the element of the homology algebra corresponding to a cycle in a DGAlgebra.
• homologyModule(DGAlgebra,Module) -- see homologyModule -- Compute the homology of a DGModule as a module over a DGAlgebra.
• identityDGAlgebraMap(DGAlgebra) -- see identityDGAlgebraMap -- The identity DGAlgebraMap on a DG algebra
• invalidateDGAlgebraCache(DGAlgebra) -- see invalidateDGAlgebraCache -- Discard cached derived data so that it is recomputed from scratch
• isAcyclic(DGAlgebra) -- see isAcyclic -- Determine whether a DG algebra has no higher homology
• isDGIdeal(DGAlgebra,Ideal) -- see isDGIdeal -- Test whether an ideal of A.natural is closed under the differential of A
• isHomogeneous(DGAlgebra) -- Determine if the DGAlgebra respects the gradings of the ring it is defined over.
• isHomologyAlgebraTrivial(DGAlgebra) -- see isHomologyAlgebraTrivial -- Determines if the homology algebra of a DGAlgebra is trivial
• isValidDGAlgebra(DGAlgebra) -- see isValidDGAlgebra -- Structural invariant check for a DG algebra
• isWellDefined(DGAlgebra) -- Check that a DG algebra has correct structure and a differential that squares to zero
• isWellDefinedDifferential(DGAlgebra) -- see isWellDefinedDifferential -- Semantic check that d^2 = 0 for a DG algebra or DG module
• killCycles(DGAlgebra) -- see killCycles -- Adjoin variables to kill non-bounding cycles in the lowest positive degree
• killHomologyAtDegree(DGAlgebra,ZZ) -- see killHomologyAtDegree -- Adjoin variables killing the homology of a DG algebra at a prescribed degree
• koszulComplexDGM(DGAlgebra,Module) -- see koszulComplexDGM -- The Koszul complex of a module as a DG module
• liftToDGMap(DGAlgebra,DGAlgebra,RingMap) -- see liftToDGMap -- Lift a ring homomorphism in degree zero to a DG algebra morphism
• masseyTripleProduct(DGAlgebra,RingElement,RingElement,RingElement) -- see masseyTripleProduct -- Computes the Massey triple product of a set of cycles or homology classes
• masseyTripleProduct(DGAlgebra,ZZ,ZZ,ZZ) -- Computes the matrix representing all triple Massey operations.
• maxDegree(DGAlgebra) -- see maxDegree -- Computes the maximum homological degree of a DGAlgebra
• minimalSemifreeResolution(DGAlgebra,Module) -- see minimalSemifreeResolution -- Build a minimal semifree DG module resolution over a DG algebra
• net(DGAlgebra) -- Short-form display of a DG algebra
• numgens(DGAlgebra) (missing documentation)
• polyDifferential(DGAlgebra,RingElement) -- see polyDifferential -- Matrix and element-level differentials of a DG algebra
• polyDifferential(ZZ,DGAlgebra) -- see polyDifferential -- Matrix and element-level differentials of a DG algebra
• polyDiffMonomial(DGAlgebra,RingElement) -- see polyDiffMonomial -- Leibniz rule on a single monomial of a DG algebra
• minimalPresentation(DGAlgebra) -- see prune(DGAlgebra) -- Pruning a DG algebra is the identity
• prune(DGAlgebra) -- Pruning a DG algebra is the identity
• restrictDifferential(DGAlgebra,List) -- see restrictDifferential -- Synonym for subDGAlgebra, named to match the restricted-differential vocabulary
• ring(DGAlgebra) (missing documentation)
• semifreeResolution(DGAlgebra,Module) -- see semifreeResolution -- Build a semifree DG module resolving a module over the base ring
• setDiff(DGAlgebra,List) -- see setDiff -- Install or replace the differential on a DG algebra
• subDGAlgebra(DGAlgebra,List) -- see subDGAlgebra -- The sub-DG algebra generated by a chosen subset of DG generators
• toComplex(DGAlgebra) -- see toComplex -- Converts a DGAlgebra to a Complex
• toComplex(DGAlgebra,ZZ) -- Converts a DGAlgebra to a Complex
• truncateGenerators(DGAlgebra,ZZ) -- see truncateGenerators -- Restrict a DG algebra to its generators of hom-degree strictly above a bound
• underlyingAlgebra(DGAlgebra) -- see underlyingAlgebra -- The graded-commutative algebra carrying the DG structure
• underlyingRing(DGAlgebra) -- see underlyingRing -- The commutative base ring of a DG algebra or DG module
• zerothHomology(DGAlgebra) -- see zerothHomology -- The zeroth homology of a DG algebra as a ring

For the programmer

The object DGAlgebra is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:743:0.