# DGAlgebra -- The class of all DGAlgebras

## Description

Some common ways to create DGAlgebras include koszulComplexDGA, freeDGAlgebra, setDiff, and acyclicClosure.

## Functions and methods returning an object of class DGAlgebra :

• acyclicClosure -- Compute theae acyclic closure of a DGAlgebra.
• freeDGAlgebra -- Constructs a DGAlgebra
• killCycles -- Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.
• koszulComplexDGA -- Returns the Koszul complex as a DGAlgebra
• setDiff -- Sets the differential of a DGAlgebra manually.

## Methods that use an object of class DGAlgebra :

• "acyclicClosure(DGAlgebra)" -- see acyclicClosure -- Compute theae acyclic closure of a DGAlgebra.
• DGAlgebra ** DGAlgebra -- Tensor product of a DGAlgebra and another ring.
• DGAlgebra ** Ring -- Tensor product of a DGAlgebra and another ring.
• "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.
• diff(DGAlgebra,RingElement) -- Computes the differential of a ring element in a DGAlgebra
• "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)
• "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 -- Returns a list of cycles whose images generate HH(A) as an algebra
• HH DGAlgebra -- Compute the homology algebra of a DGAlgebra.
• 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.
• "isAcyclic(DGAlgebra)" -- see isAcyclic -- Determines if a DGAlgebra is acyclic.
• 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
• "killCycles(DGAlgebra)" -- see killCycles -- Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.
• "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
• net(DGAlgebra) -- Outputs the pertinent information about a DGAlgebra
• "setDiff(DGAlgebra,List)" -- see setDiff -- Sets the differential of a DGAlgebra manually.
• "toComplex(DGAlgebra)" -- see toComplex -- Converts a DGAlgebra to a ChainComplex
• toComplex(DGAlgebra,ZZ) -- Converts a DGAlgebra to a ChainComplex
• "zerothHomology(DGAlgebra)" -- see zerothHomology -- Compute the zeroth homology of the DGAlgebra A as a ring.

## For the programmer

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