# 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 free (skew commutative) 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.
• 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.
• 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.
• 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.
• 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.