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# DGAlgebra -- The class of all DGAlgebras

## Description

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

## See also

- Basic operations on DG Algebras -- Outlines some basic operations on DG Algebras

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

- acyclicClosure -- Compute the acyclic closure of a DGAlgebra.
- adjoinVariables -- Adjoins variables to make the specified cycles boundaries.
- 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 the acyclic closure of a DGAlgebra.
- `adjoinVariables(DGAlgebra,List)` -- see adjoinVariables -- Adjoins variables to make the specified cycles boundaries.
- `blockDiff(DGAlgebra,ZZ)` -- see blockDiff -- prepares a map for display
- 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
- `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
- `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 Complex
- toComplex(DGAlgebra,ZZ) -- Converts a DGAlgebra to a Complex
- `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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/DGAlgebras.m2:1679:0.