DGAlgebras : Table of Contents
-
DGAlgebras -- Data types and basic functions on differential graded (DG) Algebras.
-
-
-
-
acyclicClosure(Ring) -- Compute the acyclic closure of the residue field of a ring up to a certain degree
-
adjoinVariables -- Adjoins variables to make the specified cycles boundaries.
-
AssertWellDefined -- Option to check whether the lifted map on DGAlgebras is well defined.
-
-
cycles -- Cycles chosen when computing the homology algebra of a DGAlgebra
-
deviations -- Computes the deviations of the input ring, complex, or power series.
-
-
-
-
-
-
-
dgAlgebraMap -- Define a DG algebra map between DG algebras.
-
dgAlgebraMultMap -- Returns the chain map corresponding to multiplication by a cycle.
-
-
-
EndDegree -- Option to specify the degree to stop computing killing cycles and acyclic closure
-
-
-
-
-
-
GenDegreeLimit -- Option to specify the maximum degree to look for generators
-
getBasis -- Get a basis for a particular homological degree of a DG algebra.
-
-
-
getBoundaryPreimage -- Attempt to find a preimage of a boundary under the differential of a DGAlgebra.
-
-
getGenerators -- Returns a list of cycles whose images generate HH(A) as an algebra
-
-
-
-
HH DGAlgebra -- Compute the homology algebra of a DGAlgebra.
-
HH DGAlgebraMap -- Computes the homomorphism in homology associated to a DGAlgebraMap.
-
-
-
-
-
-
homologyClass -- Computes the element of the homology algebra corresponding to a cycle in a DGAlgebra.
-
homologyModule -- Compute the homology of a DGModule as a module over a DGAlgebra.
-
isAcyclic -- Determines if a DGAlgebra is acyclic.
-
-
isGolod -- Determines if a ring is Golod
-
-
-
-
-
-
-
killCycles -- Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.
-
-
-
-
-
-
liftToDGMap -- Lift a ring homomorphism in degree zero to a DG algebra morphism
-
masseyTripleProduct -- Computes the Massey triple product of a set of cycles or homology classes
-
-
maxDegree -- Computes the maximum homological degree of a DGAlgebra
-
natural -- The underlying algebra of a DGAlgebra.
-
-
-
RelDegreeLimit -- Option to specify the maximum degree to look for relations
-
setDiff -- Sets the differential of a DGAlgebra manually.
-
-
StartDegree -- Option to specify the degree to start computing the acyclic closure and killing cycles
-
-
TMOLimit -- Option to specify the maximum arity of the trivial Massey operation
-
toComplex -- Converts a DGAlgebra to a ChainComplex
-
-
toComplexMap -- Construct the ChainComplexMap associated to a DGAlgebraMap
-
-
-
-
-
torMap -- Compute the map of Tor algebras associated to a RingMap.
-
zerothHomology -- Compute the zeroth homology of the DGAlgebra A as a ring.