DGAlgebras : Index
-
acyclicClosure -- Compute theae acyclic closure of a DGAlgebra.
-
acyclicClosure(...,EndDegree=>...) -- Option to specify the degree to stop computing the acyclic closure
-
acyclicClosure(...,StartDegree=>...) -- Option to specify the degree to start computing the acyclic closure
-
acyclicClosure(DGAlgebra) -- Compute theae acyclic closure of a DGAlgebra.
-
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.
-
adjoinVariables(DGAlgebra,List) -- Adjoins variables to make the specified cycles boundaries.
-
AssertWellDefined -- Option to check whether the lifted map on DGAlgebras is well defined.
-
Basic operations on DG Algebra Maps -- Outlines some basic operations on DGAlgebraMaps
-
Basic operations on DG Algebras -- Outlines some basic operations on DG Algebras
-
cycles -- Cycles chosen when computing the homology algebra of a DGAlgebra
-
deviations -- Computes the deviations of the input ring, complex, or power series.
-
deviations(...,DegreeLimit=>...) -- Option to specify the maximum degree to look for generators when computing the deviations
-
deviations(ChainComplex) -- Computes the deviations of the input ring, complex, or power series.
-
deviations(Ring) -- Computes the deviations of the input ring, complex, or power series.
-
deviations(RingElement,List) -- Computes the deviations of the input ring, complex, or power series.
-
deviationsToPoincare -- Computes the power series corresponding to a set of deviations.
-
deviationsToPoincare(...,DegreeLimit=>...) -- Computes the power series corresponding to a set of deviations.
-
deviationsToPoincare(HashTable) -- Computes the power series corresponding to a set of deviations.
-
DGAlgebra -- The class of all DGAlgebras
-
DGAlgebra ** DGAlgebra -- Tensor product of a DGAlgebra and another ring.
-
DGAlgebra ** Ring -- Tensor product of a DGAlgebra and another ring.
-
DGAlgebraMap -- The class of all DG Algebra maps
-
dgAlgebraMap -- Define a DG algebra map between DG algebras.
-
dgAlgebraMap(DGAlgebra,DGAlgebra,Matrix) -- Define a DG algebra map between DG algebras.
-
dgAlgebraMultMap -- Returns the chain map corresponding to multiplication by a cycle.
-
dgAlgebraMultMap(DGAlgebra,RingElement) -- Returns the chain map corresponding to multiplication by a cycle.
-
DGAlgebras -- Data types and basic functions on differential graded (DG) Algebras.
-
diff(DGAlgebra,RingElement) -- Computes the differential of a ring element in a DGAlgebra
-
EndDegree -- Option to specify the degree to stop computing killing cycles and acyclic closure
-
expandGeomSeries -- Expand a geometric series to a specified degree.
-
expandGeomSeries(List,ZZ) -- Expand a geometric series to a specified degree.
-
expandGeomSeries(RingElement,ZZ) -- Expand a geometric series to a specified degree.
-
findNaryTrivialMasseyOperation -- Finds a trivial Massey operation on a set of generators of H(A)
-
findNaryTrivialMasseyOperation(DGAlgebra,List,HashTable,ZZ) -- Finds a trivial Massey operation on a set of generators of H(A)
-
findTrivialMasseyOperation -- Finds a trivial Massey operation on a set of generators of H(A)
-
findTrivialMasseyOperation(...,GenDegreeLimit=>...) -- Option to specify the maximum degree to look for generators
-
findTrivialMasseyOperation(...,TMOLimit=>...) -- Option to specify the maximum arity of a trivial Massey operation, if one exists.
-
findTrivialMasseyOperation(DGAlgebra) -- Finds a trivial Massey operation on a set of generators of H(A)
-
freeDGAlgebra -- Constructs a DGAlgebra
-
freeDGAlgebra(...,Variable=>...) -- Constructs a DGAlgebra
-
freeDGAlgebra(Ring,List) -- Constructs a DGAlgebra
-
GenDegreeLimit -- Option to specify the maximum degree to look for generators
-
getBasis -- Get a basis for a particular homological degree of a DG algebra.
-
getBasis(...,Limit=>...) -- Option to specify the maximum number of basis elements to return
-
getBasis(ZZ,DGAlgebra) -- Get a basis for a particular homological degree of a DG algebra.
-
getBasis(ZZ,Ring) -- Get a basis for a degree of a ring.
-
getBoundaryPreimage -- Attempt to find a preimage of a boundary under the differential of a DGAlgebra.
-
getBoundaryPreimage(DGAlgebra,List) -- Attempt to find a preimage of a boundary under the differential of a DGAlgebra.
-
getBoundaryPreimage(DGAlgebra,RingElement) -- Attempt to find a preimage of a boundary under the differential of a DGAlgebra.
-
getDegNModule -- Compute a presentation of M_i as an R-module
-
getDegNModule(ZZ,Ring,Ring) -- Compute a presentation of M_i as an R-module
-
getGenerators -- Returns a list of cycles whose images generate HH(A) as an algebra
-
getGenerators(...,DegreeLimit=>...) -- Option to specify the degree to stop finding generators of HH(DGAlgebra)
-
getGenerators(...,StartDegree=>...) -- Option to specify the degree to start finding generators of HH(DGAlgebra)
-
getGenerators(...,Verbosity=>...) -- Option to specify the maximum degree to look for generators when computing the deviations
-
getGenerators(DGAlgebra) -- 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.
-
HH_ZZ DGAlgebra -- Computes the homology of a DG algebra as a module
-
homologyAlgebra -- Compute the homology algebra of a DGAlgebra.
-
homologyAlgebra(...,GenDegreeLimit=>...) -- Option to specify the maximum degree to look for generators
-
homologyAlgebra(...,RelDegreeLimit=>...) -- Option to specify the maximum degree to look for relations
-
homologyAlgebra(...,Verbosity=>...) -- Option to specify the maximum degree to look for generators when computing the deviations
-
homologyAlgebra(DGAlgebra) -- Compute the homology algebra of a DGAlgebra.
-
homologyClass -- Computes the element of the homology algebra corresponding to a cycle in a DGAlgebra.
-
homologyClass(DGAlgebra,RingElement) -- 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.
-
homologyModule(DGAlgebra,Module) -- Compute the homology of a DGModule as a module over a DGAlgebra.
-
InitializeComplex -- Sets the differential of a DGAlgebra manually.
-
InitializeDegreeZeroHomology -- Sets the differential of a DGAlgebra manually.
-
isAcyclic -- Determines if a DGAlgebra is acyclic.
-
isAcyclic(...,EndDegree=>...) -- Option to specify the degree to finish checking acyclicity
-
isAcyclic(DGAlgebra) -- Determines if a DGAlgebra is acyclic.
-
isGolod -- Determines if a ring is Golod
-
isGolod(Ring) -- Determines if a ring is Golod
-
isGolodHomomorphism -- Determines if the canonical map from the ambient ring is Golod
-
isGolodHomomorphism(...,GenDegreeLimit=>...) -- Option to specify the maximum degree to look for generators
-
isGolodHomomorphism(...,TMOLimit=>...) -- Option to specify the maximum degree to look for generators when computing the deviations
-
isGolodHomomorphism(QuotientRing) -- Determines if the canonical map from the ambient ring is Golod
-
isHomogeneous(DGAlgebra) -- Determine if the DGAlgebra respects the gradings of the ring it is defined over.
-
isHomologyAlgebraTrivial -- Determines if the homology algebra of a DGAlgebra is trivial
-
isHomologyAlgebraTrivial(...,GenDegreeLimit=>...) -- Option to specify the maximum degree to look for generators
-
isHomologyAlgebraTrivial(DGAlgebra) -- Determines if the homology algebra of a DGAlgebra is trivial
-
isWellDefined(DGAlgebraMap) -- Define a DG algebra map between DG algebras.
-
killCycles -- Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.
-
killCycles(...,EndDegree=>...) -- Option to specify the degree to stop looking for cycles
-
killCycles(...,StartDegree=>...) -- Option to specify the degree to start looking for cycles
-
killCycles(DGAlgebra) -- Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.
-
koszulComplexDGA -- Returns the Koszul complex as a DGAlgebra
-
koszulComplexDGA(...,Variable=>...) -- Returns the Koszul complex as a DGAlgebra
-
koszulComplexDGA(Ideal) -- Returns the Koszul complex as a DGAlgebra
-
koszulComplexDGA(List) -- Define the Koszul complex on a list of elements as a DGAlgebra
-
koszulComplexDGA(Ring) -- Returns the Koszul complex as a DGAlgebra
-
liftToDGMap -- Lift a ring homomorphism in degree zero to a DG algebra morphism
-
liftToDGMap(...,EndDegree=>...) -- Lift a ring homomorphism in degree zero to a DG algebra morphism
-
liftToDGMap(DGAlgebra,DGAlgebra,RingMap) -- 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
-
masseyTripleProduct(DGAlgebra,RingElement,RingElement,RingElement) -- 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 -- Computes the maximum homological degree of a DGAlgebra
-
maxDegree(DGAlgebra) -- Computes the maximum homological degree of a DGAlgebra
-
natural -- The underlying algebra of a DGAlgebra.
-
net(DGAlgebra) -- Outputs the pertinent information about a DGAlgebra
-
net(DGAlgebraMap) -- Outputs the pertinent information about a DGAlgebraMap
-
RelDegreeLimit -- Option to specify the maximum degree to look for relations
-
ringMap -- The class of all DG Algebra maps
-
setDiff -- Sets the differential of a DGAlgebra manually.
-
setDiff(...,InitializeComplex=>...) -- Sets the differential of a DGAlgebra manually.
-
setDiff(...,InitializeDegreeZeroHomology=>...) -- Sets the differential of a DGAlgebra manually.
-
setDiff(DGAlgebra,List) -- Sets the differential of a DGAlgebra manually.
-
source(DGAlgebraMap) -- Outputs the source of a DGAlgebraMap
-
StartDegree -- Option to specify the degree to start computing the acyclic closure and killing cycles
-
target(DGAlgebraMap) -- Outputs the target of a DGAlgebraMap
-
The Koszul complex as a DG Algebra -- an example
-
TMOLimit -- Option to specify the maximum arity of the trivial Massey operation
-
toComplex -- Converts a DGAlgebra to a ChainComplex
-
toComplex(DGAlgebra) -- Converts a DGAlgebra to a ChainComplex
-
toComplex(DGAlgebra,ZZ) -- Converts a DGAlgebra to a ChainComplex
-
toComplexMap -- Construct the ChainComplexMap associated to a DGAlgebraMap
-
toComplexMap(...,AssertWellDefined=>...) -- Construct the ChainComplexMap associated to a DGAlgebraMap
-
toComplexMap(...,EndDegree=>...) -- Construct the ChainComplexMap associated to a DGAlgebraMap
-
toComplexMap(DGAlgebraMap) -- Construct the ChainComplexMap associated to a DGAlgebraMap
-
toComplexMap(DGAlgebraMap,ZZ) -- Construct the ChainComplexMap associated to a DGAlgebraMap
-
torAlgebra -- Computes the Tor algebra of a ring
-
torAlgebra(...,GenDegreeLimit=>...) -- Option to specify the maximum degree to look for generators
-
torAlgebra(...,RelDegreeLimit=>...) -- Option to specify the maximum degree to look for relations
-
torAlgebra(Ring) -- Computes the Tor algebra of a ring
-
torAlgebra(Ring,Ring) -- Computes Tor_R(S,k) up to a specified generating and relating degree.
-
torMap -- Compute the map of Tor algebras associated to a RingMap.
-
torMap(...,GenDegreeLimit=>...) -- Compute the map of Tor algebras associated to a RingMap.
-
torMap(RingMap) -- Compute the map of Tor algebras associated to a RingMap.
-
zerothHomology -- Compute the zeroth homology of the DGAlgebra A as a ring.
-
zerothHomology(DGAlgebra) -- Compute the zeroth homology of the DGAlgebra A as a ring.