DGAlgebras : Index
- Acyclic closures -- an example
- 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.
- cycles -- Cycles chosen when computing the homology algebra of a DGAlgebra
- deviations -- Computes the deviations of the input ring
- deviations(..., DegreeLimit => ...) -- Option to specify the maximum degree to look for generators when computing the deviations
- deviations(Ring) -- Computes the deviations of the input ring
- 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.
- DGAlgebras -- Data types and basic functions on differential graded (DG) Algebras.
- EndDegree -- Option to specify the degree to stop computing killing cycles and acyclic closure
- 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 free (skew commutative) 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.
- 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(DGAlgebra) -- 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
- Homology algebra of a DG Algebra -- an example
- 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(DGAlgebra) -- Compute the homology algebra of 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(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
- 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(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
- 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
- Operations on DG Algebras -- Outlines some basic operations on DG Algebras
- RelDegreeLimit -- Option to specify the maximum degree to look for relations
- 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.
- StartDegree -- Option to specify the degree to start computing the acyclic closure and killing cycles
- 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
- 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.
- 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.