Macaulay2 » Documentation
Packages » DGAlgebras :: Table of Contents
next | previous | forward | backward | up | index | toc

# DGAlgebras : Table of Contents

- DGAlgebras -- Data types and basic functions on differential graded (DG) Algebras.
  - Basic operations on DG Algebras -- Outlines some basic operations on DG Algebras
  - The Koszul complex as a DG Algebra -- an example
  - Basic operations on DG Algebra Maps -- Outlines some basic operations on DGAlgebraMaps
- acyclicClosure -- Compute the 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(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.
- blockDiff -- prepares a map for display
- 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
- deviationsToPoincare -- 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.
- 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 -- Shows natural decomposition of a map in the Tate resolution
- EndDegree -- Option to specify the degree to stop computing killing cycles and acyclic closure
- expandGeomSeries -- Expand a geometric series to a specified degree.
- 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.
- freeDGAlgebra -- 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,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.
- getDegNModule -- 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
- 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
- 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.
- isAcyclic(...,EndDegree=>...) -- Option to specify the degree to finish checking acyclicity
- isGolod -- 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
- 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
- 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
- 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
- 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
- masseyTripleProduct(DGAlgebra,ZZ,ZZ,ZZ) -- Computes the matrix representing all triple Massey operations.
- maxDegree -- 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
- setDiff -- 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
- TMOLimit -- Option to specify the maximum arity of the trivial Massey operation
- toComplex -- Converts a DGAlgebra to a Complex
- toComplex(DGAlgebra,ZZ) -- Converts a DGAlgebra to a Complex
- toComplexMap -- Construct the ComplexMap 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,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.
- zerothHomology -- Compute the zeroth homology of the DGAlgebra A as a ring.