VersalDeformations : Index

• CacheName -- determines hash table in which to cache solutions to the deformation equation
• checkComparisonTheorem -- checks if the Piene-Schlessinger or Di Dennaro comparison theorem holds
• checkComparisonTheorem(Ideal) -- checks if the Piene-Schlessinger or Di Dennaro comparison theorem holds
• checkComparisonTheorem(Matrix) -- checks if the Piene-Schlessinger or Di Dennaro comparison theorem holds
• checkTangentSpace -- checks if dimension of space of sections of the normal bundle agrees with that calculated using normalMatrix
• checkTangentSpace(Ideal) -- checks if dimension of space of sections of the normal bundle agrees with that calculated using normalMatrix
• checkTangentSpace(Ideal,Matrix) -- checks if dimension of space of sections of the normal bundle agrees with that calculated using normalMatrix
• checkTangentSpace(Matrix) -- checks if dimension of space of sections of the normal bundle agrees with that calculated using normalMatrix
• checkTangentSpace(Matrix,Matrix) -- checks if dimension of space of sections of the normal bundle agrees with that calculated using normalMatrix
• correctDeformation -- correct lifting to avoid obstructions at next order
• correctDeformation(...,SanityCheck=>...) -- correct lifting to avoid obstructions at next order
• correctDeformation(...,Verbose=>...) -- control the verbosity of output
• correctDeformation(List,List,List,List) -- correct lifting to avoid obstructions at next order
• correctDeformation(Sequence,Matrix,List) -- correct lifting to avoid obstructions at next order
• CorrectionMatrix -- determines the first order deformations used in correcting liftings
• correctionMatrix -- calculate how first order deformations perturb obstruction vector
• correctionMatrix(Matrix,Matrix) -- calculate how first order deformations perturb obstruction vector
• cotangentCohomology1 -- calculate first cotangent cohomology
• cotangentCohomology1(...,ModuleDeformation=>...) -- calculate first cotangent cohomology
• cotangentCohomology1(...,SourceRing=>...) -- calculate first cotangent cohomology
• cotangentCohomology1(Ideal) -- calculate first cotangent cohomology
• cotangentCohomology1(InfiniteNumber,ZZ,Ideal) -- calculate first cotangent cohomology
• cotangentCohomology1(InfiniteNumber,ZZ,Matrix) -- calculate first cotangent cohomology
• cotangentCohomology1(List,Ideal) -- calculate first cotangent cohomology
• cotangentCohomology1(List,Matrix) -- calculate first cotangent cohomology
• cotangentCohomology1(Matrix) -- calculate first cotangent cohomology
• cotangentCohomology1(ZZ,Ideal) -- calculate first cotangent cohomology
• cotangentCohomology1(ZZ,InfiniteNumber,Ideal) -- calculate first cotangent cohomology
• cotangentCohomology1(ZZ,InfiniteNumber,Matrix) -- calculate first cotangent cohomology
• cotangentCohomology1(ZZ,Matrix) -- calculate first cotangent cohomology
• cotangentCohomology1(ZZ,ZZ,Ideal) -- calculate first cotangent cohomology
• cotangentCohomology1(ZZ,ZZ,Matrix) -- calculate first cotangent cohomology
• cotangentCohomology2 -- calculate second cotangent cohomology
• cotangentCohomology2(...,SourceRing=>...) -- calculate second cotangent cohomology
• cotangentCohomology2(Ideal) -- calculate second cotangent cohomology
• cotangentCohomology2(InfiniteNumber,ZZ,Ideal) -- calculate second cotangent cohomology
• cotangentCohomology2(InfiniteNumber,ZZ,Matrix) -- calculate second cotangent cohomology
• cotangentCohomology2(List,Ideal) -- calculate second cotangent cohomology
• cotangentCohomology2(List,Matrix) -- calculate second cotangent cohomology
• cotangentCohomology2(Matrix) -- calculate second cotangent cohomology
• cotangentCohomology2(ZZ,Ideal) -- calculate second cotangent cohomology
• cotangentCohomology2(ZZ,InfiniteNumber,Ideal) -- calculate second cotangent cohomology
• cotangentCohomology2(ZZ,InfiniteNumber,Matrix) -- calculate second cotangent cohomology
• cotangentCohomology2(ZZ,Matrix) -- calculate second cotangent cohomology
• cotangentCohomology2(ZZ,ZZ,Ideal) -- calculate second cotangent cohomology
• cotangentCohomology2(ZZ,ZZ,Matrix) -- calculate second cotangent cohomology
• CT -- cotangent cohomology
• DefParam -- deformation parameter
• DefParamX -- deformation parameter
• DefParamY -- deformation parameter
• DegreeBound -- determines the degree limit used to compute the tangent cone of obstruction equations
• extMatrix -- calculate obstruction space for modules
• extMatrix(...,SourceRing=>...) -- calculate obstruction space for modules
• extMatrix(InfiniteNumber,ZZ,Matrix) -- calculate obstruction space for modules
• extMatrix(List,Matrix) -- calculate obstruction space for modules
• extMatrix(Matrix) -- calculate obstruction space for modules
• extMatrix(ZZ,InfiniteNumber,Matrix) -- calculate obstruction space for modules
• extMatrix(ZZ,Matrix) -- calculate obstruction space for modules
• extMatrix(ZZ,ZZ,Matrix) -- calculate obstruction space for modules
• families -- outputs the perturbed families of a NestedDeformation
• families(NestedDeformation) -- outputs the perturbed families of a NestedDeformation
• firstOrderDeformations -- use tangent space to create first order perturbations and find relations
• firstOrderDeformations(...,DefParam=>...) -- use tangent space to create first order perturbations and find relations
• firstOrderDeformations(...,SanityCheck=>...) -- use tangent space to create first order perturbations and find relations
• firstOrderDeformations(Matrix,Matrix,Matrix) -- use tangent space to create first order perturbations and find relations
• HighestOrder -- sets the order to which we compute
• IncludeTrivial -- computes a nested VersalDeformation of a pair
• isPolynomial -- checks if a deformation lifts to arbitrary order
• isPolynomial(List,List,List,List) -- checks if a deformation lifts to arbitrary order
• isPolynomial(NestedDeformation) -- checks if a deformation lifts to arbitrary order
• liftDeformation -- lift a solution of the deformation equation to the next order
• liftDeformation(...,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• liftDeformation(...,SanityCheck=>...) -- checks if lifting solves deformation equation
• liftDeformation(...,Verbose=>...) -- control the verbosity of output
• liftDeformation(List,List,List,List) -- lift a solution of the deformation equation to the next order
• liftDeformation(NestedDeformation) -- lift a nested deformation to the next order
• localHilbertScheme -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,CacheName=>...) -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,CorrectionMatrix=>...) -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,DefParam=>...) -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• localHilbertScheme(...,HighestOrder=>...) -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,PolynomialCheck=>...) -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,SanityCheck=>...) -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,SmartLift=>...) -- computes a power series representation of the local Hilbert scheme
• localHilbertScheme(...,Verbose=>...) -- control the verbosity of output
• localHilbertScheme(Matrix) -- computes a power series representation of the local Hilbert scheme
• ModuleDeformation -- calculate first cotangent cohomology
• NestedDeformation -- The class of all nested deformations
• nestedHilbertScheme -- computes a nested Hilbert scheme of a pair
• nestedHilbertScheme(...,DefParamX=>...) -- deformation parameter
• nestedHilbertScheme(...,DefParamY=>...) -- deformation parameter
• nestedHilbertScheme(...,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• nestedHilbertScheme(...,HighestOrder=>...) -- sets the order to which we compute
• nestedHilbertScheme(...,PolynomialCheck=>...) -- checks if power series solution terminates
• nestedHilbertScheme(...,Projective=>...) -- computes a nested Hilbert scheme of a pair
• nestedHilbertScheme(...,SanityCheck=>...) -- checks if lifting solves deformation equation
• nestedHilbertScheme(...,Verbose=>...) -- control the verbosity of output
• nestedHilbertScheme(Matrix,Matrix) -- computes a nested Hilbert scheme of a pair
• nestedObstruction -- calculate secondary obstruction space for nested deformations
• nestedObstruction(InfiniteNumber,ZZ,Matrix,Matrix) -- calculate secondary obstruction space for nested deformations
• nestedObstruction(List,Matrix,Matrix) -- calculate secondary obstruction space for nested deformations
• nestedObstruction(Matrix,Matrix) -- calculate secondary obstruction space for nested deformations
• nestedObstruction(ZZ,InfiniteNumber,Matrix,Matrix) -- calculate secondary obstruction space for nested deformations
• nestedObstruction(ZZ,Matrix,Matrix) -- calculate secondary obstruction space for nested deformations
• nestedObstruction(ZZ,ZZ,Matrix,Matrix) -- calculate secondary obstruction space for nested deformations
• nestedTangent -- calculate first order deformations for nested deformations
• nestedTangent(...,IncludeTrivial=>...) -- calculate first order deformations for nested deformations
• nestedTangent(...,ModuleDeformation=>...) -- calculate first order deformations for nested deformations
• nestedTangent(...,SourceRing=>...) -- calculate first order deformations for nested deformations
• nestedTangent(InfiniteNumber,ZZ,Matrix,Matrix) -- calculate first order deformations for nested deformations
• nestedTangent(List,Matrix,Matrix) -- calculate first order deformations for nested deformations
• nestedTangent(Matrix,Matrix) -- calculate first order deformations for nested deformations
• nestedTangent(ZZ,InfiniteNumber,Matrix,Matrix) -- calculate first order deformations for nested deformations
• nestedTangent(ZZ,Matrix,Matrix) -- calculate first order deformations for nested deformations
• nestedTangent(ZZ,ZZ,Matrix,Matrix) -- calculate first order deformations for nested deformations
• nestedVersalDeformation -- computes a nested VersalDeformation of a pair
• nestedVersalDeformation(...,DefParamX=>...) -- deformation parameter
• nestedVersalDeformation(...,DefParamY=>...) -- deformation parameter
• nestedVersalDeformation(...,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• nestedVersalDeformation(...,HighestOrder=>...) -- sets the order to which we compute
• nestedVersalDeformation(...,IncludeTrivial=>...) -- computes a nested VersalDeformation of a pair
• nestedVersalDeformation(...,PolynomialCheck=>...) -- checks if power series solution terminates
• nestedVersalDeformation(...,Projective=>...) -- computes a nested VersalDeformation of a pair
• nestedVersalDeformation(...,SanityCheck=>...) -- checks if lifting solves deformation equation
• nestedVersalDeformation(...,Verbose=>...) -- control the verbosity of output
• nestedVersalDeformation(Matrix,Matrix) -- computes a nested VersalDeformation of a pair
• normalMatrix -- calculate normal module
• normalMatrix(...,SourceRing=>...) -- calculate normal module
• normalMatrix(Ideal) -- calculate normal module
• normalMatrix(InfiniteNumber,ZZ,Ideal) -- calculate normal module
• normalMatrix(InfiniteNumber,ZZ,Matrix) -- calculate normal module
• normalMatrix(List,Ideal) -- calculate normal module
• normalMatrix(List,Matrix) -- calculate normal module
• normalMatrix(Matrix) -- calculate normal module
• normalMatrix(ZZ,Ideal) -- calculate normal module
• normalMatrix(ZZ,InfiniteNumber,Ideal) -- calculate normal module
• normalMatrix(ZZ,InfiniteNumber,Matrix) -- calculate normal module
• normalMatrix(ZZ,Matrix) -- calculate normal module
• normalMatrix(ZZ,ZZ,Ideal) -- calculate normal module
• normalMatrix(ZZ,ZZ,Matrix) -- calculate normal module
• obstructions -- outputs the obstruction equations of a NestedDeformation
• obstructions(NestedDeformation) -- outputs the obstruction equations of a NestedDeformation
• PolynomialCheck -- checks if power series solution terminates
• SanityCheck -- checks if lifting solves deformation equation
• sanityCheck -- checks if deformation data satisfies the deformation equation at a certain order
• sanityCheck(ZZ,List) -- checks if deformation data satisfies the deformation equation at a certain order
• sanityCheck(ZZ,NestedDeformation) -- checks if deformation data satisfies the deformation equation at a certain order
• setupNestedDeformation -- create a first order NestedDeformation from tangent directions and obstruction spaces
• setupNestedDeformation(...,DefParamX=>...) -- create a first order NestedDeformation from tangent directions and obstruction spaces
• setupNestedDeformation(...,DefParamY=>...) -- create a first order NestedDeformation from tangent directions and obstruction spaces
• setupNestedDeformation(...,SanityCheck=>...) -- create a first order NestedDeformation from tangent directions and obstruction spaces
• setupNestedDeformation(...,Verbose=>...) -- create a first order NestedDeformation from tangent directions and obstruction spaces
• setupNestedDeformation(List) -- create a first order NestedDeformation from tangent directions and obstruction spaces
• SmartLift -- chooses lifting to avoid obstructions at next order
• Verbose -- control the verbosity of output
• versalDeformation -- computes a power series representation of a versal deformation
• versalDeformation(List,List,List,List) -- continues calculation of a versal deformation
• versalDeformation(List,List,List,List,CacheName=>...) -- determines hash table in which to cache solutions to the deformation equation
• versalDeformation(List,List,List,List,CorrectionMatrix=>...) -- determines the first order deformations used in correcting liftings
• versalDeformation(List,List,List,List,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• versalDeformation(List,List,List,List,HighestOrder=>...) -- sets the order to which we compute
• versalDeformation(List,List,List,List,PolynomialCheck=>...) -- checks if power series solution terminates
• versalDeformation(List,List,List,List,SanityCheck=>...) -- checks if lifting solves deformation equation
• versalDeformation(List,List,List,List,SmartLift=>...) -- chooses lifting to avoid obstructions at next order
• versalDeformation(List,List,List,List,Verbose=>...) -- control the verbosity of output
• versalDeformation(Matrix) -- computes a power series representation of a versal deformation
• versalDeformation(Matrix,CacheName=>...) -- determines hash table in which to cache solutions to the deformation equation
• versalDeformation(Matrix,CorrectionMatrix=>...) -- determines the first order deformations used in correcting liftings
• versalDeformation(Matrix,DefParam=>...) -- deformation parameter
• versalDeformation(Matrix,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• versalDeformation(Matrix,HighestOrder=>...) -- sets the order to which we compute
• versalDeformation(Matrix,Matrix,Matrix) -- computes a power series representation of a versal deformation
• versalDeformation(Matrix,Matrix,Matrix,CacheName=>...) -- determines hash table in which to cache solutions to the deformation equation
• versalDeformation(Matrix,Matrix,Matrix,CorrectionMatrix=>...) -- determines the first order deformations used in correcting liftings
• versalDeformation(Matrix,Matrix,Matrix,DefParam=>...) -- deformation parameter
• versalDeformation(Matrix,Matrix,Matrix,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• versalDeformation(Matrix,Matrix,Matrix,HighestOrder=>...) -- sets the order to which we compute
• versalDeformation(Matrix,Matrix,Matrix,PolynomialCheck=>...) -- checks if power series solution terminates
• versalDeformation(Matrix,Matrix,Matrix,SanityCheck=>...) -- checks if lifting solves deformation equation
• versalDeformation(Matrix,Matrix,Matrix,SmartLift=>...) -- chooses lifting to avoid obstructions at next order
• versalDeformation(Matrix,Matrix,Matrix,Verbose=>...) -- control the verbosity of output
• versalDeformation(Matrix,PolynomialCheck=>...) -- checks if power series solution terminates
• versalDeformation(Matrix,SanityCheck=>...) -- checks if lifting solves deformation equation
• versalDeformation(Matrix,SmartLift=>...) -- chooses lifting to avoid obstructions at next order
• versalDeformation(Matrix,Verbose=>...) -- control the verbosity of output
• versalDeformation(NestedDeformation) -- continues calculation of a versal deformation
• versalDeformation(NestedDeformation,DegreeBound=>...) -- determines the degree limit used to compute the tangent cone of obstruction equations
• versalDeformation(NestedDeformation,HighestOrder=>...) -- sets the order to which we compute
• versalDeformation(NestedDeformation,PolynomialCheck=>...) -- checks if power series solution terminates
• versalDeformation(NestedDeformation,SanityCheck=>...) -- checks if lifting solves deformation equation
• versalDeformation(NestedDeformation,Verbose=>...) -- control the verbosity of output
• VersalDeformationResults -- hash table key for cached solutions to the deformation equation
• VersalDeformations -- calculating versal deformations and local Hilbert schemes