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SRdeformations : Index
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addCokerGrading
-- Stores a cokernel grading in a polynomial ring.
addCokerGrading(PolynomialRing)
-- Stores a cokernel grading in a polynomial ring.
addCokerGrading(PolynomialRing,List)
-- Stores a cokernel grading in a polynomial ring.
addCokerGrading(PolynomialRing,Matrix)
-- Stores a cokernel grading in a polynomial ring.
addFaceDataToComplex
-- Adds to a complex face data.
addFaceDataToComplex(Complex,List)
-- Adds to a complex face data.
addFaceDataToComplex(Complex,List,List)
-- Adds to a complex face data.
addFacetDataToComplex
-- Adds to a complex facet data.
addFacetDataToComplex(Complex,List)
-- Adds to a complex facet data.
bigTorusDegree
-- The big torus degree of a deformation.
bigTorusDegree(FirstOrderDeformation)
-- The big torus degree of a deformation.
boundaryCyclicPolytope
-- The boundary complex of a cyclic polytope.
boundaryCyclicPolytope(ZZ,PolynomialRing)
-- The boundary complex of a cyclic polytope.
boundaryOfPolytope
-- The boundary of a polytope.
boundaryOfPolytope(Complex)
-- The boundary of a polytope.
closedStar
-- The closed star of a face of a complex.
closedStar(Face,Complex)
-- The closed star of a face of a complex.
CoComplex
-- The class of all embedded co-complexes.
coComplex
-- Make a co-complex.
coComplex(PolynomialRing,List)
-- Make a co-complex.
coComplex(PolynomialRing,List,List)
-- Make a co-complex.
coComplex(PolynomialRing,List,List,PolynomialRing)
-- Make a co-complex.
coComplex(PolynomialRing,List,PolynomialRing)
-- Make a co-complex.
coComplexToIdeal
-- The monomial ideal associated to a CoComplex.
coComplexToIdeal(CoComplex)
-- The monomial ideal associated to a CoComplex.
cokerElement
-- Gives an element in the cokernel of a matrix.
cokerElement(Matrix,Matrix)
-- Gives an element in the cokernel of a matrix.
cokerElement(Vector,Matrix)
-- Gives an element in the cokernel of a matrix.
complement(Complex)
-- Compute the complement CoComplex.
complement(Face)
-- Compute the complement face of a simplex.
complementComplex
-- Optional data of Complex.
Complex
-- The class of all embedded complexes.
complex
-- Make a complex.
Complex == Complex
-- Compare two complexes.
complex(PolynomialRing,List)
-- Make a complex.
complex(PolynomialRing,List,List)
-- Make a complex.
complex(PolynomialRing,List,List,PolynomialRing)
-- Make a complex.
complex(PolynomialRing,List,PolynomialRing)
-- Make a complex.
complexFromFacets
-- Make a complex from its facets.
complexFromFacets(PolynomialRing,List)
-- Make a complex from its facets.
complexFromFacets(PolynomialRing,List,PolynomialRing)
-- Make a complex from its facets.
complexToIdeal
-- The monomial ideal associated to a complex.
complexToIdeal(...,embedded=>...)
-- Use only faces of the embedding complex.
complexToIdeal(Complex)
-- The monomial ideal associated to a complex.
computeFaces
-- Compute faces of a simplex.
convHull
-- The convex hull complex.
convHull(...,file=>...)
-- Store result of a computation in a file.
convHull(List)
-- The convex hull complex.
convHull(String)
-- The convex hull complex.
coordinates
-- The coordinates of a face.
coordinates(Face)
-- The coordinates of a face.
coordinates(Face,Complex)
-- The coordinates of a face.
deform
-- Compute the deformations associated to a Stanley-Reisner complex.
deform(Complex)
-- Compute the deformations associated to a Stanley-Reisner complex.
deformationsFace
-- Compute the deformations associated to a face.
deformationsFace(Face,Complex)
-- Compute the deformations associated to a face.
deformationsFace(Face,Complex,Ideal)
-- Compute the deformations associated to a face.
degree(FirstOrderDeformation)
-- The small torus degree of a deformation.
denominator(FirstOrderDeformation)
-- The denominator of a deformation as a vector.
denominatorMonomial
-- The denominator monomial of a deformation.
denominatorMonomial(FirstOrderDeformation)
-- The denominator monomial of a deformation.
dim(Complex)
-- Compute the dimension of a complex or co-complex.
dim(Face)
-- Compute the dimension of a face.
dim(Face,Complex)
-- Compute the dimension of a face.
dim(Face,PolynomialRing)
-- Compute the dimension of a face.
dim(FirstOrderDeformation)
-- Compute the dimension of a deformation.
dualComplex
-- Optional data of Complex.
dualFace
-- Optional data of Face.
dualGrading
-- The dual vertices of a polytope.
dualGrading(Complex)
-- The dual vertices of a polytope.
dualize
-- The dual of a face or complex.
dualize(Complex)
-- The dual of a face or complex.
dualize(Face)
-- The dual of a face or complex.
edim
-- The embedding dimension of a complex or co-complex.
edim(Complex)
-- The embedding dimension of a complex or co-complex.
embedded
-- Use only faces of the embedding complex.
embeddingComplex
-- The embedding complex of a complex or co-complex.
embeddingComplex(Complex)
-- The embedding complex of a complex or co-complex.
eulerCharacteristic
-- The Euler characteristic of a complex.
eulerCharacteristic(Complex)
-- The Euler characteristic of a complex.
eulerCharacteristic(List)
-- The Euler characteristic of a complex.
Example first order deformation
-- Example accessing the data stored in a first order deformation.
Face
-- The class of all faces of complexes or co-complexes.
face
-- Generate a face.
Face == Face
-- Compare two faces.
face(List)
-- Generate a face.
face(List,Complex)
-- Generate a face.
face(List,Complex,ZZ,ZZ)
-- Generate a face.
face(Set)
-- Generate a face.
faceToMonomial
-- The monomial of a face.
faceToMonomial(Face)
-- The monomial of a face.
faceToMonomial(Face,PolynomialRing)
-- The monomial of a face.
facets
-- The maximal faces of a complex.
facets(Complex)
-- The maximal faces of a complex.
facets(List)
-- The maximal faces of a complex.
fc
-- The faces of a complex.
fc(Complex)
-- The faces of a complex.
fc(Complex,ZZ)
-- The faces of a complex.
file
-- Store result of a computation in a file.
FirstOrderDeformation
-- The class of all first order deformations of monomial ideals.
firstOrderDeformation
-- Makes a first order deformation.
FirstOrderDeformation == FirstOrderDeformation
-- Compare two first order deformations.
firstOrderDeformation(Ideal,Vector)
-- Makes a first order deformation.
firstOrderDeformation(Matrix,Vector)
-- Makes a first order deformation.
firstOrderDeformation(MonomialIdeal,Vector)
-- Makes a first order deformation.
fullCyclicPolytope
-- Cyclic polytope.
fullCyclicPolytope(ZZ,PolynomialRing)
-- Cyclic polytope.
fullCyclicPolytope(ZZ,PolynomialRing,PolynomialRing)
-- Cyclic polytope.
fvector
-- The F-vector of a complex.
fvector(Complex)
-- The F-vector of a complex.
fvector(List)
-- The F-vector of a complex.
gensSource
-- Generators of the source of a deformation.
gensSource(FirstOrderDeformation)
-- Generators of the source of a deformation.
globalSections
-- The global sections of a toric divisor.
globalSections(Matrix,Vector)
-- The global sections of a toric divisor.
globalSections(Matrix,Vector,List)
-- The global sections of a toric divisor.
grading
-- The grading of a first order deformation or complex or polynomial ring.
grading(Complex)
-- The grading of a complex.
grading(FirstOrderDeformation)
-- The small torus grading of a deformation.
grading(PolynomialRing)
-- The coker grading of a polynomial ring.
HH Complex
-- Compute the homology of a complex.
hull
-- The positive hull complex.
hull(...,file=>...)
-- Store result of a computation in a file.
hull(List)
-- The positive hull complex.
hull(String)
-- The positive hull complex.
idealToCoComplex
-- The co-complex associated to a reduced monomial ideal.
idealToCoComplex(Ideal)
-- The co-complex associated to a reduced monomial ideal.
idealToCoComplex(Ideal,Complex)
-- The co-complex associated to a reduced monomial ideal.
idealToCoComplex(MonomialIdeal)
-- The co-complex associated to a reduced monomial ideal.
idealToCoComplex(MonomialIdeal,Complex)
-- The co-complex associated to a reduced monomial ideal.
idealToComplex
-- The complex associated to a reduced monomial ideal.
idealToComplex(Ideal)
-- The complex associated to a reduced monomial ideal.
idealToComplex(Ideal,Complex)
-- The complex associated to a reduced monomial ideal.
idealToComplex(MonomialIdeal)
-- The complex associated to a reduced monomial ideal.
idealToComplex(MonomialIdeal,Complex)
-- The complex associated to a reduced monomial ideal.
indices(Face)
-- The indices of a face.
intersectFaces
-- The intersection of two faces.
intersectFaces(Face,Face)
-- The intersection of two faces.
intersectFaces(List)
-- The intersection of two faces.
isEquidimensional
-- Check whether a complex or co-complex is equidimensional.
isEquidimensional(Complex)
-- Check whether a complex or co-complex is equidimensional.
isEquidimensional(List)
-- Check whether a complex or co-complex is equidimensional.
isHomogeneous(FirstOrderDeformation)
-- Check whether a deformation is homogeneous.
isNonzero
-- Check whether a deformation is non-zero.
isNonzero(FirstOrderDeformation)
-- Check whether a deformation is non-zero.
isPolytope
-- Check whether a complex is a polytope.
isPolytope(Complex)
-- Check whether a complex is a polytope.
isPolytope(List)
-- Check whether a complex is a polytope.
isSimp
-- Check whether a complex or co-complex is simplicial.
isSimp(Complex)
-- Check whether a complex or co-complex is simplicial.
isSimp(List)
-- Check whether a complex or co-complex is simplicial.
isSubface
-- Checks whether a face is a subface of another face.
isSubface(Face,Face)
-- Checks whether a face is a subface of another face.
isTrivial
-- Check whether a deformation is trivial.
isTrivial(FirstOrderDeformation)
-- Check whether a deformation is trivial.
isTrivial(Vector)
-- Check whether a deformation is trivial.
iszero
-- Tests whether something is zero.
iszero(Thing)
-- Tests whether something is zero.
joinVectors
-- Converts a list of vectors to a matrix.
joinVectors(List)
-- Converts a list of vectors to a matrix.
laurent
-- Converts an exponent vector or a deformation into a Laurent monomial.
laurent(FirstOrderDeformation)
-- Converts an exponent vector or a deformation into a Laurent monomial.
laurent(Vector,PolynomialRing)
-- Converts an exponent vector or a deformation into a Laurent monomial.
link
-- The link of a face of a complex.
link(Face,Complex)
-- The link of a face of a complex.
loadDeformations
-- Read the deformation data of a complex from a file.
loadDeformations(Complex,String)
-- Read the deformation data of a complex from a file.
minimalNonFaces
-- The minimal non-faces of a complex.
minimalNonFaces(...,embedded=>...)
-- Use only faces of the embedding complex.
minimalNonFaces(Complex)
-- The minimal non-faces of a complex.
mirrorSphere
-- Example how to compute the mirror sphere.
net(Complex)
-- Printing complexes.
net(Face)
-- Printing faces.
net(FirstOrderDeformation)
-- Pretty print for deformations.
newEmptyComplex
-- Generates an empty complex.
newEmptyComplex(PolynomialRing)
-- Generates an empty complex.
noBoundary
-- Optional data of Complex.
numerator(FirstOrderDeformation)
-- The numerator of a deformation as a vector.
numeratorMonomial
-- The numerator monomial of a deformation.
numeratorMonomial(FirstOrderDeformation)
-- The numerator monomial of a deformation.
ofComplex
-- The complex of a face.
ofComplex(Face)
-- The complex of a face.
parameters
-- Parameters of a deformation.
parameters(FirstOrderDeformation)
-- Parameters of a deformation.
parameters(Matrix,Vector)
-- Parameters of a deformation.
polytopalFacets
-- The facets of a polytope.
polytopalFacets(Complex)
-- The facets of a polytope.
possibleDenominators
-- Possible denominators of deformations.
possibleDenominators(Ideal)
-- Possible denominators of deformations.
possibleDenominators(Ideal,List)
-- Possible denominators of deformations.
possibleDenominators(List,List)
-- Possible denominators of deformations.
preImage
-- Compute the preimage.
preImage(Matrix,Vector)
-- Compute the preimage.
PT1
-- Compute the deformation polytope associated to a Stanley-Reisner complex.
PT1(...,file=>...)
-- Store result of a computation in a file.
PT1(Complex)
-- Compute the deformation polytope associated to a Stanley-Reisner complex.
raysPPn
-- The rays of the standard fan of projective space or weighted projective space.
raysPPn(List)
-- The rays of the standard fan of projective space or weighted projective space.
raysPPn(ZZ)
-- The rays of the standard fan of projective space or weighted projective space.
relationsCoefficients
-- Relations between the coefficients of a deformation.
relationsCoefficients(FirstOrderDeformation)
-- Relations between the coefficients of a deformation.
relationsCoefficients(Matrix,Vector)
-- Relations between the coefficients of a deformation.
saveDeformations
-- Store the deformation data of a complex in a file.
saveDeformations(Complex,String)
-- Store the deformation data of a complex in a file.
simplex
-- Simplex in the variables of a polynomial ring.
simplex(...,computeFaces=>...)
-- Compute faces of a simplex.
simplex(PolynomialRing)
-- Simplex in the variables of a polynomial ring.
simplex(PolynomialRing,PolynomialRing)
-- Simplex in the variables of a polynomial ring.
simplexDim
-- The dimension of a face inside the vertex simplex.
simplexDim(Face)
-- The dimension of a face inside the vertex simplex.
simplexRing
-- The underlying polynomial ring of a deformation or face or complex.
simplexRing(Complex)
-- The underlying polynomial ring of a complex.
simplexRing(Face)
-- The underlying polynomial ring of a face.
simplexRing(FirstOrderDeformation)
-- The underlying polynomial ring of a deformation or face.
source(FirstOrderDeformation)
-- The source of a deformation.
SRdeformations
-- Deformations of Stanley-Reisner rings and related computations.
target(FirstOrderDeformation)
-- The target of a deformation.
toHom
-- Convert a first order deformation into a homomorphism.
toHom(FirstOrderDeformation)
-- Convert a first order deformation into a homomorphism.
totalSpace
-- Total space of a deformation.
totalSpace(FirstOrderDeformation,PolynomialRing)
-- Total space of a deformation.
totalSpace(List,PolynomialRing)
-- Total space of a deformation.
trivialDeformations
-- Compute the trivial deformations.
trivialDeformations(Complex)
-- Compute the trivial deformations.
trivialDeformations(Ideal,Matrix)
-- Compute the trivial deformations.
trivialDeformations(Matrix)
-- Compute the trivial deformations.
tropDef
-- The co-complex of tropical faces of the deformation polytope.
tropDef(Complex,Complex)
-- The co-complex of tropical faces of the deformation polytope.
variables
-- The variables of a complex or co-complex.
variables(Complex)
-- The variables of a complex or co-complex.
vectorToMonomial
-- Converts an exponent vector into a monomial.
vectorToMonomial(Vector,PolynomialRing)
-- Converts an exponent vector into a monomial.
vert
-- The vertices of a face or complex.
vert(Complex)
-- The vertices of a face or complex.
vert(Face)
-- The vertices of a face or complex.
verticesDualPolytope
-- The dual vertices of a polytope.
verticesDualPolytope(Complex)
-- The dual vertices of a polytope.