SRdeformations : Index

• 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.