MultiprojectiveVarieties : Index

• ? MultiprojectiveVariety -- describe a multi-projective variety
• ? MultirationalMap -- describe a multi-rational map
• |- MultiprojectiveVariety -- pick a random rational point on a multi-projective variety
• ∏ -- product of multi-projective varieties
• ∏(List) -- product of multi-projective varieties
• ⋂ -- intersection of multi-projective varieties
• ⋂(List) -- intersection of multi-projective varieties
• ⋃ -- union of multi-projective varieties
• ⋃(List) -- union of multi-projective varieties
• ambient(MultiprojectiveVariety) -- the ambient multi-projective space of the variety
• ambientVariety -- the ambient variety of a projective subvariety
• ambientVariety(MultiprojectiveVariety) -- the ambient variety of a projective subvariety
• baseLocus -- the base locus of a multi-rational map
• baseLocus(MultirationalMap) -- the base locus of a multi-rational map
• baseLocus(RationalMap) -- the base locus of a multi-rational map
• check(MultirationalMap) -- check that a multi-rational map is well-defined
• chowForm(EmbeddedProjectiveVariety) -- chow forms of a projective variety
• clean(MultirationalMap) -- clean the internal information of a multi-rational map
• clean(RationalMap) -- clean the internal information of a multi-rational map
• codim(MultiprojectiveVariety) -- the codimension of the variety
• coefficientRing(MultiprojectiveVariety) -- the coefficient ring of the variety
• coefficientRing(MultirationalMap) -- the coefficient ring of a multi-rational map
• compose(MultirationalMap,MultirationalMap) -- composition of multi-rational maps
• coneOfLines -- cone of lines on a subvariety passing through a point
• coneOfLines(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety) -- cone of lines on a subvariety passing through a point
• conormalVariety(EmbeddedProjectiveVariety) -- the conormal variety of a projective variety
• cycleClass -- determine the expression of the class of a cycle as a linear combination of Schubert classes
• cycleClass(EmbeddedProjectiveVariety) -- determine the expression of the class of a cycle as a linear combination of Schubert classes
• decompose(MultiprojectiveVariety) -- irreducible components of a variety
• degree(MultiprojectiveVariety) -- the degree of the variety
• degree(MultirationalMap) -- degree of a multi-rational map
• degree(MultirationalMap,Option) -- degree of a multi-rational map using a probabilistic approach
• degreeMap(MultirationalMap) -- degree of a multi-rational map
• degrees(MultiprojectiveVariety) -- degrees for the minimal generators
• degreeSequence -- the (multi)-degree sequence of a (multi)-rational map
• degreeSequence(MultirationalMap) -- the (multi)-degree sequence of a (multi)-rational map
• degreeSequence(RationalMap) -- the (multi)-degree sequence of a (multi)-rational map
• describe(MultiprojectiveVariety) -- describe a multi-projective variety
• describe(MultirationalMap) -- describe a multi-rational map
• dim(MultiprojectiveVariety) -- the dimension of the variety
• dual(EmbeddedProjectiveVariety) -- the variety projectively dual to an embedded projective variety
• EmbeddedProjectiveVariety -- the class of all embedded projective varieties
• EmbeddedProjectiveVariety ! -- print a more detailed description of an embedded projective variety
• EmbeddedProjectiveVariety ++ EmbeddedProjectiveVariety -- join of projective varieties
• EmbeddedProjectiveVariety <=== EmbeddedProjectiveVariety -- try to find an isomorphism between two projective varieties
• EmbeddedProjectiveVariety ===> EmbeddedProjectiveVariety -- try to find an isomorphism between two projective varieties
• entries(MultirationalMap) -- list the defining polynomials of a rational map
• euler(MultiprojectiveVariety) -- topological Euler characteristic of a (smooth) multi-projective variety
• factor(MultirationalMap) -- the list of rational maps defining a multi-rational map
• Fano(EmbeddedProjectiveVariety) -- Fano scheme of a projective variety
• Fano(ZZ,EmbeddedProjectiveVariety) -- Fano scheme of a projective variety
• fiberProduct -- fiber product of multi-projective varieties
• fiberProduct(RationalMap,RationalMap) -- fiber product of multi-projective varieties
• forceImage(MultirationalMap,MultiprojectiveVariety) -- declare which is the image of a multi-rational map
• forceImage(MultirationalMap,ZZ) -- declare which is the image of a multi-rational map
• GG -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• GG(EmbeddedProjectiveVariety) -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• GG(Ring) -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• GG(Ring,ZZ,ZZ) -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• GG(ZZ,EmbeddedProjectiveVariety) -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• GG(ZZ,MultirationalMap) -- induced automorphism of the Grassmannian
• GG(ZZ,RationalMap) -- induced automorphism of the Grassmannian
• GG(ZZ,ZZ) -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space
• graph(MultirationalMap) -- the graph of a multi-rational map
• GrassmannianVariety -- the class of all Grassmannians of linear subspaces of projective spaces
• hilbertPolynomial(EmbeddedProjectiveVariety) -- the Hilbert polynomial of the variety
• Hom(MultiprojectiveVariety,MultiprojectiveVariety) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(MultiprojectiveVariety,Nothing) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(MultiprojectiveVariety,Symbol) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(Nothing,MultiprojectiveVariety) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(Nothing,Nothing) -- get the hom-set of rational maps between two multi-projective varieties
• Hom(Nothing,Symbol) -- get the hom-set of rational maps between two multi-projective varieties
• ideal(MultiprojectiveVariety) -- the defining ideal of the variety
• image(MultirationalMap) -- image of a multi-rational map
• inverse(MultirationalMap) -- inverse of a birational map
• inverse2 -- inverse of a birational map using a faster algorithm for a special class of maps
• inverse2(MultirationalMap) -- inverse of a birational map using a faster algorithm for a special class of maps
• isIsomorphism(MultirationalMap) -- whether a birational map is an isomorphism
• isMember(MultirationalMap,RAT) -- test membership in a hom-set of rational maps
• isMorphism(MultirationalMap) -- whether a multi-rational map is a morphism
• isSubset(MultiprojectiveVariety,MultiprojectiveVariety) -- whether one variety is a subvariety of another
• isWellDefined(MultirationalMap) -- whether a multi-rational map is well-defined
• linearlyNormalEmbedding -- get the linearly normal embedding
• linearlyNormalEmbedding(EmbeddedProjectiveVariety) -- get the linearly normal embedding
• linearSpan -- the linear span of an embedded projective variety
• linearSpan(EmbeddedProjectiveVariety) -- the linear span of an embedded projective variety
• linearSpan(List) -- the linear span of an embedded projective variety
• multidegree(MultiprojectiveVariety) -- the multidegree of the variety
• multidegree(MultirationalMap) -- projective degrees of a multi-rational map
• multidegree(ZZ,MultirationalMap) -- i-th projective degree of a multi-rational map using a probabilistic approach
• MultiprojectiveVarieties -- Multi-projective varieties and multi-rational maps
• MultiprojectiveVariety -- the class of all multi-projective varieties
• MultiprojectiveVariety % MultiprojectiveVariety -- subvariety of a projective variety
• MultiprojectiveVariety * MultiprojectiveVariety -- intersection of two multi-projective varieties
• MultiprojectiveVariety ** MultiprojectiveVariety -- product of two multi-projective varieties
• MultiprojectiveVariety ** Ring -- change the coefficient ring of a multi-projective variety
• MultiprojectiveVariety + MultiprojectiveVariety -- union of two multi-projective varieties
• MultiprojectiveVariety << MultiprojectiveVariety -- force the change of the target in a multi-rational map
• MultiprojectiveVariety == MultiprojectiveVariety -- equality of multi-projective varieties
• MultiprojectiveVariety \ MultiprojectiveVariety -- difference of multi-projective varieties
• MultiprojectiveVariety \\ MultiprojectiveVariety -- difference of multi-projective varieties
• MultiprojectiveVariety ^ ZZ -- power of a multi-projective variety
• MultirationalMap -- the class of all multi-rational maps
• multirationalMap -- the multi-rational map defined by a list of rational maps
• MultirationalMap * MultirationalMap -- composition of multi-rational maps
• MultirationalMap * RationalMap -- composition of multi-rational maps
• MultirationalMap ** Ring -- change the coefficient ring of a multi-rational map
• MultirationalMap << MultiprojectiveVariety -- force the change of the target in a multi-rational map
• MultirationalMap <==> MultirationalMap -- equality of multi-rational maps with checks on internal data
• MultirationalMap == MultirationalMap -- equality of multi-rational maps
• MultirationalMap == RationalMap -- equality of multi-rational maps
• MultirationalMap == ZZ -- equality of multi-rational maps
• MultirationalMap ^ ZZ -- composition of multi-rational maps
• MultirationalMap ^* -- inverse image via a multi-rational map
• MultirationalMap ^** MultiprojectiveVariety -- inverse image via a multi-rational map
• MultirationalMap | List -- restriction of a multi-rational map
• MultirationalMap | MultiprojectiveVariety -- restriction of a multi-rational map
• MultirationalMap | MultirationalMap -- product of multi-rational maps
• MultirationalMap | RationalMap -- product of multi-rational maps
• MultirationalMap || List -- restriction of a multi-rational map
• MultirationalMap || MultiprojectiveVariety -- restriction of a multi-rational map
• MultirationalMap || MultirationalMap -- product of multi-rational maps
• MultirationalMap || RationalMap -- product of multi-rational maps
• MultirationalMap MultiprojectiveVariety -- direct image via a multi-rational map
• multirationalMap(List) -- the multi-rational map defined by a list of rational maps
• multirationalMap(List,MultiprojectiveVariety) -- the multi-rational map defined by a list of rational maps
• multirationalMap(MultiprojectiveVariety) -- identity map
• multirationalMap(MultiprojectiveVariety,MultiprojectiveVariety) -- get the natural inclusion
• multirationalMap(MultirationalMap,MultiprojectiveVariety) -- change the target of a multi-rational map
• multirationalMap(RationalMap) -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• parametrize(MultiprojectiveVariety) -- try to get a parametrization of a multi-projective variety
• permute(MultiprojectiveVariety,List) -- permute the factors of the ambient multi-projective space
• point(MultiprojectiveVariety) -- pick a random rational point on a multi-projective variety
• PP -- product of projective spaces
• projectionMaps -- projections of a multi-projective variety
• projectionMaps(MultiprojectiveVariety) -- projections of a multi-projective variety
• projectionMaps(MultirationalMap) -- get the compositions of the multi-rational map with the projections of the target
• projections -- projections of a multi-projective variety
• projections(MultiprojectiveVariety) -- projections of a multi-projective variety
• projectiveDegrees(MultirationalMap) -- projective degrees of a multi-rational map
• projectiveVariety -- the closed multi-projective subvariety defined by a multi-homogeneous ideal
• projectiveVariety(...,MinimalGenerators=>...) -- whether to trim the ideal (intended for internal use only)
• projectiveVariety(...,Saturate=>...) -- whether to compute the multi-saturation of the ideal (intended for internal use only)
• projectiveVariety(Ideal) -- the closed multi-projective subvariety defined by a multi-homogeneous ideal
• projectiveVariety(List,List,Ring) -- the Segre-Veronese variety
• projectiveVariety(List,Ring) -- product of projective spaces
• projectiveVariety(Matrix) -- the closed multi-projective subvariety defined by a multi-homogeneous ideal
• projectiveVariety(MultidimensionalMatrix) -- the multi-projective variety defined by a multi-dimensional matrix
• projectiveVariety(Ring) -- the closed multi-projective subvariety defined by a multi-homogeneous ideal
• projectiveVariety(RingElement) -- the closed multi-projective subvariety defined by a multi-homogeneous ideal
• projectiveVariety(ZZ,Ring) -- product of projective spaces
• projectiveVariety(ZZ,ZZ,Ring) -- the Segre-Veronese variety
• random(List,MultiprojectiveVariety) -- get a random hypersurface of given multi-degree containing a multi-projective variety
• random(MultiprojectiveVariety) -- apply a random automorphism of the ambient multi-projective space
• random(ZZ,MultiprojectiveVariety) -- get a random hypersurface of given multi-degree containing a multi-projective variety
• RAT -- the hom-sets of rational maps between two multi-projective varieties
• RAT List -- define a multi-rational map
• RAT MultiprojectiveVariety -- rational map defined by a linear system of hypersurfaces through a variety
• RAT Sequence -- rational map defined by a linear system of hypersurfaces through a variety
• RAT Tally -- rational map defined by an effective divisor
• RationalMap * MultirationalMap -- composition of multi-rational maps
• RationalMap == MultirationalMap -- equality of multi-rational maps
• RationalMap ^** EmbeddedProjectiveVariety -- inverse image via a multi-rational map
• RationalMap | MultiprojectiveVariety -- restriction of a multi-rational map
• RationalMap | MultirationalMap -- product of multi-rational maps
• RationalMap | RationalMap -- product of multi-rational maps
• RationalMap || MultiprojectiveVariety -- restriction of a multi-rational map
• RationalMap || MultirationalMap -- product of multi-rational maps
• RationalMap || RationalMap -- product of multi-rational maps
• RationalMap MultiprojectiveVariety -- direct image via a multi-rational map
• rationalMap(EmbeddedProjectiveVariety,Tally,ZZ) -- rational map defined by an effective divisor
• rationalMap(List,MultiprojectiveVariety) -- the multi-rational map defined by a list of rational maps
• rationalMap(MultiprojectiveVariety) -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• rationalMap(MultiprojectiveVariety,List) -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• rationalMap(MultiprojectiveVariety,MultiprojectiveVariety) -- get the natural inclusion
• rationalMap(MultiprojectiveVariety,Tally) -- rational map defined by an effective divisor
• rationalMap(MultiprojectiveVariety,Tally,List) -- rational map defined by an effective divisor
• rationalMap(MultiprojectiveVariety,ZZ) -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• rationalMap(MultiprojectiveVariety,ZZ,ZZ) -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• rationalMap(MultirationalMap) -- the multi-rational map defined by a list of rational maps
• rationalMap(MultirationalMap,MultiprojectiveVariety) -- change the target of a multi-rational map
• ring(MultiprojectiveVariety) -- the coordinate ring of the variety
• Saturate -- whether to compute the multi-saturation of the ideal (intended for internal use only)
• schubertCycle -- take a random Schubert cycle
• schubertCycle(...,Standard=>...) -- take a random Schubert cycle
• schubertCycle(VisibleList,GrassmannianVariety) -- take a random Schubert cycle
• sectionalGenus -- the sectional genus of an embedded projective variety
• sectionalGenus(EmbeddedProjectiveVariety) -- the sectional genus of an embedded projective variety
• segre(MultiprojectiveVariety) -- the Segre embedding of the variety
• segre(MultirationalMap) -- the composition of a multi-rational map with the Segre embedding of the target
• segreEmbedding -- the Segre embedding of the variety
• segreEmbedding(MultiprojectiveVariety) -- the Segre embedding of the variety
• shape(MultiprojectiveVariety) -- shape of the ambient multi-projective space of a multi-projective variety
• shortcuts -- Some convenient shortcuts for multi-rational maps consisting of a single rational map
• show(MultirationalMap) -- display a multi-rational map
• show(RationalMap) -- display a multi-rational map
• singularLocus(MultiprojectiveVariety) -- the singular locus of the variety
• source(MultirationalMap) -- the source for a multi-rational map
• sumUp -- print a more detailed description of an embedded projective variety
• sumUp(EmbeddedProjectiveVariety) -- print a more detailed description of an embedded projective variety
• super(MultirationalMap) -- get the multi-rational map whose target is a product of projective spaces
• support(MultiprojectiveVariety) -- support of a multi-projective variety
• tangentCone(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety) -- tangent cone to a projective variety at a point
• tangentialChowForm(EmbeddedProjectiveVariety,ZZ) -- higher Chow forms of a projective variety
• tangentSpace -- tangent space to a projective variety at a point
• tangentSpace(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety) -- tangent space to a projective variety at a point
• target(MultirationalMap) -- the target for a multi-rational map
• topComponents(MultiprojectiveVariety) -- union of the top dimensional components of a multi-projective variety
• toRationalMap -- convert a multi-rational map consisting of a single rational map to a standard rational map
• toRationalMap(MultirationalMap) -- convert a multi-rational map consisting of a single rational map to a standard rational map
• trim(MultirationalMap) -- trim the target of a multi-rational map
• trim(RationalMap) -- trim the target of a multi-rational map
• variety(EmbeddedProjectiveVariety) -- convert an embedded projective variety into a built-in projective variety
• WeightedProjectiveVariety -- the class of all weighted projective varieties
• WeightedRationalMap -- the class of all weighted-rational maps
• ZZ == MultirationalMap -- equality of multi-rational maps
• ZZ _ MultiprojectiveVariety -- identity map