Cremona : Table of Contents

• Cremona -- package for some computations on rational maps between projective varieties
• abstractRationalMap -- make an abstract rational map
• approximateInverseMap -- random map related to the inverse of a birational map
• BlowUpStrategy
• Certify -- whether to ensure correctness of output
• ChernSchwartzMacPherson -- Chern-Schwartz-MacPherson class of a projective scheme
• CodimBsInv
• coefficientRing(RationalMap) -- coefficient ring of a rational map
• coefficients(RationalMap) -- coefficient matrix of a rational map
• degree(RationalMap) -- degree of a rational map
• degreeMap -- degree of a rational map between projective varieties
• degreeMap(RationalMap) -- degree of a rational map
• degrees(RationalMap) -- projective degrees of a rational map
• describe(RationalMap) -- describe a rational map
• Dominant
• entries(RationalMap) -- the entries of the matrix associated to a rational map
• EulerCharacteristic -- topological Euler characteristic of a (smooth) projective variety
• exceptionalLocus -- exceptional locus of a birational map
• flatten(RationalMap) -- write source and target as nondegenerate varieties
• forceImage -- declare which is the image of a rational map
• forceInverseMap -- declare that two rational maps are one the inverse of the other
• graph -- closure of the graph of a rational map
• graph(RingMap) -- closure of the graph of a rational map
• ideal(RationalMap) -- base locus of a rational map
• image(RationalMap,String) -- closure of the image of a rational map using the F4 algorithm (experimental)
• image(RationalMap,ZZ) -- closure of the image of a rational map
• inverse(RationalMap) -- inverse of a birational map
• inverseMap -- inverse of a birational map
• inverseMap(...,Verbose=>...)
• isBirational -- whether a rational map is birational
• isDominant -- whether a rational map is dominant
• isInverseMap -- checks whether a rational map is the inverse of another
• isInverseMap(RationalMap,RationalMap) -- checks whether two rational maps are one the inverse of the other
• isIsomorphism(RationalMap) -- whether a birational map is an isomorphism
• isMorphism -- whether a rational map is a morphism
• kernel(RingMap,ZZ) -- homogeneous components of the kernel of a homogeneous ring map
• map(RationalMap) -- get the ring map defining a rational map
• matrix(RationalMap) -- the matrix associated to a rational map
• NumDegrees
• parametrize -- parametrization of a rational projective variety
• parametrize(Ideal) -- parametrization of linear varieties and hyperquadrics
• point -- pick a random rational point on a projective variety
• point(QuotientRing) -- pick a random rational point on a projective variety
• projectiveDegrees -- projective degrees of a rational map between projective varieties
• projectiveDegrees(RationalMap) -- projective degrees of a rational map
• quadroQuadricCremonaTransformation -- quadro-quadric Cremona transformations
• RationalMap -- the class of all rational maps between absolutely irreducible projective varieties over a field
• rationalMap -- makes a rational map
• RationalMap ! -- calculates every possible thing
• RationalMap * RationalMap -- composition of rational maps
• RationalMap ** Ring -- change the coefficient ring of a rational map
• RationalMap == RationalMap -- equality of rational maps
• RationalMap ^ ZZ -- power
• RationalMap ^** Ideal -- inverse image via a rational map
• RationalMap _* -- direct image via a rational map
• RationalMap | Ideal -- restriction of a rational map
• RationalMap || Ideal -- restriction of a rational map
• rationalMap(Ideal,ZZ,ZZ) -- makes a rational map from an ideal
• rationalMap(PolynomialRing,List) -- rational map defined by the linear system of hypersurfaces passing through random points with multiplicity
• rationalMap(Ring,Tally) -- rational map defined by an effective divisor
• segre -- Segre embedding
• SegreClass -- Segre class of a closed subscheme of a projective variety
• source(RationalMap) -- coordinate ring of the source for a rational map
• specialCremonaTransformation -- special Cremona transformations whose base locus has dimension at most three
• specialCubicTransformation -- special cubic transformations whose base locus has dimension at most three
• specialQuadraticTransformation -- special quadratic transformations whose base locus has dimension three
• substitute(RationalMap,PolynomialRing,PolynomialRing) -- substitute the ambient projective spaces of source and target
• super(RationalMap) -- get the rational map whose target is a projective space
• target(RationalMap) -- coordinate ring of the target for a rational map
• toExternalString(RationalMap) -- convert to a readable string
• toMap -- rational map defined by a linear system