Cremona : Index
- abstractRationalMap -- make an abstract rational map
- abstractRationalMap(PolynomialRing,PolynomialRing,FunctionClosure) -- make an abstract rational map
- abstractRationalMap(PolynomialRing,PolynomialRing,FunctionClosure,ZZ) -- make an abstract rational map
- abstractRationalMap(RationalMap) -- make an abstract rational map
- approximateInverseMap -- random map related to the inverse of a birational map
- approximateInverseMap(..., CodimBsInv => ...)
- approximateInverseMap(..., MathMode => ...) -- whether to ensure correctness of output
- approximateInverseMap(..., Verbose => ...)
- approximateInverseMap(RationalMap) -- random map related to the inverse of a birational map
- approximateInverseMap(RationalMap,ZZ) -- random map related to the inverse of a birational map
- approximateInverseMap(RingMap) -- random map related to the inverse of a birational map
- approximateInverseMap(RingMap,ZZ) -- random map related to the inverse of a birational map
- BlowUpStrategy
- ChernSchwartzMacPherson -- Chern-Schwartz-MacPherson class of a projective scheme
- ChernSchwartzMacPherson(..., BlowUpStrategy => ...)
- ChernSchwartzMacPherson(..., MathMode => ...) -- whether to ensure correctness of output
- ChernSchwartzMacPherson(..., Verbose => ...)
- ChernSchwartzMacPherson(Ideal) -- 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
- compose(RationalMap,RationalMap) -- composition of rational maps
- compose(RingMap,RingMap) -- composition of rational maps
- Cremona -- package for some computations on rational maps between projective varieties
- degree(RationalMap) -- degree of a rational map
- degreeOfRationalMap -- degree of a rational map between projective varieties
- degreeOfRationalMap(..., BlowUpStrategy => ...)
- degreeOfRationalMap(..., MathMode => ...) -- whether to ensure correctness of output
- degreeOfRationalMap(..., Verbose => ...)
- degreeOfRationalMap(RationalMap) -- degree of a rational map
- degreeOfRationalMap(RingMap) -- degree of a rational map between projective varieties
- degrees(RationalMap) -- projective degrees of 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
- EulerCharacteristic(..., BlowUpStrategy => ...)
- EulerCharacteristic(..., MathMode => ...) -- whether to ensure correctness of output
- EulerCharacteristic(..., Verbose => ...)
- EulerCharacteristic(Ideal) -- topological Euler characteristic of a (smooth) projective variety
- exceptionalLocus -- exceptional locus of a birational map
- exceptionalLocus(RationalMap) -- 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
- forceImage(RationalMap,Ideal) -- declare which is the image of a rational map
- forceInverseMap -- declare that two rational maps are one the inverse of the other
- forceInverseMap(RationalMap,RationalMap) -- declare that two rational maps are one the inverse of the other
- graph -- closure of the graph of a rational map
- graph(..., BlowUpStrategy => ...)
- graph(RationalMap) -- 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) -- closure of the image of a rational map
- 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(..., BlowUpStrategy => ...)
- inverseMap(..., MathMode => ...) -- whether to ensure correctness of output
- inverseMap(..., Verbose => ...)
- inverseMap(RationalMap) -- inverse of a birational map
- inverseMap(RingMap) -- inverse of a birational map
- isBirational -- whether a rational map is birational
- isBirational(..., BlowUpStrategy => ...)
- isBirational(..., MathMode => ...) -- whether to ensure correctness of output
- isBirational(..., Verbose => ...)
- isBirational(RationalMap) -- whether a rational map is birational
- isBirational(RingMap) -- whether a rational map is birational
- isDominant -- whether a rational map is dominant
- isDominant(..., MathMode => ...) -- whether to ensure correctness of output
- isDominant(..., Verbose => ...)
- isDominant(RationalMap) -- whether a rational map is dominant
- isDominant(RingMap) -- 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
- isInverseMap(RingMap,RingMap) -- checks whether a rational map is the inverse of another
- isIsomorphism(RationalMap) -- whether a birational map is an isomorphism
- isMorphism -- whether a rational map is a morphism
- isMorphism(RationalMap) -- 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
- MathMode -- whether to ensure correctness of output
- matrix(RationalMap) -- the matrix associated to a rational map
- multidegree(RationalMap) -- projective degrees of a rational map
- NumDegrees
- parametrize -- parametrization of linear varieties and hyperquadrics
- parametrize(Ideal) -- parametrization of linear varieties and hyperquadrics
- parametrize(PolynomialRing) -- parametrization of linear varieties and hyperquadrics
- parametrize(QuotientRing) -- parametrization of linear varieties and hyperquadrics
- point -- pick a random rational point on a projective variety
- point(PolynomialRing) -- 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(..., BlowUpStrategy => ...)
- projectiveDegrees(..., MathMode => ...) -- whether to ensure correctness of output
- projectiveDegrees(..., NumDegrees => ...)
- projectiveDegrees(..., Verbose => ...)
- projectiveDegrees(RationalMap) -- projective degrees of a rational map
- projectiveDegrees(RingMap) -- projective degrees of a rational map between projective varieties
- quadroQuadricCremonaTransformation -- quadro-quadric Cremona transformations
- quadroQuadricCremonaTransformation(Ring,ZZ,ZZ) -- quadro-quadric Cremona transformations
- quadroQuadricCremonaTransformation(ZZ,ZZ) -- quadro-quadric Cremona transformations
- quadroQuadricCremonaTransformation(ZZ,ZZ,Ring) -- 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 == RationalMap -- equality of rational maps
- RationalMap == ZZ -- equality of rational maps
- RationalMap ^ ZZ -- power
- RationalMap ^* -- inverse image via a rational map
- RationalMap ^** Ideal -- inverse image via a rational map
- RationalMap _* -- direct image via a rational map
- RationalMap | Ideal -- restriction of a rational map
- RationalMap | Ring -- restriction of a rational map
- RationalMap | RingElement -- restriction of a rational map
- RationalMap || Ideal -- restriction of a rational map
- RationalMap || Ring -- restriction of a rational map
- RationalMap || RingElement -- restriction of a rational map
- RationalMap Ideal -- direct image via a rational map
- rationalMap(..., Dominant => ...)
- rationalMap(Ideal) -- makes a rational map
- rationalMap(Ideal,List) -- makes a rational map
- rationalMap(Ideal,ZZ) -- makes a rational map
- rationalMap(Ideal,ZZ,ZZ) -- makes a rational map
- rationalMap(List) -- makes a rational map
- rationalMap(Matrix) -- makes a rational map
- rationalMap(RationalMap) -- makes a rational map
- rationalMap(Ring) -- makes a rational map
- rationalMap(Ring,Ring) -- makes a rational map
- rationalMap(Ring,Ring,List) -- makes a rational map
- rationalMap(Ring,Ring,Matrix) -- makes a rational map
- rationalMap(RingMap) -- makes a rational map
- segre -- Segre embedding
- segre(PolynomialRing) -- Segre embedding
- segre(QuotientRing) -- Segre embedding
- segre(RationalMap) -- Segre embedding
- SegreClass -- Segre class of a closed subscheme of a projective variety
- SegreClass(..., BlowUpStrategy => ...)
- SegreClass(..., MathMode => ...) -- whether to ensure correctness of output
- SegreClass(..., Verbose => ...)
- SegreClass(Ideal) -- Segre class of a closed subscheme of a projective variety
- SegreClass(RationalMap) -- Segre class of a closed subscheme of a projective variety
- SegreClass(RingMap) -- 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
- specialCremonaTransformation(Ring,ZZ) -- special Cremona transformations whose base locus has dimension at most three
- specialCremonaTransformation(ZZ) -- special Cremona transformations whose base locus has dimension at most three
- specialCremonaTransformation(ZZ,Ring) -- special Cremona transformations whose base locus has dimension at most three
- specialCubicTransformation -- special cubic transformations whose base locus has dimension at most three
- specialCubicTransformation(Ring,ZZ) -- special cubic transformations whose base locus has dimension at most three
- specialCubicTransformation(ZZ) -- special cubic transformations whose base locus has dimension at most three
- specialCubicTransformation(ZZ,Ring) -- special cubic transformations whose base locus has dimension at most three
- specialQuadraticTransformation -- special quadratic transformations whose base locus has dimension three
- specialQuadraticTransformation(Ring,ZZ) -- special quadratic transformations whose base locus has dimension three
- specialQuadraticTransformation(ZZ) -- special quadratic transformations whose base locus has dimension three
- specialQuadraticTransformation(ZZ,Ring) -- special quadratic transformations whose base locus has dimension three
- 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
- toMap(..., Dominant => ...)
- toMap(Ideal) -- rational map defined by a linear system
- toMap(Ideal,List) -- rational map defined by a linear system
- toMap(Ideal,ZZ) -- rational map defined by a linear system
- toMap(Ideal,ZZ,ZZ) -- rational map defined by a linear system
- toMap(List) -- rational map defined by a linear system
- toMap(Matrix) -- rational map defined by a linear system
- toMap(RingMap) -- rational map defined by a linear system
- ZZ == RationalMap -- equality of rational maps