RationalMaps : Index
- AssumeDominant -- If true, certain functions assume that the map from X to Y is dominant.
- baseLocusOfMap -- Computes base locus of a map from a projective variety to projective space
- baseLocusOfMap(..., SaturateOutput => ...) -- If false, certain functions will not saturate their output.
- baseLocusOfMap(List) -- Computes base locus of a map from a projective variety to projective space
- baseLocusOfMap(Matrix) -- Computes base locus of a map from a projective variety to projective space
- baseLocusOfMap(RingMap) -- Computes base locus of a map from a projective variety to projective space
- CheckBirational -- If true, functions will check birationality.
- HybridLimit -- An option to control HybridStrategy
- HybridStrategy -- A strategy for inverseOfMap, isBirationalMap and isEmbedding.
- idealOfImageOfMap -- Finds defining equations for the image of a rational map between varieties or schemes
- idealOfImageOfMap(..., QuickRank => ...) -- An option for computing how rank is computed
- idealOfImageOfMap(..., Verbose => ...) -- Finds defining equations for the image of a rational map between varieties or schemes
- idealOfImageOfMap(Ideal,Ideal,BasicList) -- Finds defining equations for the image of a rational map between varieties or schemes
- idealOfImageOfMap(Ideal,Ideal,Matrix) -- Finds defining equations for the image of a rational map between varieties or schemes
- idealOfImageOfMap(Ring,Ring,BasicList) -- Finds defining equations for the image of a rational map between varieties or schemes
- idealOfImageOfMap(Ring,Ring,Matrix) -- Finds defining equations for the image of a rational map between varieties or schemes
- idealOfImageOfMap(RingMap) -- Finds defining equations for the image of a rational map between varieties or schemes
- inverseOfMap -- Computes the inverse map of a given birational map between projective varieties. Returns an error if the map is not birational onto its image.
- inverseOfMap(..., AssumeDominant => ...) -- If true, certain functions assume that the map from X to Y is dominant.
- inverseOfMap(..., CheckBirational => ...) -- If true, functions will check birationality.
- inverseOfMap(..., HybridLimit => ...) -- An option to control HybridStrategy
- inverseOfMap(..., MinorsCount => ...) -- An option controlling the behavior of isBirational and inverseOfMap (and other functions which call those).
- inverseOfMap(..., QuickRank => ...) -- An option for computing how rank is computed
- inverseOfMap(..., Strategy => ...) -- Determines the desired Strategy in each function.
- inverseOfMap(..., Verbose => ...) -- generate informative output
- inverseOfMap(Ideal,Ideal,BasicList) -- Computes the inverse map of a given birational map between projective varieties. Returns an error if the map is not birational onto its image.
- inverseOfMap(Ring,Ring,BasicList) -- Computes the inverse map of a given birational map between projective varieties. Returns an error if the map is not birational onto its image.
- inverseOfMap(RingMap) -- Computes the inverse map of a given birational map between projective varieties. Returns an error if the map is not birational onto its image.
- isBirationalMap -- Checks if a map between projective varieties is birational.
- isBirationalMap(..., AssumeDominant => ...) -- If true, certain functions assume that the map from X to Y is dominant.
- isBirationalMap(..., HybridLimit => ...) -- An option to control HybridStrategy
- isBirationalMap(..., MinorsCount => ...) -- An option controlling the behavior of isBirational and inverseOfMap (and other functions which call those).
- isBirationalMap(..., QuickRank => ...) -- An option for computing how rank is computed
- isBirationalMap(..., Strategy => ...) -- Determines the desired Strategy in each function.
- isBirationalMap(..., Verbose => ...) -- generate informative output
- isBirationalMap(Ideal,Ideal,BasicList) -- Checks if a map between projective varieties is birational.
- isBirationalMap(Ring,Ring,BasicList) -- Checks if a map between projective varieties is birational.
- isBirationalMap(RingMap) -- Checks if a map between projective varieties is birational.
- isBirationalOntoImage -- Checks if a map between projective varieties is birational onto its image.
- isBirationalOntoImage(..., AssumeDominant => ...) -- If true, certain functions assume that the map from X to Y is dominant.
- isBirationalOntoImage(..., HybridLimit => ...) -- An option to control HybridStrategy
- isBirationalOntoImage(..., MinorsCount => ...) -- An option controlling the behavior of isBirational and inverseOfMap (and other functions which call those).
- isBirationalOntoImage(..., QuickRank => ...) -- An option for computing how rank is computed
- isBirationalOntoImage(..., Strategy => ...) -- Determines the desired Strategy in each function.
- isBirationalOntoImage(..., Verbose => ...) -- generate informative output
- isBirationalOntoImage(Ideal,Ideal,BasicList) -- Checks if a map between projective varieties is birational onto its image.
- isBirationalOntoImage(Ring,Ring,BasicList) -- Checks if a map between projective varieties is birational onto its image.
- isBirationalOntoImage(RingMap) -- Checks if a map between projective varieties is birational onto its image.
- isEmbedding -- Checks whether a map of projective varieties is a closed embedding.
- isEmbedding(..., AssumeDominant => ...) -- If true, certain functions assume that the map from X to Y is dominant.
- isEmbedding(..., CheckBirational => ...) -- If true, functions will check birationality.
- isEmbedding(..., HybridLimit => ...) -- An option to control HybridStrategy
- isEmbedding(..., MinorsCount => ...) -- An option controlling the behavior of isBirational and inverseOfMap (and other functions which call those).
- isEmbedding(..., QuickRank => ...) -- An option for computing how rank is computed
- isEmbedding(..., Strategy => ...) -- Determines the desired Strategy in each function.
- isEmbedding(..., Verbose => ...) -- generate informative output
- isEmbedding(Ideal,Ideal,BasicList) -- Checks whether a map of projective varieties is a closed embedding.
- isEmbedding(Ring,Ring,BasicList) -- Checks whether a map of projective varieties is a closed embedding.
- isEmbedding(RingMap) -- Checks whether a map of projective varieties is a closed embedding.
- isRegularMap -- Checks whether a map to projective space is regular
- isRegularMap(List) -- Checks whether a map to projective space is regular
- isRegularMap(Matrix) -- Checks whether a map to projective space is regular
- isRegularMap(RingMap) -- Checks whether a map to projective space is regular
- isSameMap -- Checks whether two maps to projective space are really the same
- isSameMap(List,List) -- Checks whether two maps to projective space are really the same
- isSameMap(List,List,Ring) -- Checks whether two maps to projective space are really the same
- isSameMap(RingMap,RingMap) -- Checks whether two maps to projective space are really the same
- jacobianDualMatrix -- Computes the Jacobian Dual Matrix, a matrix whose kernel describing the syzygies of the inverse map.
- jacobianDualMatrix(..., AssumeDominant => ...) -- If true, certain functions assume that the map from X to Y is dominant.
- jacobianDualMatrix(..., QuickRank => ...) -- An option for computing how rank is computed
- jacobianDualMatrix(..., Strategy => ...) -- Determines the desired Strategy in each function.
- jacobianDualMatrix(Ideal,Ideal,BasicList) -- Computes the Jacobian Dual Matrix, a matrix whose kernel describing the syzygies of the inverse map.
- jacobianDualMatrix(Ring,Ring,BasicList) -- Computes the Jacobian Dual Matrix, a matrix whose kernel describing the syzygies of the inverse map.
- jacobianDualMatrix(RingMap) -- Computes the Jacobian Dual Matrix, a matrix whose kernel describing the syzygies of the inverse map.
- mapOntoImage -- Given a map of rings, correspoing to X mapping to Y, this returns the map of rings corresponding to X mapping to f(X).
- mapOntoImage(..., QuickRank => ...) -- An option for computing how rank is computed
- mapOntoImage(Ideal,Ideal,BasicList) -- Given a map of rings, correspoing to X mapping to Y, this returns the map of rings corresponding to X mapping to f(X).
- mapOntoImage(Ring,Ring,BasicList) -- Given a map of rings, correspoing to X mapping to Y, this returns the map of rings corresponding to X mapping to f(X).
- mapOntoImage(RingMap) -- Given a map of rings, correspoing to X mapping to Y, this returns the map of rings corresponding to X mapping to f(X).
- MinorsCount -- An option controlling the behavior of isBirational and inverseOfMap (and other functions which call those).
- QuickRank -- An option for computing how rank is computed
- RationalMaps -- rational maps
- ReesStrategy -- A strategy for inverseOfMap, isBirationalMap, and is Embedding.
- SaturateOutput -- If false, certain functions will not saturate their output.
- SaturationStrategy -- A strategy for inverseOfMap, isBirationalMap, isEmbedding.
- SimisStrategy -- A strategy for inverseOfMap, isBirationalMap and isEmbedding.
- sourceInversionFactor -- Computes the the common factor among the the components of the composition of the inverse map and the original map.
- sourceInversionFactor(..., AssumeDominant => ...) -- If true, certain functions assume that the map from X to Y is dominant.
- sourceInversionFactor(..., CheckBirational => ...) -- If true, functions will check birationality.
- sourceInversionFactor(..., HybridLimit => ...) -- An option to control HybridStrategy
- sourceInversionFactor(..., MinorsCount => ...) -- An option controlling the behavior of isBirational and inverseOfMap (and other functions which call those).
- sourceInversionFactor(..., QuickRank => ...) -- An option for computing how rank is computed
- sourceInversionFactor(..., Strategy => ...) -- Determines the desired Strategy in each function.
- sourceInversionFactor(..., Verbose => ...) -- generate informative output
- sourceInversionFactor(RingMap) -- Computes the the common factor among the the components of the composition of the inverse map and the original map.