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