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