Divisor : Index

• - BasicDivisor -- add or subtract two divisors, or negate a divisor
• AmbientRing -- an option used to tell divisor construction that a particular ambient ring is expected.
• applyToCoefficients -- apply a function to the coefficients of a divisor
• applyToCoefficients(...,CoefficientType=>...) -- apply a function to the coefficients of a divisor
• applyToCoefficients(...,Safe=>...) -- apply a function to the coefficients of a divisor
• applyToCoefficients(BasicDivisor,Function) -- apply a function to the coefficients of a divisor
• baseLocus -- compute the locus where a graded module (or O(D) of a Weil divisor) is not globally generated
• baseLocus(Module) -- compute the locus where a graded module (or O(D) of a Weil divisor) is not globally generated
• baseLocus(WeilDivisor) -- compute the locus where a graded module (or O(D) of a Weil divisor) is not globally generated
• BasicDivisor -- the Types of divisors
• BasicDivisor + BasicDivisor -- add or subtract two divisors, or negate a divisor
• BasicDivisor - BasicDivisor -- add or subtract two divisors, or negate a divisor
• canonicalDivisor -- compute a canonical divisor of a ring
• canonicalDivisor(...,IsGraded=>...) -- compute a canonical divisor of a ring
• canonicalDivisor(Ring) -- compute a canonical divisor of a ring
• ceiling(RWeilDivisor) -- produce a WeilDivisor whose coefficients are ceilings or floors of the divisor
• cleanSupport -- removes primes with coefficient zero from a divisor
• cleanSupport(BasicDivisor) -- removes primes with coefficient zero from a divisor
• clearCache -- creates a new divisor with most entries from the cache removed
• clearCache(BasicDivisor) -- creates a new divisor with most entries from the cache removed
• coefficient(BasicList,BasicDivisor) -- get the coefficient of an ideal for a fixed divisor
• coefficient(Ideal,BasicDivisor) -- get the coefficient of an ideal for a fixed divisor
• coefficients(BasicDivisor) -- get the list of coefficients of a divisor
• CoefficientType -- an option used to tell divisor construction that a particular type of coefficients are expected.
• Divisor -- divisors
• divisor -- constructor for (Weil/Q/R)-divisors
• divisor(...,AmbientRing=>...) -- constructor for (Weil/Q/R)-divisors
• divisor(...,CoefficientType=>...) -- constructor for (Weil/Q/R)-divisors
• divisor(...,IsGraded=>...) -- constructor for (Weil/Q/R)-divisors
• divisor(...,Section=>...) -- constructor for (Weil/Q/R)-divisors
• divisor(BasicList) -- constructor for (Weil/Q/R)-divisors
• divisor(BasicList,BasicList) -- constructor for (Weil/Q/R)-divisors
• divisor(Ideal) -- constructor for (Weil/Q/R)-divisors
• divisor(Matrix) -- constructor for (Weil/Q/R)-divisors
• divisor(Module) -- constructor for (Weil/Q/R)-divisors
• divisor(RingElement) -- constructor for (Weil/Q/R)-divisors
• dualize -- finds an ideal or module isomorphic to Hom(M, R)
• dualize(...,KnownDomain=>...) -- finds an ideal or module isomorphic to Hom(M, R)
• dualize(...,Strategy=>...) -- finds an ideal or module isomorphic to Hom(M, R)
• dualize(Ideal) -- finds an ideal or module isomorphic to Hom(M, R)
• dualize(Module) -- finds an ideal or module isomorphic to Hom(M, R)
• embedAsIdeal -- embed a module as an ideal of a ring
• embedAsIdeal(...,IsGraded=>...) -- embed a module as an ideal of a ring
• embedAsIdeal(...,MTries=>...) -- embed a module as an ideal of a ring
• embedAsIdeal(...,ReturnMap=>...) -- embed a module as an ideal of a ring
• embedAsIdeal(...,Section=>...) -- embed a module as an ideal of a ring
• embedAsIdeal(Matrix) -- embed a module as an ideal of a ring
• embedAsIdeal(Module) -- embed a module as an ideal of a ring
• embedAsIdeal(Ring,Matrix) -- embed a module as an ideal of a ring
• embedAsIdeal(Ring,Module) -- embed a module as an ideal of a ring
• findElementOfDegree -- find an element of a specified degree
• findElementOfDegree(BasicList,Ring) -- find an element of a specified degree
• findElementOfDegree(ZZ,Ring) -- find an element of a specified degree
• floor(RWeilDivisor) -- produce a WeilDivisor whose coefficients are ceilings or floors of the divisor
• gbs -- get the list of Groebner bases corresponding to the height-one primes in the support of a divisor
• gbs(BasicDivisor) -- get the list of Groebner bases corresponding to the height-one primes in the support of a divisor
• getLinearDiophantineSolution -- find a solution of the linear Diophantine equation Ax = b
• getLinearDiophantineSolution(...,Safe=>...) -- find a solution of the linear Diophantine equation Ax = b
• getLinearDiophantineSolution(BasicList,BasicList) -- find a solution of the linear Diophantine equation Ax = b
• getLinearDiophantineSolution(BasicList,Matrix) -- find a solution of the linear Diophantine equation Ax = b
• getPrimeCount -- get the number of height-one primes in the support of the divisor
• getPrimeCount(BasicDivisor) -- get the number of height-one primes in the support of the divisor
• getPrimeDivisors -- get the list of prime divisors of a given divisor
• getPrimeDivisors(BasicDivisor) -- get the list of prime divisors of a given divisor
• ideal(QWeilDivisor) -- calculate the corresponding module of a divisor and represent it as an ideal
• ideal(RWeilDivisor) -- calculate the corresponding module of a divisor and represent it as an ideal
• ideal(WeilDivisor) -- calculate the corresponding module of a divisor and represent it as an ideal
• idealPower -- compute the ideal generated by the generators of the ideal raised to a power
• idealPower(ZZ,Ideal) -- compute the ideal generated by the generators of the ideal raised to a power
• ideals -- a symbol used as a key within the divisor cache
• IdealStrategy -- a valid value for the Strategy option in dualize or reflexify
• isCartier -- whether a Weil divisor is Cartier
• isCartier(...,IsGraded=>...) -- whether a Weil divisor is Cartier
• isCartier(WeilDivisor) -- whether a Weil divisor is Cartier
• isDomain -- whether a ring is a domain
• isDomain(Ring) -- whether a ring is a domain
• isEffective -- whether a divisor is effective
• isEffective(BasicDivisor) -- whether a divisor is effective
• IsGraded -- an option used by numerous functions which tells it to treat the divisors as if we were working on the Proj of the ambient ring.
• isHomogeneous(BasicDivisor) -- whether the divisor is graded (homogeneous)
• isLinearEquivalent -- whether two Weil divisors are linearly equivalent
• isLinearEquivalent(...,IsGraded=>...) -- whether two Weil divisors are linearly equivalent
• isLinearEquivalent(WeilDivisor,WeilDivisor) -- whether two Weil divisors are linearly equivalent
• isPrime(BasicDivisor) -- whether a divisor is prime
• isPrincipal -- whether a Weil divisor is globally principal
• isPrincipal(...,IsGraded=>...) -- whether a Weil divisor is globally principal
• isPrincipal(WeilDivisor) -- whether a Weil divisor is globally principal
• isQCartier -- whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
• isQCartier(...,IsGraded=>...) -- whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
• isQCartier(ZZ,QWeilDivisor) -- whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
• isQCartier(ZZ,WeilDivisor) -- whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
• isQLinearEquivalent -- whether two Q-divisors are linearly equivalent
• isQLinearEquivalent(...,IsGraded=>...) -- whether two Q-divisors are linearly equivalent
• isQLinearEquivalent(ZZ,QWeilDivisor,QWeilDivisor) -- whether two Q-divisors are linearly equivalent
• isReduced -- whether a divisor is reduced
• isReduced(BasicDivisor) -- whether a divisor is reduced
• isReflexive -- whether an ideal or module is reflexive
• isReflexive(...,KnownDomain=>...) -- whether an ideal or module is reflexive
• isReflexive(...,Strategy=>...) -- whether an ideal or module is reflexive
• isReflexive(Ideal) -- whether an ideal or module is reflexive
• isReflexive(Module) -- whether an ideal or module is reflexive
• isSmooth -- whether R mod the ideal is smooth
• isSmooth(...,IsGraded=>...) -- whether R mod the ideal is smooth
• isSmooth(Ideal) -- whether R mod the ideal is smooth
• isSNC -- whether the divisor is simple normal crossings
• isSNC(...,IsGraded=>...) -- whether the divisor is simple normal crossings
• isSNC(BasicDivisor) -- whether the divisor is simple normal crossings
• isVeryAmple -- whether a divisor is very ample.
• isVeryAmple(...,Verbose=>...) -- whether a divisor is very ample.
• isVeryAmple(WeilDivisor) -- whether a divisor is very ample.
• isWeilDivisor -- whether a rational/real divisor is in actuality a Weil divisor
• isWeilDivisor(RWeilDivisor) -- whether a rational/real divisor is in actuality a Weil divisor
• isWellDefined(BasicDivisor) -- whether a divisor is valid
• isZeroDivisor -- whether the divisor is the zero divisor
• isZeroDivisor(BasicDivisor) -- whether the divisor is the zero divisor
• KnownCartier -- an option used to specify to certain functions that we know that the divisor is Cartier
• KnownDomain -- an option used to specify to certain functions that we know that the ring is a domain
• mapToProjectiveSpace -- compute the map to projective space associated with the global sections of a Cartier divisor
• mapToProjectiveSpace(...,KnownCartier=>...) -- compute the map to projective space associated with the global sections of a Cartier divisor
• mapToProjectiveSpace(...,Variable=>...) -- compute the map to projective space associated with the global sections of a Cartier divisor
• mapToProjectiveSpace(WeilDivisor) -- compute the map to projective space associated with the global sections of a Cartier divisor
• ModuleStrategy -- a valid value for the Strategy option in dualize or reflexify
• MTries -- an option used by embedAsIdeal how many times to try embedding the module as an ideal in a random way.
• negativePart -- get the effective part or anti-effective part of a divisor
• negativePart(RWeilDivisor) -- get the effective part or anti-effective part of a divisor
• nonCartierLocus -- the non-Cartier locus of a Weil divisor
• nonCartierLocus(...,IsGraded=>...) -- the non-Cartier locus of a Weil divisor
• nonCartierLocus(WeilDivisor) -- the non-Cartier locus of a Weil divisor
• NoStrategy -- a valid value for the Strategy option in dualize or reflexify
• Number * BasicDivisor -- multiply a divisor by a number
• OO RWeilDivisor -- calculate module corresponding to divisor
• positivePart -- get the effective part or anti-effective part of a divisor
• positivePart(RWeilDivisor) -- get the effective part or anti-effective part of a divisor
• Primes -- a value for the option Strategy for the pullback method
• primes -- get the list of height-one primes in the support of a divisor
• primes(BasicDivisor) -- get the list of height-one primes in the support of a divisor
• pullback -- pullback a divisor under a ring map
• pullback(...,Strategy=>...) -- pullback a divisor under a ring map
• pullback(RingMap,RWeilDivisor) -- pullback a divisor under a ring map
• QQ * RWeilDivisor -- multiply a divisor by a number
• QQ * WeilDivisor -- multiply a divisor by a number
• QWeilDivisor -- the Types of divisors
• ramificationDivisor -- compute the ramification divisor of a finite inclusion of normal domains or a blowup over a smooth base
• ramificationDivisor(...,IsGraded=>...) -- compute the ramification divisor of a finite inclusion of normal domains or a blowup over a smooth base
• ramificationDivisor(RingMap) -- compute the ramification divisor of a finite inclusion of normal domains or a blowup over a smooth base
• reflexify -- calculate the double dual of an ideal or module Hom(Hom(M, R), R)
• reflexify(...,KnownDomain=>...) -- calculate the double dual of an ideal or module Hom(Hom(M, R), R)
• reflexify(...,ReturnMap=>...) -- calculate the double dual of an ideal or module Hom(Hom(M, R), R)
• reflexify(...,Strategy=>...) -- calculate the double dual of an ideal or module Hom(Hom(M, R), R)
• reflexify(Ideal) -- calculate the double dual of an ideal or module Hom(Hom(M, R), R)
• reflexify(Module) -- calculate the double dual of an ideal or module Hom(Hom(M, R), R)
• reflexivePower -- computes a reflexive power of an ideal in a normal domain
• reflexivePower(...,Strategy=>...) -- computes a reflexive power of an ideal in a normal domain
• reflexivePower(ZZ,Ideal) -- computes a reflexive power of an ideal in a normal domain
• ReturnMap -- an option for embedAsIdeal
• ring(BasicDivisor) -- get the ambient ring of a divisor
• RR * QWeilDivisor -- multiply a divisor by a number
• RR * RWeilDivisor -- multiply a divisor by a number
• RWeilDivisor -- the Types of divisors
• RWeilDivisor == RWeilDivisor -- whether two divisors are equal
• Safe -- an option used to tell functions whether not to do checks.
• Section -- an option used in a number of functions
• Sheaves -- a value for the option Strategy for the pullback method
• toQWeilDivisor -- create a Q-Weil divisor from a Weil divisor
• toQWeilDivisor(QWeilDivisor) -- create a Q-Weil divisor from a Weil divisor
• toQWeilDivisor(WeilDivisor) -- create a Q-Weil divisor from a Weil divisor
• torsionSubmodule -- create the torsion submodule of a module
• torsionSubmodule(...,KnownDomain=>...) -- create the torsion submodule of a module
• torsionSubmodule(...,Strategy=>...) -- create the torsion submodule of a module
• torsionSubmodule(Module) -- create the torsion submodule of a module
• toRWeilDivisor -- create a R-divisor from a Q or Weil divisor
• toRWeilDivisor(QWeilDivisor) -- create a R-divisor from a Q or Weil divisor
• toRWeilDivisor(RWeilDivisor) -- create a R-divisor from a Q or Weil divisor
• toRWeilDivisor(WeilDivisor) -- create a R-divisor from a Q or Weil divisor
• toWeilDivisor -- create a Weil divisor from a Q or R-divisor
• toWeilDivisor(RWeilDivisor) -- create a Weil divisor from a Q or R-divisor
• trim(BasicDivisor) -- trims the ideals displayed to the user and removes primes with coefficient zero
• WeilDivisor -- the Types of divisors
• zeroDivisor -- constructs the zero Weil divisor for the ring
• zeroDivisor(Ring) -- constructs the zero Weil divisor for the ring