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