Divisor : Index
- - BasicDiv -- Negation of a divisor
- AmbRing -- An option used to tell divisor construction that a particular ambient ring is expected.
- applyToCoefficients -- Applies a function to the coefficients of a divisor
- applyToCoefficients(..., CoeffType => ...) -- Applies a function to the coefficients of a divisor
- applyToCoefficients(..., Unsafe => ...) -- Applies a function to the coefficients of a divisor
- applyToCoefficients(BasicDiv,Function) -- Applies a function to the coefficients of a divisor
- baseLocus -- Computes the locus where a graded module (or O(D) Weil divisor) is not globally generated.
- baseLocus(Module) -- Computes the locus where a graded module (or O(D) Weil divisor) is not globally generated.
- baseLocus(WDiv) -- Computes the locus where a graded module (or O(D) Weil divisor) is not globally generated.
- BasicDiv -- the class of divisors with unspecified coefficients
- BasicDiv + BasicDiv -- Sum two divisors.
- BasicDiv - BasicDiv -- Subtract two divisors.
- canonicalDivisor -- Compute the canonical divisor of a ring
- canonicalDivisor(..., IsGraded => ...) -- Compute the canonical divisor of a ring
- canonicalDivisor(Ring) -- Compute the canonical divisor of a ring
- ceilingDiv -- Get a divisor whose coefficients are ceilings of the given divisor
- ceilingDiv(RDiv) -- Get a divisor whose coefficients are ceilings of the given divisor
- coeff -- Get the coefficient of a given ideal for a fixed divisor
- coeff(BasicList,BasicDiv) -- Get the coefficient of a given ideal for a fixed divisor
- coeff(Ideal,BasicDiv) -- Get the coefficient of a given ideal for a fixed divisor
- CoeffType -- An option used to tell divisor construction that a particular type of coefficients are expected.
- Divisor -- A package for divisors on normal rings (graded or not).
- divisor -- Constructor for (Weil/Q/R)-divisors
- divisor(..., AmbRing => ...) -- Constructor for (Weil/Q/R)-divisors
- divisor(..., CoeffType => ...) -- Constructor for (Weil/Q/R)-divisors
- divisor(..., Unsafe => ...) -- 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(RingElement) -- Constructor for (Weil/Q/R)-divisors
- divisorToIdeal -- Calculate the corresponding module of a given divisor and represent it as an ideal
- divisorToIdeal(QDiv) -- Calculate the corresponding module of a given divisor and represent it as an ideal
- divisorToIdeal(RDiv) -- Calculate the corresponding module of a given divisor and represent it as an ideal
- divisorToIdeal(WDiv) -- Calculate the corresponding module of a given divisor and represent it as an ideal
- divisorToModule -- Calculate the corresponding module of a given divisor
- divisorToModule(QDiv) -- Calculate the corresponding module of a given divisor
- divisorToModule(RDiv) -- Calculate the corresponding module of a given divisor
- divisorToModule(WDiv) -- Calculate the corresponding module of a given divisor
- divMinus -- Get the negative part of a divisor
- divMinus(RDiv) -- Get the negative part of a divisor
- divPlus -- Get the positive part of a given divisor
- divPlus(RDiv) -- Get the positive part of a given divisor
- divPullBack -- Compute the pullback of a divisor under a ring map
- divPullBack(..., Strategy => ...) -- Compute the pullback of a divisor under a ring map
- divPullBack(RingMap,RDiv) -- Compute the pullback of a divisor under a ring map
- dualizeIdeal -- Finds an ideal isomorphic to Hom(I, R)
- dualizeIdeal(..., KnownNormal => ...) -- Finds an ideal isomorphic to Hom(I, R)
- dualizeIdeal(Ideal) -- Finds an ideal isomorphic to Hom(I, R)
- 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
- floorDiv -- Get a divisor whose coefficients are floors of the given divisor
- floorDiv(RDiv) -- Get a divisor whose coefficients are floors of the given divisor
- getAmbientRing -- Get the ambient ring of a divisor
- getAmbientRing(BasicDiv) -- Get the ambient ring of a divisor
- getCoeffList -- Get the list of coefficients of a divisor
- getCoeffList(BasicDiv) -- Get the list of coefficients of a divisor
- getGBList -- Get the list of Groebner bases corresponding to the height-one primes in the support of a divisor
- getGBList(BasicDiv) -- 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(..., Unsafe => ...) -- 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(BasicDiv) -- Get the number of height one primes in the support of the divisor
- getPrimeDivisors -- Returns the list of prime divisors of a given divisor
- getPrimeDivisors(BasicDiv) -- Returns the list of prime divisors of a given divisor
- getPrimeList -- Get the list of height-one primes in the support of a divisor
- getPrimeList(BasicDiv) -- Get the list of height-one primes in the support of a divisor
- idealPower -- Compute the ideal generated by the generators of the given ideal raised to a power
- idealPower(ZZ,Ideal) -- Compute the ideal generated by the generators of the given ideal raised to a power
- idealToDivisor -- Calculate the divisor D so that O_X(D) = I
- idealToDivisor(Ideal) -- Calculate the divisor D so that O_X(D) = I
- idealWithSectionToDivisor -- Calculate the divisor D so that D corresponds to the section f of I
- idealWithSectionToDivisor(RingElement,Ideal) -- Calculate the divisor D so that D corresponds to the section f of I
- isCartier -- Check if a Weil divisor is Cartier
- isCartier(..., IsGraded => ...) -- Check if a Weil divisor is Cartier
- isCartier(WDiv) -- Check if a Weil divisor is Cartier
- isDivAmbient -- Checks whether the ambient ring of a given divisor is the given ring
- isDivAmbient(BasicDiv,Ring) -- Checks whether the ambient ring of a given divisor is the given ring
- isDivGraded -- Checks to see if the divisor is graded (homogeneous)
- isDivGraded(BasicDiv) -- Checks to see if the divisor is graded (homogeneous)
- isDivPrime -- Check if a divisor is prime
- isDivPrime(BasicDiv) -- Check if a divisor is prime
- isDivPrincipal -- Check if a Weil divisor is globally principal
- isDivPrincipal(..., IsGraded => ...) -- Check if a Weil divisor is globally principal
- isDivPrincipal(WDiv) -- Check if a Weil divisor is globally principal
- isDivReduced -- Check if a divisor is reduced
- isDivReduced(BasicDiv) -- Check if a divisor is reduced
- isDomain -- Checks if a ring is a domain
- isDomain(Ring) -- Checks if a ring is a domain
- isEffective -- Check if a divisor is effective
- isEffective(BasicDiv) -- Check if 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.
- isLinearEquivalent -- Check if two Weil divisor are linearly equivalent
- isLinearEquivalent(..., IsGraded => ...) -- Check if two Weil divisor are linearly equivalent
- isLinearEquivalent(WDiv,WDiv) -- Check if two Weil divisor are linearly equivalent
- isQCartier -- Check whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
- isQCartier(..., IsGraded => ...) -- Check whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
- isQCartier(ZZ,QDiv) -- Check whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
- isQCartier(ZZ,WDiv) -- Check whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.
- isQLinearEquivalent -- Check if two rational divisors are linearly equivalent
- isQLinearEquivalent(..., IsGraded => ...) -- Check if two rational divisors are linearly equivalent
- isQLinearEquivalent(QDiv,QDiv) -- Check if two rational divisors are linearly equivalent
- isReflexive -- Checks whether an ideal or module is reflexive
- isReflexive(Ideal) -- Checks whether an ideal or module is reflexive
- isReflexive(Module) -- Checks whether an ideal or module is reflexive
- isRegular -- Checks to see if R mod the given ideal is regular
- isRegular(..., IsGraded => ...) -- Checks to see if R mod the given ideal is regular
- isRegular(Ideal) -- Checks to see if R mod the given ideal is regular
- isSNC -- Checks to see if the divisor is simple normal crossings
- isSNC(..., IsGraded => ...) -- Checks to see if the divisor is simple normal crossings
- isSNC(BasicDiv) -- Checks to see if the divisor is simple normal crossings
- isWDiv -- Check if a rational/real divisor is a Weil divisor
- isWDiv(RDiv) -- Check if a rational/real divisor is a Weil divisor
- isZeroDivisor -- Checks to see if the divisor is the zero divisor
- isZeroDivisor(BasicDiv) -- Checks to see if the divisor is the zero divisor
- KnownCartier -- An option used to specify to certain functions that we know that the divisor is Cartier.
- KnownNormal -- An option used to specify to certain functions that we know that the ambient ring is normal.
- 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(WDiv) -- Compute the map to projective space associated with the global sections of a Cartier divisor
- moduleToDivisor -- Compute a divisor associated to a module in a ring
- moduleToDivisor(..., IsGraded => ...) -- Compute a divisor associated to a module in a ring
- moduleToDivisor(Module) -- Compute a divisor associated to a module in a ring
- moduleToDivisor(Ring,Module) -- Compute a divisor associated to a module in a ring
- moduleToIdeal -- Turn a module to an ideal of a ring
- moduleToIdeal(..., IsGraded => ...) -- Turn a module to an ideal of a ring
- moduleToIdeal(..., MTries => ...) -- Turn a module to an ideal of a ring
- moduleToIdeal(..., ReturnMap => ...) -- Turn a module to an ideal of a ring
- moduleToIdeal(Module) -- Turn a module to an ideal of a ring
- moduleToIdeal(Ring,Module) -- Turn a module to an ideal of a ring
- moduleWithSectionToDivisor -- Compute the effective divisor associated to the section of a module
- moduleWithSectionToDivisor(Matrix) -- Compute the effective divisor associated to the section of a module
- moduleWithSectionToIdeal -- Turn a module to an ideal of a ring and keep track of a module element
- moduleWithSectionToIdeal(..., MTries => ...) -- Turn a module to an ideal of a ring and keep track of a module element
- moduleWithSectionToIdeal(..., ReturnMap => ...) -- Turn a module to an ideal of a ring and keep track of a module element
- moduleWithSectionToIdeal(Matrix) -- Turn a module to an ideal of a ring and keep track of a module element
- MTries -- An option used by moduleToIdeal how many times to try embedding the module as an ideal in a random way.
- net(BasicDiv) -- Controls how divisors are displayed to the user
- nonCartierLocus -- Returns the non-Cartier locus of a Weil divisor
- nonCartierLocus(..., IsGraded => ...) -- Returns the non-Cartier locus of a Weil divisor
- nonCartierLocus(WDiv) -- Returns the non-Cartier locus of a Weil divisor
- Primes -- A value for the option Strategy for the divPullBack method
- QDiv -- the class of divisors with rational coefficients
- QQ * RDiv -- Multiply a real divisor by a rational number
- QQ * WDiv -- Multiply a Weil divisor by a rational number
- ramificationDivisor -- Compute the ramification divisor of a finite inclusion of normal domains
- ramificationDivisor(..., IsGraded => ...) -- Compute the ramification divisor of a finite inclusion of normal domains
- ramificationDivisor(RingMap) -- Compute the ramification divisor of a finite inclusion of normal domains
- rationalDivisor -- Constructs a Q-divisor
- rationalDivisor(..., AmbRing => ...) -- Constructs a Q-divisor
- rationalDivisor(..., Unsafe => ...) -- Constructs a Q-divisor
- rationalDivisor(BasicList) -- Constructs a Q-divisor
- rationalDivisor(BasicList,BasicList) -- Constructs a Q-divisor
- RDiv -- the class of divisors with real coefficients
- RDiv == RDiv -- Check if two divisors are equal
- realDivisor -- Constructs an R-divisor
- realDivisor(..., AmbRing => ...) -- Constructs an R-divisor
- realDivisor(..., Unsafe => ...) -- Constructs an R-divisor
- realDivisor(BasicList) -- Constructs an R-divisor
- realDivisor(BasicList,BasicList) -- Constructs an R-divisor
- reflexifyIdeal -- Calculate the double dual of an ideal
- reflexifyIdeal(..., KnownNormal => ...) -- Calculate the double dual of an ideal
- reflexifyIdeal(Ideal) -- Calculate the double dual of an ideal
- reflexifyModule -- Calculate the double dual of a module
- reflexifyModule(Module) -- Calculate the double dual of a module
- reflexifyModuleWithMap -- Compute the canonical map from a module to its double-dual
- reflexifyModuleWithMap(Module) -- Compute the canonical map from a module to its double-dual
- reflexivePower -- Computes a reflexive power of an ideal
- reflexivePower(ZZ,Ideal) -- Computes a reflexive power of an ideal
- ReturnMap -- An option for moduleToIdeal and moduleWithSectionToIdeal
- RR * QDiv -- Multiply a rational divisor by a real number
- RR * RDiv -- Multiply a real divisor by a real number
- sameDivAmbient -- Checks whether the ambient ring of the given divisors are equal
- sameDivAmbient(BasicDiv,BasicDiv) -- Checks whether the ambient ring of the given divisors are equal
- Sheaves -- A value for the option Strategy for the divPullBack method
- simplifyDiv -- Removes primes with coefficient zero
- simplifyDiv(BasicDiv) -- Removes primes with coefficient zero
- toQDiv -- Turn a Weil divisor to a rational divisor
- toQDiv(QDiv) -- Turn a Weil divisor to a rational divisor
- toQDiv(WDiv) -- Turn a Weil divisor to a rational divisor
- toRDiv -- Turn a integer/rational divisor to a real divisor
- toRDiv(QDiv) -- Turn a integer/rational divisor to a real divisor
- toRDiv(RDiv) -- Turn a integer/rational divisor to a real divisor
- toRDiv(WDiv) -- Turn a integer/rational divisor to a real divisor
- torsionSubmodule -- Finds the torsion submodule of a given module
- torsionSubmodule(Module) -- Finds the torsion submodule of a given module
- toWDiv -- Turn a rational/real divisor with integer coefficients into to a Weil Divisor
- toWDiv(RDiv) -- Turn a rational/real divisor with integer coefficients into to a Weil Divisor
- Unsafe -- An option used to tell divisor construction not to do various checks
- verifyDivisor -- Checks to make sure a divisor is valid
- verifyDivisor(..., Verbose => ...) -- Checks to make sure a divisor is valid
- verifyDivisor(BasicDiv) -- Checks to make sure a divisor is valid
- WDiv -- the class of divisors with integer coefficients
- zeroDivisor -- Constructs the zero Weil divisor for the given ring
- zeroDivisor(Ring) -- Constructs the zero Weil divisor for the given ring
- ZZ * BasicDiv -- Multiply a divisor by an integer