WeilDivisors : Table of Contents

• WeilDivisors -- divisors
• 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
• baseLocus -- 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
• canonicalDivisor -- 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
• clearCache -- 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 -- constructor for (Weil/Q/R)-divisors
• dualize -- finds an ideal or module isomorphic to Hom(M, R)
• embedAsIdeal -- embed a module as an ideal of a ring
• findElementOfDegree -- find an element of a specified degree
• gbs -- 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
• getPrimeCount -- get the number of height-one primes in the support of the divisor
• getPrimeDivisors -- get the list of prime divisors of a given divisor
• ideal(RWeilDivisor) -- 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
• 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
• isDomain -- whether a ring is a domain
• isEffective -- 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
• isPrime(BasicDivisor) -- whether a divisor is prime
• isPrincipal -- 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.
• isQLinearEquivalent -- whether two Q-divisors are linearly equivalent
• isReduced -- whether a divisor is reduced
• isReflexive(Ideal) -- whether an ideal or module is reflexive
• isSmooth(Ideal) -- whether R mod the ideal is smooth
• isSNC -- whether the divisor is simple normal crossings
• isVeryAmple(WeilDivisor) -- whether a divisor is very ample.
• isWeilDivisor -- 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
• 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
• MTries -- an option used by embedAsIdeal how many times to try embedding the module as an ideal in a random way.
• nonCartierLocus -- the non-Cartier locus of a Weil divisor
• 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
• 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
• pullback(RingMap,RWeilDivisor) -- pullback a divisor under a ring map
• ramificationDivisor -- 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)
• reflexivePower -- 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
• 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
• torsionSubmodule -- create the torsion submodule of a module
• toRWeilDivisor -- create a R-divisor from a Q or Weil divisor
• toWeilDivisor -- 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
• zeroDivisor -- constructs the zero Weil divisor for the ring