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Divisor :: BasicDiv

BasicDiv -- the class of divisors with unspecified coefficients

Description

The class of divisors whose coefficients are unspecified, a base class. Not typically for use. All subtypes have the same essential structure.

The basic structure is a HashTable. There is one key which has a value which specifies the ambient ring. The other keys are a Groebner basis L for each prime ideal P in the support with corresponding value a list n, P where n is the coefficient of the prime and P is how the user entered the ideal initially.
i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing
i2 : D = divisor(x*y^2*z^3)

o2 = 3*Div(z) + 2*Div(y) + 1*Div(x) of R

o2 : WDiv
i3 : H = new HashTable from D

o3 = HashTable{{x} => {1, ideal x}}
               {y} => {2, ideal y}
               {z} => {3, ideal z}
               ambRing => R

o3 : HashTable

See also

  • WDiv -- the class of divisors with integer coefficients
  • QDiv -- the class of divisors with rational coefficients
  • RDiv -- the class of divisors with real coefficients

Types of BasicDiv :

  • RDiv -- the class of divisors with real coefficients

Methods that use an object of class BasicDiv :

  • - BasicDiv -- Negation of a divisor
  • BasicDiv + BasicDiv -- Sum two divisors.
  • BasicDiv - BasicDiv -- Subtract two divisors.
  • coeff(BasicList,BasicDiv), see coeff -- Get the coefficient of a given ideal for a fixed divisor
  • coeff(Ideal,BasicDiv), see coeff -- Get the coefficient of a given ideal for a fixed divisor
  • getAmbientRing(BasicDiv), see getAmbientRing -- Get the ambient ring of a divisor
  • getCoeffList(BasicDiv), see getCoeffList -- Get the list of coefficients of a divisor
  • getGBList(BasicDiv), see getGBList -- Get the list of Groebner bases corresponding to the height-one primes in the support of a divisor
  • getPrimeCount(BasicDiv), see getPrimeCount -- Get the number of height one primes in the support of the divisor
  • getPrimeDivisors(BasicDiv), see getPrimeDivisors -- Returns the list of prime divisors of a given divisor
  • getPrimeList(BasicDiv), see getPrimeList -- Get the list of height-one primes in the support of a divisor
  • isDivAmbient(BasicDiv,Ring), see isDivAmbient -- Checks whether the ambient ring of a given divisor is the given ring
  • isDivGraded(BasicDiv), see isDivGraded -- Checks to see if the divisor is graded (homogeneous)
  • isDivPrime(BasicDiv), see isDivPrime -- Check if a divisor is prime
  • isDivReduced(BasicDiv), see isDivReduced -- Check if a divisor is reduced
  • isEffective(BasicDiv), see isEffective -- Check if a divisor is effective
  • isSNC(BasicDiv), see isSNC -- Checks to see if the divisor is simple normal crossings
  • isZeroDivisor(BasicDiv), see isZeroDivisor -- Checks to see if the divisor is the zero divisor
  • net(BasicDiv) -- Controls how divisors are displayed to the user
  • sameDivAmbient(BasicDiv,BasicDiv), see sameDivAmbient -- Checks whether the ambient ring of the given divisors are equal
  • simplifyDiv(BasicDiv), see simplifyDiv -- Removes primes with coefficient zero
  • ZZ * BasicDiv -- Multiply a divisor by an integer

For the programmer

The object BasicDiv is a type, with ancestor classes HashTable < Thing.