IntegralClosure : Table of Contents

• IntegralClosure -- routines for integral closure of affine domains and ideals
• AllCodimensions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• conductor -- the conductor of a finite ring map
• ConductorElement -- Specifies a particular non-zerodivisor in the conductor.
• icFracP -- compute the integral closure in prime characteristic
• icFracP(...,ConductorElement=>...) -- Specifies a particular non-zerodivisor in the conductor.
• icFracP(...,Limit=>...) -- Limits the number of computed intermediate modules.
• icFracP(...,Verbosity=>...) -- Prints out the conductor element and the number of intermediate modules it computed.
• icFractions -- fractions integral over an affine domain
• icMap -- natural map from an affine domain into its integral closure
• icPIdeal -- compute the integral closure in prime characteristic of a principal ideal
• idealizer -- compute Hom(I,I) as a quotient ring
• idealizer(...,Index=>...) -- Sets the starting index on the new variables used to build the endomorphism ring Hom(J,J)
• idealizer(...,Variable=>...) -- Sets the name of the indexed variables introduced in computing the endomorphism ring Hom(J,J).
• Index -- Optional input for idealizer
• integralClosure -- integral closure of an ideal or a domain
• integralClosure(...,Keep=>...) -- list ring generators which should not be simplified away
• integralClosure(...,Limit=>...) -- do a partial integral closure
• integralClosure(...,Strategy=>...) -- control the algorithm used
• integralClosure(...,Variable=>...) -- set the base letter for the indexed variables introduced while computing the integral closure
• integralClosure(...,Verbosity=>...) -- display a certain amount of detail about the computation
• integralClosure(Ideal,RingElement,ZZ) -- integral closure of an ideal in an affine domain
• integralClosure(Ring) -- compute the integral closure (normalization) of an affine domain
• integralClosure(Ring,Ring) -- compute the integral closure (normalization) of an affine reduced ring over a base ring
• isNormal -- determine if a reduced ring is normal
• Keep -- an optional argument for various functions
• makeS2 -- compute the S2ification of a reduced ring
• makeS2(...,Variable=>...) -- Sets the name of the indexed variables introduced in computing the S2-ification.
• Radical -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• RadicalCodim1 -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• ringFromFractions -- find presentation for f.g. ring
• SimplifyFractions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• StartWithOneMinor -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
• testHunekeQuestion -- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
• Vasconcelos -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)