IntegralClosure : Index
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AllCodimensions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
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conductor -- the conductor of a finite ring map
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conductor(Ring) -- the conductor of a finite ring map
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conductor(RingMap) -- the conductor of a finite ring map
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ConductorElement -- Specifies a particular non-zerodivisor in the conductor.
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icFracP -- compute the integral closure in prime characteristic
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icFracP(..., ConductorElement => ...) -- Specifies a particular non-zerodivisor in the conductor.
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icFracP(..., Limit => ...) -- Limits the number of computed intermediate modules.
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icFracP(..., Verbosity => ...) -- Prints out the conductor element and the number of intermediate modules it computed.
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icFracP(Ring) -- compute the integral closure in prime characteristic
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icFractions -- fractions integral over an affine domain
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icFractions(Ring) -- fractions integral over an affine domain
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icMap -- natural map from an affine domain into its integral closure
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icMap(Ring) -- natural map from an affine domain into its integral closure
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icPIdeal -- compute the integral closure in prime characteristic of a principal ideal
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icPIdeal(RingElement,RingElement,ZZ) -- compute the integral closure in prime characteristic of a principal ideal
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idealizer -- compute Hom(I,I) as a quotient ring
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idealizer(..., Index => ...) -- Sets the starting index on the new variables used to build the endomorphism ring Hom(J,J). If the program idealizer is used independently, the user will generally want to use the default value of 0. However, when used as part of the integralClosure computation the number needs to start higher depending on the level of recursion involved.
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idealizer(..., Strategy => ...) -- compute Hom(I,I) as a quotient ring
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idealizer(..., Variable => ...) -- Sets the name of the indexed variables introduced in computing the endomorphism ring Hom(J,J).
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idealizer(..., Verbosity => ...) -- compute Hom(I,I) as a quotient ring
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idealizer(Ideal,RingElement) -- compute Hom(I,I) as a quotient ring
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Index -- Optional input for idealizer
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IntegralClosure -- routines for integral closure of affine domains and ideals
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integralClosure -- integral closure of an ideal or a domain
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integralClosure(..., Keep => ...) -- list ring generators which should not be simplified away
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integralClosure(..., Limit => ...) -- do a partial integral closure
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integralClosure(..., Strategy => ...) -- control the algorithm used
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integralClosure(..., Variable => ...) -- set the base letter for the indexed variables introduced while computing the integral closure
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integralClosure(..., Verbosity => ...) -- display a certain amount of detail about the computation
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integralClosure(Ideal) -- integral closure of an ideal in an affine domain
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integralClosure(Ideal,RingElement) -- integral closure of an ideal in an affine domain
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integralClosure(Ideal,RingElement,ZZ) -- integral closure of an ideal in an affine domain
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integralClosure(Ideal,ZZ) -- integral closure of an ideal in an affine domain
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integralClosure(Ring) -- compute the integral closure (normalization) of an affine domain
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isNormal -- determine if a reduced ring is normal
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isNormal(Ring) -- determine if a reduced ring is normal
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Keep -- an optional argument for various functions
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makeS2 -- compute the S2ification of a reduced ring
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makeS2(..., Variable => ...) -- Sets the name of the indexed variables introduced in computing the S2-ification.
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makeS2(..., Verbosity => ...) -- compute the S2ification of a reduced ring
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makeS2(Ring) -- compute the S2ification of a reduced ring
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Radical -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
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RadicalCodim1 -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
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ringFromFractions -- find presentation for f.g. ring
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ringFromFractions(..., Index => ...) -- find presentation for f.g. ring
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ringFromFractions(..., Variable => ...) -- find presentation for f.g. ring
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ringFromFractions(..., Verbosity => ...) -- find presentation for f.g. ring
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ringFromFractions(Matrix,RingElement) -- find presentation for f.g. ring
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SimplifyFractions -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
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StartWithOneMinor -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)
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testHunekeQuestion -- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
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testHunekeQuestion(RingElement) -- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
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Vasconcelos -- a symbol denoting a strategy element usable with integralClosure(...,Strategy=>...)