der(...,Strategy=>...)
Description
If an arrangement has (squarefree) defining polynomial Q, then the logarithmic derivations are those f for which f(Q) is in the ideal (Q). The Classic strategy assumes that the arrangement is simple and implements this definition. By contrast, the default strategy treats all arrangements as multiarrangements.
Further information
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Default value: null
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Function: der -- Module of logarithmic derivations
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Option key: Strategy -- an optional argument
Functions with optional argument named Strategy :
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"addHook(...,Strategy=>...)" -- see addHook -- add a hook function to an object for later processing
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"annihilator(...,Strategy=>...)" -- see annihilator -- the annihilator ideal
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"associatedPrimes(...,Strategy=>...)" -- see associatedPrimes -- find associated primes
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"mingens(...,Strategy=>...)" -- see Complement -- a Strategy option value
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"trim(...,Strategy=>...)" -- see Complement -- a Strategy option value
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der(...,Strategy=>...)
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determinant(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
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"dual(MonomialIdeal,List,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
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"dual(MonomialIdeal,RingElement,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
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dual(MonomialIdeal,Strategy=>...)
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exteriorPower(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
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"gb(...,Strategy=>...)" -- see gb -- compute a Gröbner basis
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gcdLLL(...,Strategy=>...) (missing documentation)
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"GF(...,Strategy=>...)" -- see GF -- make a finite field
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"groebnerBasis(...,Strategy=>...)" -- see groebnerBasis -- Gröbner basis, as a matrix
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hermite(...,Strategy=>...) (missing documentation)
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"hooks(...,Strategy=>...)" -- see hooks -- list hooks attached to a key
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"idealizer(...,Strategy=>...)" -- see idealizer -- compute Hom(I,I) as a quotient ring
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integralClosure(...,Strategy=>...) -- control the algorithm used
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"intersect(...,Strategy=>...)" -- see intersect(List) -- compute an intersection of ideals or modules
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"intersectInP(...,Strategy=>...)" -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
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"isPrimary(...,Strategy=>...)" -- see isPrimary -- determine whether a submodule is primary
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"isPrime(Ideal,Strategy=>...)" -- see isPrime(Ideal) -- whether an ideal is prime
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LLL(...,Strategy=>...) -- choose among different algorithms
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"localize(...,Strategy=>...)" -- see localize -- localize an ideal at a prime ideal
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"match(...,Strategy=>...)" -- see match -- regular expression matching
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"decompose(Ideal,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
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"minimalPrimes(...,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
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minors(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
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"primaryComponent(...,Strategy=>...)" -- see primaryComponent -- find a primary component corresponding to an associated prime
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quotient(...,Strategy=>...)
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"radical(...,Strategy=>...)" -- see radical -- the radical of an ideal
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"radicalContainment(...,Strategy=>...)" -- see radicalContainment -- whether an element is contained in the radical of an ideal
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"analyticSpread(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"distinguished(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"isLinearType(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"isReduction(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"minimalReduction(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"multiplicity(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"normalCone(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"reesAlgebra(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"specialFiber(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"specialFiberIdeal(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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"regSeqInIdeal(...,Strategy=>...)" -- see regSeqInIdeal -- a regular sequence contained in an ideal
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resolution(...,Strategy=>...)
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saturate(...,Strategy=>...)
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"primaryDecomposition(...,Strategy=>...)" -- see strategies for computing primary decomposition
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"syz(...,Strategy=>...)" -- see syz(Matrix) -- compute the syzygy matrix
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"tangentCone(...,Strategy=>...)" -- see tangentCone(Ideal)