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extrasForTheKernel : Index
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artinianReduction
-- compute an artinian quotient of an Cohen-Macaulay ideal
artinianReduction(Ideal)
-- compute an artinian quotient of an Cohen-Macaulay ideal
criticalKoszulDegrees
-- compute all d with $\sum_{p+q=d} (-1)^q dim K_{p,q}(S/I)==0$ for an artinian ideal I
criticalKoszulDegrees(Ideal)
-- compute all d with $\sum_{p+q=d} (-1)^q dim K_{p,q}(S/I)==0$ for an artinian ideal I
expectedSyzygies
-- compute the expected Betti numbers of an artinian module
expectedSyzygies(ZZ,List)
-- compute the expected Betti numbers of an artinian module
extrasForTheKernel
-- constructions of prime fields and artinian reductions
getPrimeWithRootOfUnity
-- find a prime p with a primitive n-th root of unity r in ZZ/p
getPrimeWithRootOfUnity(ZZ,ZZ)
-- find a prime p with a primitive n-th root of unity r in ZZ/p
koszulMap
-- compute the Koszul homology map whose kernel correspond the Koszulzycles for K_(p,q)(S/I)
koszulMap(Ideal,ZZ,ZZ)
-- compute the Koszul homology map whose kernel correspond the Koszulzycles for K_(p,q)(S/I)
koszulMaps
-- compute all Koszul maps of total degree p for an artinian ideal I
koszulMaps(Ideal,ZZ)
-- compute all Koszul maps of total degree p for an artinian ideal I
nextPrime
-- compute the smallest prime which is at least n.
nextPrime(ZZ)
-- compute the smallest prime which is at least n.
randomKRationalPoint
-- Pick a random K rational point on the scheme X defined by I
randomKRationalPoint(Ideal)
-- Pick a random K rational point on the scheme X defined by I
Range
-- can be assigned a integral interval