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isHF -- is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal



Macaulay's Theorem characterizes the sequences of integers that occur as the Hilbert function of a polynomial ring modulo a homogeneous ideal. isHF checks that the input is a list of integers and that the first entry of the list is 1, and then it checks Macaulay's bound in each degree, using macaulayBound. The function returns true if the sequence of numbers in the list satisfies the conditions of Macaulay's Theorem and false otherwise.

i1 : isHF({1,3,6,7,5,3})

o1 = true
i2 : isHF({2,3,4,3,2}) --doesn't start with a 1 in degree 0

o2 = false
i3 : isHF({1,3,6,8,14,3}) --growth from 8 to 14 is too high

o3 = false

See also

Ways to use isHF :

For the programmer

The object isHF is a method function.