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

Synopsis

Usage:

b=isHF L
Inputs:
- L, a list, a finite list of integers
Outputs:
- b, a Boolean value, true if L is a Hilbert function of a polynomial ring modulo a homogeneous ideal and false otherwise

Description

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

Ways to use isHF :

isHF(List)

For the programmer

The object isHF is a method function.

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

Synopsis

Description

See also

Ways to use isHF :

For the programmer