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burchIndex -- Compute the burchIndex of the Burch ring of a semigroup

Synopsis

Usage:

b = burchIndex L
Inputs:
- L, a list, of generators of a semigroup
Outputs:
- b, an integer,

Description

The Burch index of an artinian local ring A = S/I, where (S,n,k) is regular local, is dim_k (n/(nI:(I:n))). The number returned by

burchIndex L

where L is a list of integers, is the burch index of the Kunz ring of L, that is, the semigroup ring of L modulo the lowest degree element.

i1 : burchIndex {3,4,5}

o1 = 2

References

Dao, HL and Eisenbud, D, Burch index, summands of syzygies and linearity in resolutions. Bull. Iranian Math. Soc. 49 (2023).

See also

kunzRing -- artinian reduction of a semigroup ring

Ways to use burchIndex:

burchIndex(List)

For the programmer

The object burchIndex is a method function.