97 research outputs found
The minimal components of the Mayr-Meyer ideals
Mayr and Meyer found ideals (in a polynomial ring in
variables over a field and generators of degree at most ) with ideal
membership property which is doubly exponential in . This paper is a first
step in understanding the primary decomposition of these ideals: it is proved
here that has minimal prime ideals. Also, all the minimal
components are computed, and the intersection of the minimal components as
well
A new family of ideals with the doubly exponential ideal membership property
Mayr and Meyer found ideals with the doubly exponential ideal membership
property. In the analysis of the associated primes of these ideals (in
math.AC/0209344), a new family of ideals arose. This new family is presented
and analyzed in this paper. It is proved that this new family also satisfies
the doubly exponential ideal membership property. Furthermore, the set of
associated primes of this family can be computed inductively
Computing Instanton Numbers of Curve Singularities
We present an algorithm for computing instanton numbers of curve
singularities. A comparison is made between these and some other invariants of
curve singularities. The algorithm has been implemented in the symbolic
computer algebra program Macaulay2, and can be downloaded from
http://www.math.nmsu.edu/\~{}iswanson/instanton.m2.}Comment: Revised version, several new examples have been added. To appear in
J. Symbolic Computatio
An algorithm for computing the integral closure
We present an algorithm for computing the integral closure of a reduced ring
that is finitely generated over a finite field
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