A parallel Buchberger algorithm for multigraded ideals
نویسندگان
چکیده
We demonstrate a method to parallelize the computation of a Gröbner basis for a homogenous ideal in a multigraded polynomial ring. Our method uses anti-chains in the lattice N to separate mutually independent S-polynomials for reduction.
منابع مشابه
Strategy-Accurate Parallel Buchberger Algorithms
We describe two parallel versions of the Buchberger algorithm for computing Gröbner bases, one for the general case and one for homogeneous ideals, which exploit coarse grain parallelism. For the general case, to avoid the growth in number and complexity of the polynomials to reduce, the algorithm adheres strictly to the same strategies as the best sequential implementation. A suitable communic...
متن کامل- Invariant and the Minimal Free Resolution Huy
In recent years, two different multigraded variants of Castelnuovo-Mumford regularity have been developed, namely multigraded regularity, defined by the vanishing of multigraded pieces of local cohomology modules, and the resolution regularity vector, defined by the multi-degrees in a minimal free resolution. In this paper, we study the relationship between multigraded regularity and the resolu...
متن کاملHomogeneous Buchberger algorithms and Sullivant’s computational commutative algebra challenge
We give a variant of the homogeneous Buchberger algorithm for positively graded lattice ideals. Using this algorithm we solve the Sullivant computational commutative algebra challenge1 .
متن کاملThe Graph of Monomial Ideals
There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring K[x1, . . . , xn]. The definition involves Gröbner bases or the action of the algebraic torus (K∗)n. We present algorithms for computing the (affine schemes representing) edges in this graph. We study the induced subgraphs on multigraded Hilbert schemes and on square-free monomial ideals. In the latter...
متن کاملHilbert Functions of Multigraded Algebras, Mixed Multiplicities of Ideals and Their Applications
This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated singularity, multiplicities of blowup algebras and mixed volumes of polytopes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1105.5509 شماره
صفحات -
تاریخ انتشار 2010