Local Decomposition Algorithms

  title={Local Decomposition Algorithms},
  author={Maria Emilia Alonso and Teo Mora and Mario Di Raimondo},
INTRODUCTION For an ideal I ⊂ P := k[X 1 ,…,X n ], many algorithms using Gröbner techniques are a direct consequence of the definition itself of Gröbner basis: among them we can list algorithms for computing syzygies, dimension, minimal bases, free resolutions, Hilbert function and other algebro-geometric invariants of an ideal; the explicit knowledge of syzygies allows moreover to compute ideal intersection and quotients. Other algorithms require a specific property of Gröbner bases w.r.t. of… 

Algorithms in Local Algebra

This work uses the generalization of Mora's tangent cone algorithm to arbitrary term orders to give a detailed description of the necessary modifications and restrictions for term orders of mixed type.

Algorithms in Local Algebra

Let k be a eld, S = k[xv : v 2 V ] be the polynomial ring over the nite set of variables (xv : v 2 V), and m = (x v : v 2 V) the ideal dening the origin of Spec S. It is theoretically known (see e.g.

Effective Computation of Radical of Ideals and Its Application to Invariant Theory

This paper introduces a new notion of genericity and exhibits a novel deterministic algorithm to put an ideal in Nœther position and uses this algorithm and also the algorithm due to Krick and Logar to present an efficient algorithm to calculate the radical of a complete intersection ideal.

Extractions: Computable and Visible Analogues of Localizations for Polynomial Ideals

It is proved that extractions are as powerful as localizations in the sense that for any multiplicatively closed subset of $S$ of $K[x_1,\ldots,x_n]$ and any polynomial ideal $I$, there always exists a polynometric ideal $J$ such that $\beta(I,J)=(S^{-1}I)^c$.

Minimal Primary Decomposition and Factorized Gröbner Bases

  • Hans-Gert Gräbe
  • Computer Science
    Applicable Algebra in Engineering, Communication and Computing
  • 1997
A way to interweave factorized Gröbner bases and the ideas in [5] that leads to a significant speed up in the computation of isolated primes for well splitting examples is described and a method to detect necessary embedded primes in the output collection of the algorithm is outlined.

On the Computation of the Radical of Polynomial Complete Intersection Ideals

A single exponential algorithm is exhibited which computes a system of generators of certain polynomial ideals with radical d:=maxj deg fj, the generated ideal and its radical.

Constructive Ideal Theory

This chapter introduces some algorithms of constructive ideal theory, almost all of which are based on Grobner bases, and provides the basic algorithmic tools which will be used in later chapters.

Decision of Algebra Isomorphisms Using Gröbner Bases

Given two finite-dimensional non-commutative finitely presented algebras A and B over a field k, this paper presents two algorithms for deciding whether or not they are isomorphic as k-algebras. We

Derivations and Radicals of Polynomial Ideals over Fields of Arbitrary Characteristic

A complete effective solution to the problem of computing radicals of polynomial ideals over general fields of arbitrary characteristic by using derivations and ideal quotients to recover as much of the radical as possible.



Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals

Borders are given for the complexity of the above problems which are simply exponential in the number n of variables in the one-dimensional case, and it is shown that in the general case the first two problems are doubly exponential only in the dimension of the ideal.

Computing with algebraic series

An effective version of Weierstrass theorems are given, which allow us to have effective elimination theory for algebraic series and an effective Noether Normalization Lemma for Noether normal position of an ideal of algebraic formal power series.

Solving Zero-Dimensional Algebraic Systems

  • D. Lazard
  • Computer Science, Mathematics
    J. Symb. Comput.
  • 1992

Algorithmes – disons rapides – pour la décomposition d’une variété algébrique en composantes irréductibles et équidimensionnelles

Resume. Nous decrivons dans cet article deux algorithmes qui construisent les decompositions irreductible et equidimensionnelle d’une variete algebrique affine (ou projective), definie par un

An introduction to the tangent cone algorithm, Issues in nonlinear geometry and robotics

  • An introduction to the tangent cone algorithm, Issues in nonlinear geometry and robotics

conferences at COCOA I (1986), Luminy (1988) and elsewhere A Jacobian method for finding the radical of an ideal

  • conferences at COCOA I (1986), Luminy (1988) and elsewhere A Jacobian method for finding the radical of an ideal
  • 1989