A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
Yet another ideal decomposition algorithm
[chapter]
1997
Lecture Notes in Computer Science
Preserved Fulltext
Conclusion of the Algorithm for the Reduced Decomposition. ...
Another possible reduction test uses jacobians. ...
doi:10.1007/3-540-63163-1_4
fatcat:odoiil4ztbc3hnq2oqbgzmprsm
Prime Decompositions of Radicals in Polynomial Rings
1994
Journal of symbolic computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
We show that prime decomposition algorithms in R can be lifted to R[x] if for every prime ideal P in R univariate polynomials can be factored over the quotient field of the residue class ring R/P . ...
In the proof of this result a lifting algorithm is constructed which can be considered as a generalization of the algorithm of Ritt and Wu. ...
Another method based on a similar strategy is the algorithm for computing equidimensional decompositions of varieties in Kalkbrener (1993) . Compare also with Lazard (1991) and Wang (1993) . ...
doi:10.1006/jsco.1994.1052
fatcat:36lszgijy5hnhib56ckk4swolq
Page 1573 of Mathematical Reviews Vol. , Issue 99c
[page]
1991
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Franz Pauer (Innsbruck)
99¢:13051 13P10 68Q40
Caboara, Massimo (I-PISA; Pisa);
Conti, Pasqualina (I-PISA-DA; Pisa); Traverso, Carlo (I-PISA; Pisa) Yet another ideal decomposition algorithm. ...
), and the primary or the irreducible reduced decomposition can be more easily obtained from a pure-dimensional decomposition. ...
On the generalized Ritt problem as a computational problem
2009
Journal of Mathematical Sciences
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2008; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The Ritt problem asks if there is an algorithm that tells whether one prime differential ideal is contained in another one if both are given by their characteristic sets. ...
The technique used in the proof of equivalence yields algorithms for computing a canonical decomposition of a radical differential ideal into prime components and a canonical generating set of a radical ...
Then in the above decomposition we can remove all redundant components, i.e., those P i that contain another P j . ...
doi:10.1007/s10958-009-9689-3
fatcat:4gv3j2u3crgk7gm5izny2a4zpu
Triangular systems and factorized Gröbner bases
[chapter]
1995
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Such a refinement guarantees, different to the usual Gröbner factorizer, to produce a quasi prime decomposition, i.e. the resulting components are at least pure dimensional radical ideals. ...
Triangular systems are a very helpful tool between factorization at a heuristical level and full decomposition into prime components. ...
Below we present a quasi prime decomposition algorithm. ...
doi:10.1007/3-540-60114-7_18
fatcat:dhezik5bnnhgtlamqek54rshza
An algorithm for the Euclidean cell decomposition of a cusped strictly convex projective surface
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We show that Weeks' algorithm to compute this decomposition for a hyperbolic surface generalises to strictly convex projective surfaces. ...
Cooper and Long generalised Epstein and Penner's Euclidean cell decomposition of cusped hyperbolic manifolds of finite volume to non-compact strictly convex projective manifolds of finite volume. ...
Introduction The Epstein-Penner decomposition [2] is an elegant yet powerful construction in the study of non-compact hyperbolic manifolds of finite volume. ...
arXiv:1512.01645v1
fatcat:uto3cw7bjndyfhuwwjnl6wfo6i
Efficient parallelization of molecular dynamics simulations with short-ranged forces
2014
Journal of Physics, Conference Series
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
The results show that the new algorithm gives consistent speedups which are depending on the properties of the simulated system either comparable or superior to those obtained with spatial decomposition ...
In this work, this algorithm is tested on a variety of multi-core systems using three types of benchmark simulations. ...
This system is very homogeneous and therefore nearly ideal for the spatial decomposition method. ...
doi:10.1088/1742-6596/540/1/012006
fatcat:n3shy55lqrd5jjbmvhirgn4sq4
Thirty years of Polynomial System Solving, and now?
2009
Journal of symbolic computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
decomposition seems to be less frequently needed, maybe because the ideals coming from applications are usually prime (in the above example of the implicitization, the ideal obtained by the saturation ...
On the other hand, when solving a system, it is a priori unknown if the solution set is irreducible, and its decomposition in irreducible components is a difficult task, not yet well solved; therefore ...
doi:10.1016/j.jsc.2008.03.004
fatcat:umelra7aarag3fcsehfu67is6u
On Computation of Kolchin Characteristic Sets: Ordinary and Partial Cases
[article]
2006
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We also discuss the usefulness of regular and characteristic decompositions of radical differential ideals. ...
In the partial differential case we give an algorithm for computing characteristic sets in the special case of radical differential ideals satisfying the property of consistency. ...
Denote [9, Algorithm 7.1] by χ-Decomposition. ...
arXiv:math/0606124v2
fatcat:reesxlqwcjeh3icdfq2oeauqpy
Computing strong regular characteristic pairs with Groebner bases
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We present some properties about strong regular characteristic pairs and characteristic decomposition and illustrate the proposed algorithm and its performance by examples and experimental results. ...
Based on this strategy of splitting by means of quotient and with Groebner basis and ideal computations, we devise a simple algorithm to decompose an arbitrary polynomial set F into finitely many strong ...
The W-characteristic set of an ideal may be morbid and it is not yet clear when morbidity happens. ...
arXiv:1907.13537v2
fatcat:4rlktjog7jfjdc726vlgn3vtua
Using Multi-Objective Bat Algorithm for Solving Multi-Objective Non-linear Programming Problem
2021
Iraqi Journal of Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
MOBATD is a multi-objective bat algorithm that incorporates the dominance concept with the decomposition approach. ...
Decomposition is a basic strategy in traditional multi-objective optimization. However, it has not yet been widely used in multi-objective evolutionary optimization. ...
In multi-objective enhancement, for the most part, there is no single ideal arrangement, yet rather a lot of Pareto ideal arrangements. ...
doi:10.24996/ijs.2021.62.3.29
fatcat:tegl5lf66zedvbz7p4d3ihfl2u
Block Stanley decompositions I. Elementary and gnomon decompositions
2015
Journal of Pure and Applied Algebra
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We give two algorithms that generate different block decompositions, which we call elementary and gnomon decompositions, and give examples. ...
In a sequel to this paper we will introduce two additional algorithms that generate block decompositions that may not always be subprime, but are always incompressible. ...
We have not yet found an algorithm that always produces a minimal block decomposition (one with the fewest blocks), but since any such block decomposition must be incompressible, these algorithms are a ...
doi:10.1016/j.jpaa.2014.07.030
fatcat:rqhibi2tjbajlhm5bvpyrz3yb4
Numerical primary decomposition
[article]
2008
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We propose an algorithm to produce a collection of witness sets that contains a NPD and that can be used to solve the ideal membership problem for I. ...
Consider an ideal I ⊂ R = [x_1,...,x_n] defining a complex affine variety X ⊂^n. We describe the components associated to I by means of numerical primary decomposition (NPD). ...
Another example is a solution to the ideal membership problem given via NPD. ...
arXiv:0801.3105v2
fatcat:jgqa6qojljexzoszjrdslekw2a
The Canonical Decomposition of $\mathcal{C}^n_d$ and Numerical Gröbner and Border Bases
2014
SIAM Journal on Matrix Analysis and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
An SVD-based algorithm is presented that numerically computes the canonical decomposition. ...
The SVD-based canonical decomposition algorithm is also extended to numerically compute border bases. A tolerance for each of the algorithms is derived using perturbation theory of principal angles. ...
All algorithms are illustrated with numerical examples. To our knowledge, no SVD-based method to compute a Gröbner basis has been proposed yet. ...
doi:10.1137/130927176
fatcat:6xmh7zjv3bdvtd57al6ody27dy
Noether normalization guided by monomial cone decompositions
2009
Journal of symbolic computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
Such a decomposition of the complement of the corresponding initial ideal in the set of all monomials -also known as a Stanley decomposition -is constructed in the context of Janet bases, in order to come ...
up with sparse coordinate changes which achieve Noether normal position for the given ideal. ...
We call the cone decomposition of S (of Mon(R) \ S) which is constructed by Algorithm 1 (resp. 2) the Janet decomposition of S (resp. of Mon(R) \ S, or of R/I if S = lm(I) for an ideal I of R). ...
doi:10.1016/j.jsc.2009.02.004
fatcat:7zadhdynzjcahikkak5bvljwim
« Previous
Showing results 1 — 15 out of 62,693 results