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Yet another ideal decomposition algorithm
[chapter]

1997
*
Lecture Notes in Computer Science
*

Conclusion of the

doi:10.1007/3-540-63163-1_4
fatcat:odoiil4ztbc3hnq2oqbgzmprsm
*Algorithm*for the Reduced*Decomposition*. ...*Another*possible reduction test uses jacobians. ...##
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Prime Decompositions of Radicals in Polynomial Rings

1994
*
Journal of symbolic computation
*

We show that prime

doi:10.1006/jsco.1994.1052
fatcat:36lszgijy5hnhib56ckk4swolq
*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) . ...##
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Page 1573 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

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*. ...##
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On the generalized Ritt problem as a computational problem

2009
*
Journal of Mathematical Sciences
*

The Ritt problem asks if there is an

doi:10.1007/s10958-009-9689-3
fatcat:4gv3j2u3crgk7gm5izny2a4zpu
*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 . ...##
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Triangular systems and factorized Gröbner bases
[chapter]

1995
*
Lecture Notes in Computer Science
*

Such a refinement guarantees, different to the usual Gröbner factorizer, to produce a quasi prime

doi:10.1007/3-540-60114-7_18
fatcat:dhezik5bnnhgtlamqek54rshza
*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*. ...##
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An algorithm for the Euclidean cell decomposition of a cusped strictly convex projective surface
[article]

2015
*
arXiv
*
pre-print

We show that Weeks'

arXiv:1512.01645v1
fatcat:uto3cw7bjndyfhuwwjnl6wfo6i
*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. ...##
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Efficient parallelization of molecular dynamics simulations with short-ranged forces

2014
*
Journal of Physics, Conference Series
*

The results show that the new

doi:10.1088/1742-6596/540/1/012006
fatcat:n3shy55lqrd5jjbmvhirgn4sq4
*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. ...##
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Thirty years of Polynomial System Solving, and now?

2009
*
Journal of symbolic computation
*

*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 ...

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On Computation of Kolchin Characteristic Sets: Ordinary and Partial Cases
[article]

2006
*
arXiv
*
pre-print

We also discuss the usefulness of regular and characteristic

arXiv:math/0606124v2
fatcat:reesxlqwcjeh3icdfq2oeauqpy
*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*. ...##
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Computing strong regular characteristic pairs with Groebner bases
[article]

2020
*
arXiv
*
pre-print

We present some properties about strong regular characteristic pairs and characteristic

arXiv:1907.13537v2
fatcat:4rlktjog7jfjdc726vlgn3vtua
*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. ...##
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Using Multi-Objective Bat Algorithm for Solving Multi-Objective Non-linear Programming Problem

2021
*
Iraqi Journal of Science
*

MOBATD is a multi-objective bat

doi:10.24996/ijs.2021.62.3.29
fatcat:tegl5lf66zedvbz7p4d3ihfl2u
*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. ...##
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Block Stanley decompositions I. Elementary and gnomon decompositions

2015
*
Journal of Pure and Applied Algebra
*

We give two

doi:10.1016/j.jpaa.2014.07.030
fatcat:rqhibi2tjbajlhm5bvpyrz3yb4
*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 ...##
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Numerical primary decomposition
[article]

2008
*
arXiv
*
pre-print

We propose an

arXiv:0801.3105v2
fatcat:jgqa6qojljexzoszjrdslekw2a
*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. ...##
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The Canonical Decomposition of $\mathcal{C}^n_d$ and Numerical Gröbner and Border Bases

2014
*
SIAM Journal on Matrix Analysis and Applications
*

An SVD-based

doi:10.1137/130927176
fatcat:6xmh7zjv3bdvtd57al6ody27dy
*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*. ...##
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Noether normalization guided by monomial cone decompositions

2009
*
Journal of symbolic computation
*

Such a

doi:10.1016/j.jsc.2009.02.004
fatcat:7zadhdynzjcahikkak5bvljwim
*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). ...
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