• Corpus ID: 14393653

An Algorithm for Computing the Limit Points of the Quasi-component of a Regular Chain

@article{Alvandi2013AnAF,
  title={An Algorithm for Computing the Limit Points of the Quasi-component of a Regular Chain},
  author={Parisa Alvandi and Changbo Chen and Marc Moreno Maza},
  journal={ArXiv},
  year={2013},
  volume={abs/1302.4688}
}
For a regular chain $R$, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of $R$, that is, the set $\bar{W(R)} \setminus W(R)$. Our procedure relies on Puiseux series expansions and does not require to compute a system of generators of the saturated ideal of $R$. We focus on the case where this saturated ideal has dimension one and we discuss extensions of this work in higher dimensions. We provide experimental results illustrating the benefits of our… 

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SHOWING 1-10 OF 35 REFERENCES
Puiseux expansion for space curves
For any ideal I in a convergent power series ring ℌ {X1,..,Xn} (n≥2) with one dimensional zero set X ⊂ (ℌn, 0) we give a method of computing a parametrization of each irreducible component of the
On Fulton's Algorithm for Computing Intersection Multiplicities
TLDR
Fulton's Algorithm is adapted such that it can work at any point of V(f,g), rational or not, and algorithmic criteria for reducing the case of n variables to the bivariate one is proposed.
Comprehensive Triangular Decomposition
TLDR
The concept of comprehensive triangular decomposition (CTD) for a parametric polynomial system F with coefficients in a field is introduced and an algorithm for computing the CTD of F is proposed, based on the RegularChains library in MAPLE.
When does (T) equal sat(T)?
TLDR
By generalizing the notion of primitivity from univariate polynomials to regular chains, this work establishes a necessary and sufficient condition, together with a Grobner basis free algorithm, for testing whether the equality {T}=Sat(T) holds.
Representation for the radical of a finitely generated differential ideal
TLDR
An algorithm is given which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals and provides an algorithm for testing membership in J.
When does equal sat(T)?
Triangular decomposition of semi-algebraic systems
TLDR
It is shown that any regular chains and triangular decomposition system can be decomposed into finitely many regular semi-algebraic systems, and two specifications of such a decomposition are proposed and corresponding algorithms are presented.
Characteristic set method for differential-difference polynomial systems
A complete algorithm for automated discovering of a class of inequality-type theorems
TLDR
This work presents a practical algorithm for automated inequality discovering which can discover new inequalities automatically without requiring to put forward any conjectures beforehand, complete for an extensive class of inequality-type theorems.
Localization and Primary Decomposition of Polynomial Ideals
TLDR
A new method for primary decomposition of a polynomial ideal, not necessarily zero-dimensional, is proposed and a detailed study for its practical implementation is reported on.
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