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On the Theories of Triangular Sets
TLDR
We study the theoretical relationship between these various approaches to triangular sets, namely characteristic set (Ritt, 1932; Wu, 1984a), regular chain and representation of a regular chain. Expand
Using Galois Ideals for Computing Relative Resolvents
TLDR
We present a new algebraic method for computing relative resolvents which works with any polynomial invariant. Expand
Real Solving for Positive Dimensional Systems
TLDR
We propose a new efficient and practical algorithm for computing a set of zero-dimensional systems whose zeros contain at least one point on each semi-algebraically connected component of the studied variety, without any assumption either on the variety (smoothness or compactness for example) or on the system of equations which define it. Expand
Triangular Sets for Solving Polynomial Systems: a Comparative Implementation of Four Methods
TLDR
Four methods for solving polynomial systems by means of triangular sets are presented and implemented in a unified way. Expand
Algebraic computation of resolvents without extraneous powers
TLDR
This paper presents an algorithm for computing algebraically relative resolvents which enhances an existing algorithm by avoiding the accumulation of superfluous powers in the intermediate computations. Expand
Reasoning about Surfaces Using Differential Zero and Ideal Decomposition
TLDR
This paper presents methods for zero and ideal decomposition of partial differential polynomial systems and the application of these methods to deal with problems from the local theory of surfaces. Expand
Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints
TLDR
We show that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints. Expand
Computing real solutions of polynomial fuzzy systems
TLDR
This paper presents an efficient algorithm called SolvingFuzzySystem, or SFS, for finding real solutions of polynomial systems whose coefficients are fuzzy numbers with finite support and bijective spread functions. Expand
Computing real solutions of fuzzy polynomial systems
TLDR
This paper presents an efficient algorithm called SolveFuzzySystem , or SFS , for finding real solutions of polynomial systems whose coefficients are symmetrical L-R fuzzy numbers with bounded support for which the spread functions L and R are bijective. Expand
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