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Algorithms for computing triangular decompositions of polynomial systems
We propose new algorithms for computing triangular decompositions of polynomial systems
incrementally. With respect to previous works, our improvements are based on a weakened …
incrementally. With respect to previous works, our improvements are based on a weakened …
Computing cylindrical algebraic decomposition via triangular decomposition
Cylindrical algebraic decomposition is one of the most important tools for computing with
semi-algebraic sets, while triangular decomposition is among the most important …
semi-algebraic sets, while triangular decomposition is among the most important …
The RegularChains library in MAPLE
Performing calculations modulo a set of relations is a basic technique in algebra. For
instance, computing the inverse of an integer modulo a prime integer or computing the …
instance, computing the inverse of an integer modulo a prime integer or computing the …
Lifting techniques for triangular decompositions
We present lifting techniques for triangular decompositions of zero-dimensional varieties,
that extend the range of the previous methods. We discuss complexity aspects, and report …
that extend the range of the previous methods. We discuss complexity aspects, and report …
Algorithmic Thomas decomposition of algebraic and differential systems
In this paper, we consider systems of algebraic and non-linear partial differential equations
and inequations. We decompose these systems into so-called simple subsystems and …
and inequations. We decompose these systems into so-called simple subsystems and …
Comprehensive triangular decomposition
We introduce the concept of comprehensive triangular decomposition (CTD) for a parametric
polynomial system F with coefficients in a field. In broad words, this is a finite partition of the …
polynomial system F with coefficients in a field. In broad words, this is a finite partition of the …
Fast arithmetic for triangular sets: from theory to practice
We study arithmetic operations for triangular families of polynomials, concentrating on
multiplication in dimension zero. By a suitable extension of fast univariate Euclidean …
multiplication in dimension zero. By a suitable extension of fast univariate Euclidean …
Characteristic set algorithms for equation solving in finite fields
Efficient characteristic set methods for computing zeros of polynomial equation systems in a
finite field are proposed. The concept of proper triangular sets is introduced and an explicit …
finite field are proposed. The concept of proper triangular sets is introduced and an explicit …
Well known theorems on triangular systems and the D5 principle
Well known theorems on triangular systems and the D5 principle Page 1 HAL Id: hal-00137158
https://hal.science/hal-00137158 Submitted on 22 Mar 2007 HAL is a multi-disciplinary open …
https://hal.science/hal-00137158 Submitted on 22 Mar 2007 HAL is a multi-disciplinary open …
[HTML][HTML] Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case
This paper presents algorithms for decomposing any zero-dimensional polynomial set into
simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a …
simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a …