Algorithms for computing triangular decompositions of polynomial systems

C Chen, M Moreno Maza - … of the 36th international symposium on …, 2011‏ - dl.acm.org
We propose new algorithms for computing triangular decompositions of polynomial systems
incrementally. With respect to previous works, our improvements are based on a weakened …

Computing cylindrical algebraic decomposition via triangular decomposition

C Chen, MM Maza, B **a, L Yang - Proceedings of the 2009 international …, 2009‏ - dl.acm.org
Cylindrical algebraic decomposition is one of the most important tools for computing with
semi-algebraic sets, while triangular decomposition is among the most important …

The RegularChains library in MAPLE

F Lemaire, MM Maza, Y **e - ACM SIGSAM Bulletin, 2005‏ - dl.acm.org
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 …

Lifting techniques for triangular decompositions

X Dahan, MM Maza, E Schost, W Wu… - Proceedings of the 2005 …, 2005‏ - dl.acm.org
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 …

Algorithmic Thomas decomposition of algebraic and differential systems

T Bächler, V Gerdt, M Lange-Hegermann… - Journal of Symbolic …, 2012‏ - Elsevier
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 …

Comprehensive triangular decomposition

C Chen, O Golubitsky, F Lemaire, MM Maza… - Computer Algebra in …, 2007‏ - Springer
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 …

Fast arithmetic for triangular sets: from theory to practice

X Li, MM Maza, É Schost - … of the 2007 international symposium on …, 2007‏ - dl.acm.org
We study arithmetic operations for triangular families of polynomials, concentrating on
multiplication in dimension zero. By a suitable extension of fast univariate Euclidean …

Characteristic set algorithms for equation solving in finite fields

XS Gao, Z Huang - Journal of Symbolic Computation, 2012‏ - Elsevier
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 …

Well known theorems on triangular systems and the D5 principle

F Boulier, F Lemaire, MM Maza - Transgressive Computing 2006, 2006‏ - hal.science
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 …

[HTML][HTML] Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case

X Li, C Mou, D Wang - Computers & Mathematics with Applications, 2010‏ - Elsevier
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 …