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Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering
TLDR
We present an efficient algorithm for the transformation of a Grobner basis of a zero-dimensional ideal with respect to any given ordering into a GroBner basis withrespect to any other ordering. Expand
  • 624
  • 28
Representation for the radical of a finitely generated differential ideal
TLDR
We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. Expand
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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
  • 256
  • 25
  • PDF
Resolution des Systemes d'Equations Algebriques
  • D. Lazard
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1981
TLDR
We reduce the computations of multivariate polynomials which have a finite number of common zeros in the algebraic closure of the ground field to the resolution of a single univariate equation. Expand
  • 261
  • 19
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
  • D. Lazard
  • Mathematics, Computer Science
  • EUROCAL
  • 28 March 1983
TLDR
In the past few years, two very different methods have been developed for solving systems of algebraic equations : the method of Gr6bner bases or standard bases [Buc I, Buc 2, Tri, P.Y] and the one which I presented in Eurosam 79 [Laz 2, Laz 3] based on gaussian elimination in some matrices. Expand
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  • 18
Autour de la platitude
© Bulletin de la S. M. F., 1969, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accordExpand
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  • PDF
Solving parametric polynomial systems
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems of the form C={x@?C^n,p"1(x)=0,...,p"s(x)=0,f"1(x) 0,...,f"l(x) 0} orExpand
  • 98
  • 15
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Solving Zero-Dimensional Algebraic Systems
  • D. Lazard
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 February 1992
TLDR
It is shown that a good output for a solver of algebraic systems of dimension zero consists of a family of ''triangular sets of polynomials''. Expand
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  • PDF
Computing representations for radicals of finitely generated differential ideals
TLDR
This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. Expand
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  • 10
  • PDF
A new method for solving algebraic systems of positive dimension
  • D. Lazard
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 1 October 1991
TLDR
A new algorithm is presented for solving algebraic systems of equations, which is designed from the structure which is wanted for the result. Expand
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