An algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations
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Authors
Ali Ayad
- Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban.
Ali Fares
- Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban.
Youssef Ayyad
- Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban.
Abstract
This paper presents a new algorithm for solving zero-dimensional parametric systems of polynomial homogeneous
equations. This algorithm is based on the computation of what we call parametric U-resultants.
The parameters space, i.e., the set of values of the parameters is decomposed into a finite number of constructible
sets. The solutions of the input polynomial system are given uniformly in each constructible set
by Polynomial Univariate Representations. The complexity of this algorithm is single exponential in the
number n of the unknowns and the number r of the parameters.
Share and Cite
ISRP Style
Ali Ayad, Ali Fares, Youssef Ayyad, An algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 6, 426--438
AMA Style
Ayad Ali, Fares Ali, Ayyad Youssef, An algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations. J. Nonlinear Sci. Appl. (2012); 5(6):426--438
Chicago/Turabian Style
Ayad, Ali, Fares, Ali, Ayyad, Youssef. "An algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations." Journal of Nonlinear Sciences and Applications, 5, no. 6 (2012): 426--438
Keywords
- Symbolic computation
- complexity analysis
- theory of resultants
- algebraic polynomial systems
- parametric systems
- Rational Univariate Representation
- parametric Gaussian elimination.
MSC
- 11Y16
- 08A40
- 11R09
- 12D05
- 15A06
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