Triangular sets for solving polynomial systems: a comparative implementation of four methods
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Publication:1808665
zbMath0943.12004MaRDI QIDQ1808665
Marc Moreno Maza, Philippe Aubry
Publication date: 5 September 2000
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Symbolic computation and algebraic computation (68W30) Solving polynomial systems; resultants (13P15)
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Uses Software
Cites Work
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- Hilbert functions and the Buchberger algorithm
- Some examples for solving systems of algebraic equations by calculating Gröbner bases
- A new method for solving algebraic systems of positive dimension
- Solving zero-dimensional algebraic systems
- A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
- Decomposing polynomial systems into simple systems
- Algorithmic properties of polynomial rings
- On decomposing systems of polynomial equations with finitely many solutions
- Efficient computation of zero-dimensional Gröbner bases by change of ordering
- An elimination method for polynomial systems
- Converting bases with the Gröbner walk
- On the theories of triangular sets
- The complexity of the word problems for commutative semigroups and polynomial ideals
- Applied algebra, algebraic algorithms and error-correcting codes. 11th international symposium, AAECC-11, Paris, France, July 17-22, 1995. Proceedings
- A superexponential lower bound for Gröbner bases and Church-Rosser commutative thue systems
- Solving systems of algebraic equations by using gröbner bases
- Properties of Gröbner bases under specializations