Computing centre conditions for certain cubic systems
Journal of Computational and Applied Mathematics
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Algebraic and geometric reasoning using Dixon resultants
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Comparison of various multivariate resultant formulations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Local bifurcations of critical periods for cubic Liénard equations with cubic damping
Journal of Computational and Applied Mathematics
Recursion formulas in determining isochronicity of a cubic reversible system
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
| Hi-index | 7.29 |
There are many methods such as Grobner basis, characteristic set and resultant, in computing an algebraic set of a system of multivariate polynomials. The common difficulties come from the complexity of computation, singularity of the corresponding matrices and some unnecessary factors in successive computation. In this paper, we decompose algebraic sets, stratum by stratum, into a union of constructible sets with Sylvester resultants, so as to simplify the procedure of elimination. Applying this decomposition to systems of multivariate polynomials resulted from period constants of reversible cubic differential systems which possess a quadratic isochronous center, we determine the order of weak centers and discuss the bifurcation of critical periods.