Abstract
Solving systems of bivariate polynomials is a critical operation: curves plotting, curves topology, parametric systems, general solvers which are recursive on the number of variables, etc. Several strategies currently exist from numerical algorithms (bisections for example, interval arithmetic) to general rewriting methods (Gröbner bases, triangular sets, resultants, etc.) with advantages and drawbacks.
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Rouillier, F. (2010). On Solving Systems of Bivariate Polynomials. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_21
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DOI: https://doi.org/10.1007/978-3-642-15582-6_21
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