ACS Algorithms for Complex Shapes with Certified Numerics and Topology Cross-benchmarks of univariate algebraic kernels
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چکیده
We summarize the results of the cross-benchmarks for two univariate algebraic kernels (AK) developed in ACS. The kernels, developed at INRIA and MPI, were tested on 6 types of univariate polynomials of various degrees and bitsizes. The methods included were: Sturm, Sleeve, CF, NCF, NCF2 for the INRIA kernel, and Descartes and Bitstream-Descartes for the MPI kernel. NCF, NCF2, Descartes and Bitstream-Descartes are the most robust and never give wrong results. With respect to speed, the results are not decisive in most cases. Overall NCF and NCF2 seem faster, while for very large bitsizes Bitstream-Descartes seems more efficient, provided the degree is not very high. Special algorithms for polynomials of degree up to 4 give better results. We also compare against an external AK developed at LORIA-Nancy and based on the RS solver from INRIARocquencourt.
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ACS Algorithms for Complex Shapes with Certified Numerics and Topology Application of algebraic tools to CSG operations on curves and surfaces
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