On the verification of polynomial system solvers

CHEN Changbo, MORENO MAZA Marc, PAN Wei, XIE Yuzhen

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PDF(160 KB)
Front. Comput. Sci. ›› DOI: 10.1007/s11704-008-0006-y

On the verification of polynomial system solvers

  • CHEN Changbo, MORENO MAZA Marc, PAN Wei, XIE Yuzhen
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Abstract

We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to polynomial systems which are easy to solve. We exhibit a new approach which manipulates constructible sets represented by regular systems. We provide comparative benchmarks of different verification procedures applied to four solvers on a large set of well-known polynomial systems. Our experimental results illustrate the high efficiency of our new approach. In particular, we are able to verify triangular decompositions of polynomial systems which are not easy to solve.

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CHEN Changbo, MORENO MAZA Marc, PAN Wei, XIE Yuzhen. On the verification of polynomial system solvers. Front. Comput. Sci., https://doi.org/10.1007/s11704-008-0006-y

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