Abstract
Some methods for polynomial system solving require efficient techniques for computing univariate polynomial gcd over algebraic extensions of a field. Currently used techniques compute generic univariate polynomial gcd before specializing the result using algebraic relations in the ring of coefficients. This strategy generates very big intermediate data and fails for many problems. We present here a new approach which takes permanently into account those algebraic relations. It is based on a property of subresultant remainder sequences and leads to a great increase of the speed of computation and thus the size of accessible problems.
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Maza, M.M., Rioboo, R. (1995). Polynomial gcd computations over towers of algebraic extensions. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_28
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DOI: https://doi.org/10.1007/3-540-60114-7_28
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