Download PDFOpen PDF in browserBit-size reduction of triangular sets in two and three variables14 pages•Published: March 27, 2016AbstractAt ISSAC 2004, Schost and D.introduced a transformation of triangular lexicographic Groebner bases generating a radical ideal of dimension zero, which reduces significantly the bit-size of coefficients. The case where the triangular lexicographic Groebner basis does not generate a radical ideal is far more complicated. This work treats the case of n=2 variables, and in some extent the case of n=3 variables. It resorts to an extra operation, the squarefree factorization; nevertheless this operation has low complexity cost. But as soon as n>2 variables a lack of simple and efficient gcd-like operation over non-reduced rings prevents to undertake meaningful algorithmic considerations. An implementation in Maple for the case n=2 confirms the expected reduction of the expected size coefficients. Keyphrases: bit size, lagrange interpolation, lexicographic groebner bases, multiplicity, triangular sets In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 169-182.
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