TY - GEN

T1 - On the bit-size of non-radical triangular sets

AU - Dahan, Xavier

N1 - Funding Information:
Work supported by the JSPS grant Wakate B No. 50567518.
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - We present upper bounds on the bit-size of coefficients of non-radical purely lexicographical Gröbner bases (triangular sets) in dimension zero. This extends a previous work [4], constrained to radical triangular sets; it follows the same technical steps, based on interpolation. However, key notion of height of varieties is not available for points with multiplicities; therefore the bounds obtained are thus less universal and depend on some input data. We also introduce a related family of non-monic polynomials that have smaller coefficients, and smaller bounds. It is not obvious to compute them from the initial triangular set though.

AB - We present upper bounds on the bit-size of coefficients of non-radical purely lexicographical Gröbner bases (triangular sets) in dimension zero. This extends a previous work [4], constrained to radical triangular sets; it follows the same technical steps, based on interpolation. However, key notion of height of varieties is not available for points with multiplicities; therefore the bounds obtained are thus less universal and depend on some input data. We also introduce a related family of non-monic polynomials that have smaller coefficients, and smaller bounds. It is not obvious to compute them from the initial triangular set though.

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U2 - 10.1007/978-3-319-72453-9_19

DO - 10.1007/978-3-319-72453-9_19

M3 - Conference contribution

AN - SCOPUS:85039451697

SN - 9783319724522

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 264

EP - 269

BT - Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings

A2 - Kotsireas, Ilias S.

A2 - Blomer, Johannes

A2 - Simos, Dimitris E.

A2 - Kutsia, Temur

PB - Springer Verlag

T2 - 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017

Y2 - 15 November 2017 through 17 November 2017

ER -