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.
UR - http://www.scopus.com/inward/record.url?scp=85039451697&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85039451697&partnerID=8YFLogxK
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 -