抄録
Multivariate Hermitian quadratic forms play an important role in the real quantifier elimination algorithm based on the computation of comprehensive Gröbner systems introduced by V. Weispfenning and further improved by us. Our algorithm needs the computation of a certain type of saturation ideal in a parametric polynomial ring. In this paper, we study multivariate Hermitian quadratic forms in more detail and show several facts which have special importance in a parametric polynomial ring. Our results enable us to have an efficient method to compute the saturation ideal, which brings us a drastic improvement of our real quantifier elimination software.
| 元の言語 | 英語 |
|---|---|
| ページ（範囲） | 79-93 |
| ページ数 | 15 |
| ジャーナル | Mathematics in Computer Science |
| 巻 | 13 |
| 発行部数 | 1-2 |
| DOI | |
| 出版物ステータス | 出版済み - 6 1 2019 |
| 外部発表 | Yes |
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All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics
これを引用
On Multivariate Hermitian Quadratic Forms. / Fukasaku, Ryoya; Iwane, Hidenao; Sato, Yosuke.
：: Mathematics in Computer Science, 巻 13, 番号 1-2, 01.06.2019, p. 79-93.研究成果: ジャーナルへの寄稿 › 記事
}
TY - JOUR
T1 - On Multivariate Hermitian Quadratic Forms
AU - Fukasaku, Ryoya
AU - Iwane, Hidenao
AU - Sato, Yosuke
PY - 2019/6/1
Y1 - 2019/6/1
N2 - Multivariate Hermitian quadratic forms play an important role in the real quantifier elimination algorithm based on the computation of comprehensive Gröbner systems introduced by V. Weispfenning and further improved by us. Our algorithm needs the computation of a certain type of saturation ideal in a parametric polynomial ring. In this paper, we study multivariate Hermitian quadratic forms in more detail and show several facts which have special importance in a parametric polynomial ring. Our results enable us to have an efficient method to compute the saturation ideal, which brings us a drastic improvement of our real quantifier elimination software.
AB - Multivariate Hermitian quadratic forms play an important role in the real quantifier elimination algorithm based on the computation of comprehensive Gröbner systems introduced by V. Weispfenning and further improved by us. Our algorithm needs the computation of a certain type of saturation ideal in a parametric polynomial ring. In this paper, we study multivariate Hermitian quadratic forms in more detail and show several facts which have special importance in a parametric polynomial ring. Our results enable us to have an efficient method to compute the saturation ideal, which brings us a drastic improvement of our real quantifier elimination software.
UR - http://www.scopus.com/inward/record.url?scp=85055314922&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85055314922&partnerID=8YFLogxK
U2 - 10.1007/s11786-018-0387-8
DO - 10.1007/s11786-018-0387-8
M3 - Article
VL - 13
SP - 79
EP - 93
JO - Mathematics in Computer Science
JF - Mathematics in Computer Science
SN - 1661-8270
IS - 1-2
ER -