TY - JOUR
T1 - On Multivariate Hermitian Quadratic Forms
AU - Fukasaku, Ryoya
AU - Iwane, Hidenao
AU - Sato, Yosuke
N1 - Funding Information:
This work was partially supported by JSPS KAKENHI Grant Numbers 17K12642 and 18K03426.
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.
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U2 - 10.1007/s11786-018-0387-8
DO - 10.1007/s11786-018-0387-8
M3 - Article
AN - SCOPUS:85055314922
VL - 13
SP - 79
EP - 93
JO - Mathematics in Computer Science
JF - Mathematics in Computer Science
SN - 1661-8270
IS - 1-2
ER -