On Multivariate Hermitian Quadratic Forms
On Multivariate Hermitian Quadratic Forms
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DOI：
10.1007/s11786-018-0387-8
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发表时间：
2018-10
影响因子：
0.8
通讯作者：
Ryoya Fukasaku;Hidenao Iwane;Yosuke Sato
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文献类型：
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作者：
Ryoya Fukasaku;Hidenao Iwane;Yosuke Sato
多元Hermitian二次型在V.Weispfenning提出的基于综合Gröbner系统计算的真实的量词消去算法中起着重要的作用。我们的算法需要在一个参数多项式环中计算某种类型的饱和理想。本文对多元厄米特二次型作了较详细的研究，并证明了在参数多项式环中具有特殊重要性的几个事实。我们的结果使我们有一个有效的方法来计算饱和理想，这带来了我们的真实的量词消除软件的显着改进。
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.