Speeding Up Cylindrical Algebraic Decomposition by Gröbner Bases

Speeding Up Cylindrical Algebraic Decomposition by Gröbner Bases
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DOI：
10.1007/978-3-642-31374-5_19
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发表时间：
2012-05
期刊：
ArXiv
影响因子：
--
通讯作者：
D. Wilson;R. Bradford;J. Davenport
D. Wilson;R. Bradford;J. Davenport
中科院分区：
其他
文献类型：
--
作者：
D. Wilson;R. Bradford;J. Davenport

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Gröbner基[Buc70]和柱代数分解[Col75，CMMXY09]通常被认为是两种截然不同的方法来研究方程组和在柱代数分解的情况下的不等式。然而，即使对于等式和不等式的混合系统，也可以在调用CAD之前将Gröbner基应用于(相连的)等式。我们看到，这经常但不总是是CAD问题的有益的前置条件，也可能是关于等式的(连接的)不等式的前置条件，这在许多情况下也是有用的。
Gröbner Bases [Buc70] and Cylindrical Algebraic Decomposition [Col75,CMMXY09] are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gröbner bases to the (conjoined) equalities before invoking CAD. We see that this is, quite often but not always, a beneficial preconditioning of the CAD problem.It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.