Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients
Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients
复制标题
多项式系数微分方程组特征变异和奇异轨迹的计算
DOI：
10.1007/bf03167233
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发表时间：
1994
影响因子：
0.9
通讯作者：
T. Oaku
中科院分区：
文献类型：
--
作者：
T. Oaku
事实证明，对于具有多项式系数的线性微分方程系统，Weyl代数中的Gröbner基础足以计算特征品种，这会产生正确的算法。多项式系数。通过纯粹的代数程序，可以在计算机代数系统上很容易地计算具有多项式系数的微分方程系统的特征性变体和奇异局部。
It is proved that for a system of linear partial differential equations with polynomial coefficients, the Gröbner basis in the Weyl algebra is sufficient for the computation of the characteristic variety. In particular, this yields a correct algorithm of computing the singular locus of a holonomic system with polynomial coefficients. The characteristic variety is defined analytically, i.e. by using the ring of power series, and it has not been obvious that it can be computed by purely algebraic procedure. Thus the algorithm of computing the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients can be readily implemented on a computer algebra system.
DOI：
10.1145/143242.143362
发表时间：
1992-08
期刊：
--
影响因子：
--
作者：
M. Noro;T. Takeshima
通讯作者：
M. Noro;T. Takeshima