By Ziming Li; William Y Sit (eds.)
Released in honour of Professor Gu Chaohao, this paintings covers matters heavily relating to differential geometry, partial differential equations and mathematical physics, the main parts within which Professor Gu has acquired striking achievements at the department of Generalized Polynomials (N Aris & A Rahman); On One estate of Hurwitz Determinants (L Burlakova); mixing Quadric Surfaces through a Base Curve process (J Cheng); An Exploration of Homotopy fixing in Maple (K Hazaveh et al.); a whole Maple package deal for Noncommutative Rational strength sequence (V Houseaux et al.); Implicitization of Polynomial Curves (I S Kotsireas & E S C Lau); Discrete accomplished Grobner Bases, II (Y Sato et al.); Displacement constitution in Computing Approximate GCD of Univariate Polynomials (L Zhi); and different papers
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Additional resources for Computer mathematics : proceedings of the Sixth Asian Symposium (ASCM 2003), Beijing, China, 17-19 April 2003
0 .. .. . . an A polynomial satisfying this property is called Hurwitzean, and the linear differential system, for which this polynomial is the characteristic one, possesses the property of asymptotic stability. The Routh-Hurwitz criterion is one of several alternative formulations of the criterion, and is frequently used in problems of stability, when the characteristic polynomial coefficients ai are functions of the parameters of the system under scrutiny. If the polynomial coefficients are given numerically then it is preferable to use other schemes to verify the Hurwitzean property [1,2].
We will sketch some applications of computation of holonomic functions to these areas. A system of linear differential equations P1u = .. = P,u = 0, where PI,. . ,P, are elements of the Weyl algebra 0, = C(x1,... ,x,, ax,.. ,an) over the field of the complex numbers with ai = a,, = and whose solutions, including higher order solutions (see Remark below), form a finite dimensional vector space, is called holonomic. Holonomic systems play a key role in the theory of D-modules. A function u is called holonomic, roughly speaking, if u satisfies a holonomic system.
M. Noro. An efficient modular algorithm for computing the global bfunction, Mathematical Software ( I C M S 2002) (2002), 147-157. 10. T. Oaku. Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients. Japan Journal of Industrial and Applied Mathematics 11 (1994), 485-497. 11. T. Oaku. Algorithms for the bfunction and D-modules associated with a polynomial. Journal of Pure and Applied Algebra 117 (1997), 495-518. 12. T. Oaku.