HOMOGENEOUS BIVARIATE DECOMPOSITIONS

被引：9

作者：

VONZURGATHEN, J

WEISS, J

机构：

[1] UNIV TORONTO, DEPT COMP SCI, TORONTO, ON M5S 1A4, CANADA

[2] UNIV BONN, INST INFORMAT 1, D-53731 ST AUGUSTIN, GERMANY

[3] GMD, INST I1, D-53731 ST AUGUSTIN, GERMANY

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 1995年 / 19卷 / 05期

关键词：

D O I：

10.1006/jsco.1995.1024

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A homogeneous bivariate decomposition of a univariate polynomial f is of the form f = g(h, k) with polynomials g, h, Ic, where g is bivariate and homogeneous. Such decompositions are of interest in robotics applications. This paper gives a Structure Theorem relating these decompositions to certain block decompositions of the roots of f, decomposition algorithms, and a classification of all constellations of degrees for which ''almost all'' polynomials f have such a decomposition.

引用

页码：409 / 434

页数：26

共 26 条

[1]

Dickerson M.T., The Functional Decomposition of Polynomials. Phd Thesis, Cornell University, (1989)

[2]

Von Zur Gathen J., Irreducibility of multivariate polynomials, Journal of Computer and System Sciences, 31, pp. 225-264, (1985)

[3]

Von Zur Gathen J., Functional decomposition of polynomials: The tame case, J. Symbolic Computation, 9, pp. 281-299, (1990)

[4]

Vonzur Gathen J., Functional decomposition of polynomials: The wild case, J. Symbolic Computation, 10, pp. 437-452, (1990)

[5]

Ghazvini M., Reducing the inverse kinematics of manipulators to the solution of a generalized eigenproblem, Computational Kinematics, Vol. 28. Solid Mechanics and Its Application, pp. 15-26, (1993)

[6]

Gutierrez J., Recio T., A practical implementation of two rational function decomposition algorithms, Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 92, pp. 152-157, (1992)

[7]

Heintz J., Sieveking M., Lower bounds for polynomials with algebraic coefficients, Theoretical Computer Science, 11, pp. 321-330, (1980)

[8]

Kovacs P., Hommel G., Factorization and decomposition in kinematic equation systems, Forschungsbericht 1990-23, (1990)

[9]

Kovacs P., Hommel G., An expert system for the optimal symbolic solution of the inverse kinematics problem, Proc. Int. Conf. Autom., Robotics and Computer Vision, Singapore, (1992)

[10]

Kozen D., Landau S., Polynomial decomposition algorithms, J. Symbolic Computation, 7, pp. 445-456, (1989)

← 1 2 3 →