On Multiple Zeros of Systems of Algebraic Equations

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn 1999-January, Issue , 1999, Pages 23-30

  Moritsugu, Shuichi ^a   Kuriyama, Kazuko ^b  

^a UNIVERSITY OF TSUKUBA   (Japan)

^b NATIONAL INSTITUTE OF INFORMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; EIGENVALUES AND EIGENFUNCTIONS;

BLOCK DIAGONAL; DIFFERENTIAL CONDITIONS; DUAL BASIS; DUAL SPACES; EIGEN-VALUE; JORDAN NORMAL FORMS; MATRIX; NORMAL SETS; RESIDUE CLASS RING; SYSTEMS OF ALGEBRAIC EQUATIONS;

MATRIX ALGEBRA;

EID: 0013301023     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/309831.309846     Document Type: Conference Paper

References (21)

1. AUZINGER, W., AND STETTER, H. J. An Elimination Algorithm for the Computation of All Zeros of a System of Multivariate Polynomial Equations. In Numerical, Mathematics Singapore 1988 (1988), vol. 80 of Interna-tional Series of Numerical Mathematics, pp. 11-30.
2. BUCHBERGER, B. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenririfies nach einem nulldimensionalen Polynomideal. PhD thesis, Univer-sitat Innsbruck, 1905.
3. BUCHBERGER, B. Ein Algorithmisches Kritcrium fiir die Losbarkeit eines algebraischen Gleichungssystems. Aequationes Mathematical 4, 3 (1970), 374-383.
4. CORLKSS, R. M. Editor's Corner: Grobner Bases and Matrix Eigenproblems. ACM SIGSAM Dull. 30, A (1990), 20- 32.
5. CORLESS. R. M., GIANNI, P., AND TRACER, B. M. A Reordered Schur Factorization Method for Zero-dimensional Polynomial Systems with Multiple Roots. In ISSAC '97 (1997), pp. 133-140.
6. Cox. D., LITTLE, J., AND O'SHEA, D. Using Algebraic Geometry. Springer. 1998.
7. FAUGERE, J. C, GIANNI, P., LAZARD, D., AND MORA, T. Efficient Computation of Zero-Dimensional Grobner Basis bv Change of Ordering. J.Symbolic Computation 16, 4 (1993), 329-344.
8. GELFAND, I. M., KAPKANOV, M. M., AND ZELEVIN-SKY, A. V. Discriminants, Resultants and Multidimen-sional Determinants. Birkhauser, 1994.
9. KAN, T., AND IRI, M. Jordan Normal Form. Univ. of Tokyo Press, 1982. (in Japanese).
10. KOBAYASHI, H.. FUJISE, T., AND Furukawa. A. Solv-ing Systems of Algebraic Equations by a General Elim-ination Method. J.Symbolic Computation 5, 3 (1988), 303-320.
11. n] et elimination. Dull.Soc. Math. France 105. 2 (1977), 105-190.
12. LAZARD, D. Resolution des systèmes d'èquations algebriques. Theor.Comp.Sci. 15 (1981), 77-110.
13. MARINARI, M. G., MOLLER, H. M., AND MORA, T. Gobner Bases of Ideals Given by Dual Bases. In ISSAC '91 (1991), pp. 55-63.
14. MOLLER, H. M. Systems of Algebraic Equations Solved by Means of Endomorphisms. In AAECC 10 (1993), vol. 073 of Lcct. Notes in Comp. Sci., pp. 43-50.
15. MOLLER, H. M., AND STETTER, H. J. Multivariate Polynomial Equations with Multiple Zeros Solved by-Matrix Eigenproblems. Numer.Math. 70, 3 (1995), 311-329.
16. MORITSUGU, S., AND KURIYAMA, K. A Linear Al-gebra Method for Solving Systems of Algebraic Equa-tions. RISC-Linz Report Series 97-35, RISC-Linz. 1997. (http://www.risc.uni-linz.ac.at/library/).
17. STETTER, H. J. Multivariate Polynomial Equations as Matrix Eigenproblems. In Contributions in Numerical Mathematics (1993), vol. 2 of World Scientific Series in Applicable Analysis, pp. 355-371.
18. STETTER, H. J. Matrix Eigenproblem are at. the Heart of Polynomial System Solving. ACM SIGSAM Dull. 30, A (1990), 22-25.
19. TAKESHIMA, T., AND YOKOYAMA, K. A Solution of Systems of Algebraic Equations - Application of Eigenvectors of Linear Maps on Residue Class Rings. Comm.Symb.Algeb.Manip. 6, 4 (1990), 27-30. (in Japanese).
20. VAN DER WAERDEN, B. L. Modeme Algebra, vol. II. Springer, 1931.
21. YOKOYAMA. K., NORO, M., AND TAKESHIMA, T. So-lutions of Systems of Algebraic Equations and Linear Maps on Residue Class Rings. J. Symbolic Computation 14, 4 (1992), 399-417.