Multivariate polynomial decomposition

Applicable Algebra in Engineering, Communications and Computing

Volumn 14, Issue 1, 2003, Pages 11-31

  Von Zur Gathen, Joachim ^a   Gutierrez, Jaime ^b   Rubio, Rosario ^c  

^a UNIVERSITY OF PADERBORN   (Germany)

^b UNIVERSITY OF CANTABRIA   (Spain)

^c UNIVERSIDAD ANTONIO DE NEBRIJA   (Spain)

Author keywords

L roth's theorem; Polynomial decomposition algorithms

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTER SCIENCE; NETWORK PROTOCOLS; PROBLEM SOLVING; ROBOTICS; THEOREM PROVING;

LUROTHS THEOREM; MULTIVARIATE POLYNOMIAL DECOMPOSITION;

POLYNOMIALS;

EID: 0038105515     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-003-0122-8     Document Type: Article

References (35)

1. Alagar, V.S., Thanh, M.: Fast polynomial decomposition algorithms. Proceedings of Eurocal'85. Vol. II, B.F. Caviness, Ed. L.N. Computer Science, 204, Springer-Verlag, 1985, pp. 150-153
2. Alonso, C., Gutierrez, J., Recio, T.: A rational function decomposition algorithm by near-separated polynomials. J. Symbolic Comput. 19, 527-544 (1995)
3. Barton, R., Zippel, R. Polynomial Decomposition Algorithms. J. Symbolic Comput. 1, 159-168 (1985)
4. Binder, F.: Polynomial Decomposition. Diplomarbeit Universität Linz, June 1995
5. Cade, J.: A new public-key cipher which allows signatures. Proc. 2nd SIAM Conf on Appl. Linear Algebra. Raleigh NC. 1985
6. Casperson, D., Ford, D., MacKay, J.: An ideal decomposition Algorithm. J. Symbolic Comput. 21(2), 133-137 (1996)
7. Cooperman, G., Feisel, S., von zur Gathen, J., Havas, G.: GCD of Many Integers. Proceedings COCOON '99, number 1627 in Lecture Notes in Computer Science, 1999, pp. 310-317, Springer Verlag, 1999
8. Dickerson, M.: Functional Decomposition of Polynomials. Tech. Rep. 89-1023, Department of Computer Science, Cornell University, Ithaca NY. 1989.
9. von zur Gathen, J.: Functional decomposition of polynomials: the tame case. J. of Symbolic Computation 9, 281-299 (1990)
10. von zur Gathen, J.: Functional decomposition of polynomials: the wild case. J. of Symbolic Computation 10, 437-452 (1991)
11. von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, 1999
12. von zur Gathen, J., Gutierrez, J., Rubio, R.: On Multivariate Polynomial Decomposition. Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, CASC '99, München. Germany 1999, 463-478 (1999)
13. von zur Gathen, J., Kozen, D., Landau, S.: Functional decomposition of polynomials. Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, Los Angeles CA, 1987, 127-131 (1987)
14. von zur Gathen, J., Weiss, J.: Homogeneous Bivariate Decompositions. J. Symbolic Comput. 19, 409-434 (1995)
15. Gutierrez, J.: A polynomial decomposition algorithm over factorial domains. Tech. Report Math. Acad. Science Canada, Vol. xIII-2, pp. 437-452 (1992)
16. Gutierrez, J., Recio, T., Ruiz de Velasco, C.: A polynomial decomposition algorithm of almost quadratic complexity. Proc. AAECC-6/88. L. N. Computer Science 357, 471-476 (1989)
17. Gutierrez, J., Recio, T.: Advances on the simplification of sine-cosine equations. J. Symbolic Comput. 26, 31-70 (1998)
18. Gutierrez, J., Rubio, R.: Reduced Gröbner basis under composition. J. Symbolic Comput. 26, 433-444 (1998)
19. Gutierrez, J., Rubio, R.: Computing subfields in pure transcendental Extensions. Proc. IMACS'99, 1999
20. Gutierrez, J., Rubio, R.: CADECOM: Computer Algebra software for functional DECOMposition. Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, CASC-00, Samarkand, Uzbekistan, Springer-Verlag, 2000, pp. 233-248
21. Hommel, G., Kovács, P.: Simplification of symbolic inverse kinematic transformations through functional decomposition. Proc. of the Conference Adv. in Robotics. Ferrara, 88-95 (1992)
22. Hong, H.: Gröbner Basis Under Composition II. Proc. ISSAC-96, ACM press, 79-85 (1996)
23. Hong, H.: Gröbner basis under composition. J. Symbolic Comput. 25, 643-663 (1998)
24. Kozen, D., Landau, S.: Polynomial decomposition algorithms. Tech. Report, Department of Computer Science, Cornell University, Ithaca NY, 1986
25. Kozen, D., Landau, S.: Polynomial decomposition algorithms. J. Symbolic Comput. 7, 445-456 (1989)
26. Kozen, D., Landau, S., Zippel, R.: Decomposition of algebraic functions. J. Symbolic Comput. 22, 235-246 (1996)
27. Lang, S.: Algebra. Addison-Wesley, Reading, Mass, 1967
28. Luröth, J.: Beweis eines Satzes über rationale Curven. Mathematische Annalen 9, 163-165 (1876)
29. McKay, J., Wang, S.: A chain rule for the resultant of two polynomials. Arch. Math. 53, 347-351 (1989)
30. Nagata, M.: Theory of commutative fields. translations of Mathematical Monographs, vol. 125, American Mathematical Society, 1993
31. Pilz, G., So, Y.: Near-rings of polynomials and polynomial functions. J. Austral. Math. Soc. (series A) 29, 61-70 (1980)
32. Ritt, J.F.: Prime and composite polynomials. Trans. Amer. Math. Soc. 23, 51-66 (1922)
33. Schinzel, A.: Selected topics on polynomials. Ann Arbor, University of Michigan Press, 1982
34. Sweedler, M.: Using groebner based to determine the algebraic and transcedental nature of field extensions: return of the killer tag variables. Proc. AAECC-10/93, L. N. Computer Science, 678, 66-75 (1993)
35. Zippel, R.: Rational Function Decomposition. Proc. ISSAC-91, ACM Press, 1-6 (1991)