On Multivariate Polynomial Decomposition

In this paper, we discuss the decomposition problem for multivariate polynomials and the possible definitions of decomposable/indecomposable polynomial. We also present a polynomial time algorithm for decomposing multivariate polynomials over an arbitrary field.

[1]  Moss Sweedler,et al.  Using Groebner Bases to Determine the Algebraic and Transcendental Nature of Field Extensions: Return of the Killer Tag Variables , 1993, AAECC.

[2]  César Luis Alonso González.  Desarrollo, análisis e implementación de algoritmos para la manipulación de variedades paramétricas , 1994 .

[3]  Susan Landau,et al.  Polynomial Decomposition Algorithms , 1989, J. Symb. Comput..

[4]  Günter Pilz,et al.  Near-rings of polynomials and polynomial functions , 1980 .

[5]  Joachim von zur Gathen,et al.  Functional Decomposition of Polynomials: The Wild Case , 1990, J. Symb. Comput..

[6]  John McKay,et al.  Ideal Decompositions and Subfields , 1996, J. Symb. Comput..

[7]  Tomás Recio,et al.  A Rational Function Decomposition Algorithm by Near-Separated Polynomials , 1995, J. Symb. Comput..

[8]  Vangalur S. Alagar,et al.  Fast Polynominal Decomposition Algorithms , 1985, European Conference on Computer Algebra.

[9]  Hoon Hong.  Groebner Basis Under Composition I , 1998, J. Symb. Comput..

[10]  Jaime Gutierrez,et al.  Reduced Gröbner Bases Under Composition , 1998, J. Symb. Comput..

[11]  Jürgen Klüners,et al.  On Polynomial Decompositions , 1999, J. Symb. Comput..

[12]  M. Dickerson,et al.  The Functional Decomposition of Polynomials , 1989 .

[13]  W. Greub.  Linear Algebra , 1981 .

[14]  Joachim von zur Gathen,et al.  Homogeneous Bivariate Decompositions , 1995, J. Symb. Comput..

[15]  Joachim von zur Gathen,et al.  Functional Decomposition of Polynomials: The Tame Case , 1990, J. Symb. Comput..

[16]  Richard Zippel,et al.  Rational function decomposition , 1991, ISSAC '91.

[17]  Joachim von zur Gathen,et al.  Functional decomposition of polynomials , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[18]  Tomás Recio,et al.  Polynomial Decomposition Algorithm of Almost Quadratic Complexity , 1988, AAECC.

[19]  Andrzej Schinzel,et al.  Selected topics on polynomials , 1982 .

[20]  Tomás Recio,et al.  FRAC: A Maple Package for Computing in the Rational Function Field K(X) , 1994 .

[21]  Richard Zippel,et al.  Polynomial Decomposition Algorithms , 1985, J. Symb. Comput..

[22]  Tomás Recio,et al.  Advances on the Simplification of Sine-Cosine Equations , 1998, J. Symb. Comput..

[23]  Robert J. Lopez.  Maple V: Mathematics and its Applications , 1994 .