Rational function decomposition

This paper presents a polynomial time algorithm for determining whether a given univariate rational function over an arbitrary field is the composition of two rational functions over that field, and finds them if so.

[1]  Barry M. Trager,et al.  Algebraic factoring and rational function integration , 1976, SYMSAC '76.

[2]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[3]  F. Dorey,et al.  Prime and composite polynomials , 1974 .

[4]  Peter J. Weinberger,et al.  Factoring Polynomials Over Algebraic Number Fields , 1976, TOMS.

[5]  James B. Shearer,et al.  A Property of Euclid’s Algorithm and an Application to Padé Approximation , 1978 .

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

[7]  Donald Ervin Knuth,et al.  The Art of Computer Programming, Volume II: Seminumerical Algorithms , 1970 .

[8]  Matthew Dickerson The Inverse of an Automorphism in Polynomial Time , 1992, J. Symb. Comput..

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

[10]  Nöbeling Algebraische Theorie der Körper , 1931 .

[11]  H. T. Kung,et al.  All Algebraic Functions Can Be Computed Fast , 1978, JACM.

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

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

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

[15]  Gary L. Miller,et al.  Solvability by radicals is in polynomial time , 1983, STOC.

[16]  Richard Zippel,et al.  A polynomial decomposition algorithm , 1976, SYMSAC '76.

[17]  J. Lüroth,et al.  Beweis eines Satzes über rationale Curven , 1875 .

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

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

[20]  J. Ritt,et al.  Prime and composite polynomials , 1922 .

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

[22]  Erich Kaltofen,et al.  Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization , 1985, SIAM J. Comput..