- 1.ABBOTT, J. A., BRADFORD, R. J., AND DAVENPORT, J. H. A remark on factorization. SIGSAM Bulletin 19, 2 (1985), 31 33 and 37.]] Google ScholarDigital Library
- 2.CARLITZ, L. The arithmetic of polynomials in a Galois field. American Journal of Mathematics 54 (1932), 39- 50.]]Google ScholarCross Ref
- 3.COLLINS, G. F,., AND ENCARNACION, M. J. Improved techniques for factoring univaxiate polynomials. Journal of Symbolic Computation 21 (1996), 313-327.]] Google ScholarDigital Library
- 4.ENC:ARNA(_:ION, N'I. J. Factoring polynomials over algebraic number fields via norms. Proceedings of ISSAC '97 (Hawaii, USA, I997), ACM Press, pp. 265-270.]] Google ScholarDigital Library
- 5.KALTOFEN, E., MUSSER, D. R., AND SAUNDERS, B. D. A generalized class of polynomials that are hard to factor. SIAM Journal on Computing 12, 3 (1983), 473- 483.]]Google ScholarCross Ref
- 6.KNOPFMA('.ItER, A., AND KNOPFMACttER, 3. Counting irreducible factors of polynomials over a finite field. Discrete Mathematics i12 (1993), 103--.118.]] Google ScholarDigital Library
- 7.KNUTH. D. E. Fundamental Algorithms: The Art of Computer Programming I, second ed. Addison-Wesley, 1973.]] Google ScholarDigital Library
- 8.KNUTtt, D. E. Seminumerical Algorithms: The Art of Computer PrograTnming 2, second ed. Addison-Wesley, 1981.]]Google Scholar
- 9.TRAGER, B. M. Algebraic factoring and rational function integration. In Proceedings of the 1975 Symposium on Symbolic and Algebraic Computation (1976), ACM Press, pp. 219- 226.]] Google ScholarDigital Library
Index Terms
- The average number of modular factors in Trager's polynomial factorization algorithm
Recommendations
Exact polynomial factorization by approximate high degree algebraic numbers
SNC '09: Proceedings of the 2009 conference on Symbolic numeric computationFor factoring polynomials in two variables with rational coefficients, an algorithm using transcendental evaluation was presented by Hulst and Lenstra. In their algorithm, transcendence measure was computed. However, a constant c is necessary to compute ...
Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization
Consider a polynomial f with an arbitrary but fixed number of variables and with integral coefficients. We present an algorithm which reduces the problem of finding the irreducible factors of f in polynomial-time in the total degree of f and the ...
Average characteristic polynomials for multiple orthogonal polynomial ensembles
Multiple orthogonal polynomials (MOP) are a non-definite version of matrix orthogonal polynomials. They are described by a Riemann-Hilbert matrix Y consisting of four blocks Y"1","1, Y"1","2, Y"2","1 and Y"2","2. In this paper, we show that detY"1","1 (...
Comments