REDUCE - A Case Study in Algebra System Development
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
Algebraic factoring and rational function integration
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Implementing a polynomial factorization and GCD package
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
The Bath algebraic number package
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Factoring polynomials over algebraic number fields via norms
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
The average number of modular factors in Trager's polynomial factorization algorithm
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Factorization in Z[x]: the searching phase
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Small algorithms for small systems
ACM Communications in Computer Algebra
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We are concerned with factoring polynomials over algebraic extensions of the rationals, and have implemented a variant of Trager's [1976] algorithm, which reduces this problem to that of factoring polynomials over the integers, for which we use Wang's [1978] algorithm (as implemented in REDUCE [Hearn 82] by Moore and Norman [1981]). However, Trager's method often produces a norm polynomial which factors profusely modulo every prime, leading to a combinatorial explosion of trial divisions in Wang's algorithm. We present some simple divisibility tests for polynomials to help combat the cost of this explosion.