Abstract
The problem of factorising polynomials: that is to say, given a polynomial with integer coefficients, to find the irreducible polynomials that divide it, is one with a long history. While the last word has not been said on the subject, we can say that the past 15 years have seen major break-throughs, and many computer algebra systems now include efficient algorithms for this problem. When it comes to polynomials with algebraic number coefficients, the problem is far harder, and several major questions remain to be answered. Nevertheless, the last few years have seen substantial improvements, and such factorisations are now possible.
This research is partially supported by the Science and Engineering Research Council, and the University of Bath Research Fund
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Abbott, J.A., Bradford, R.J., Davenport, J.H. (1988). Factorisation of polynomials: Old ideas and recent results. In: Janßen, R. (eds) Trends in Computer Algebra. Lecture Notes in Computer Science, vol 296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18928-9_6
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