The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Modern computer algebra
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
A long note on Mulders' short product
Journal of Symbolic Computation
Fast library for number theory: an introduction
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
On the boolean complexity of real root refinement
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Arb: a C library for ball arithmetic
ACM Communications in Computer Algebra
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We investigate two practical divide-and-conquer style algorithms for univariate polynomial arithmetic. First we revisit an algorithm originally described by Brent and Kung for composition of power series, showing that it can be applied practically to composition of polynomials in Z[x] given in the standard monomial basis. We offer a complexity analysis, showing that it is asymptotically fast, avoiding coefficient explosion in Z[x]. Secondly we provide an improvement to Mulders' polynomial division algorithm. We show that it is particularly efficient compared with the multimodular algorithm. The algorithms are straightforward to implement and available in the open source FLINT C library. We offer a practical comparison of our implementations with various computer algebra systems.