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arXiv · 1407.5898

On degrees of modular common divisors and the Big prime gcd algorithm

Vahagn H. Mikaelian
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Abstract

We consider a few modifications of the Big prime modular $\gcd$ algorithm for polynomials in $\Z[x]$. Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors of a resultant and on finding preliminary bounds on degrees of common divisors using auxiliary primes. These modifications are used to suggest improved algorithms for $\gcd$ calculation and for coprime polynomials detection. To illustrate the ideas we apply the constructed algorithms on certain polynomials, in particular, on polynomials from Knuth's example of intermediate expression swell.

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Vahagn H. Mikaelian. 2014-07-22. On degrees of modular common divisors and the Big prime gcd algorithm. https://arxiv.org/abs/1407.5898

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