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

Vahagn H. Mikaelian
2014 arXiv   pre-print
We consider a few modifications of the Big prime modular algorithm for polynomials in [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 calculation and for coprime polynomials detection. To illustrate the ideas we apply the constructed
more » ... ithms on certain polynomials, in particular, on polynomials from Knuth's example of intermediate expression swell.
arXiv:1407.5898v1 fatcat:2t7blorqmzcxvizienlfktb7t4