Advanced Computer Algebra:
The resultant and gcd computation

Marc Moreno Maza
University of Western Ontario
CS424 / CS 556 - Winter 2005

Date: January 7, 2008

Coefficients growth in the Euclidean Algorithm over ${\mbox{${\mathbb{Q}}$}}[x]$
Relation between gcds in ${\mbox{${\mathbb{Q}}$}}[x]$ and ${\mbox{${\mathbb{Z}}$}}[x]$ . Polynomial gcds in non Euclidean domains.
The resultant
Lucky and unlucky modular reductions
Mignotte's factor bound
Modular Gcd Algorithms in ${\mbox{${\mathbb{Z}}$}}[x]$
A modular Gcd Algorithm in ${\mbox{${\mathbb{Z}}$}}[x_1, \ldots, x_n]$
A modular Gcd Algorithm in with Euclidean
Gcd Algorithms in ${\bf k}[x_1, \ldots , x_n]$ where ${\bf k}$ is a field
Bibliography
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Next: Coefficients growth in the Euclidean

Marc Moreno Maza
2008-01-07

Advanced Computer Algebra: The resultant and gcd computation

Advanced Computer Algebra:
The resultant and gcd computation