Course Content

• A review of objects and data-structures in computer algebra.
• Using distributivity for speeding up multiplication of polynomials and matrices (algorithms of Karatsuba and Strassen).
• Modular computations. Interpolation and Chinese remaindering.
• Fast multiplication of polynomials based on the fast Fourier transform.
• Newton iteration. Fast division using Newton iteration.
• Fast interpolation and fast Chinese remaindering.
• Fast linear algebra.
• Lifting techniques.
• Polynomial gcd and factorization.
• Fast computation over algebraic number fields.

Each topic will be illustrated by practical experiments using

• the AXIOM Computer Algebra system and
• the ALDOR compiler and libraries.

For more information about ALDOR please visit:

http://www.aldor.org.