High Degree Toom´n´Half for Balanced and Unbalanced Multiplication

Some hints and tricks to automatically obtain high degree Toom-Cook implementations, i.e. functions for integer or polynomial multiplication with a reduced complexity. The described method generates quite an efficient sequence of operations and the memory footprint is kept low by using a new strategy: mixing evaluation, interpolation and recomposition phases. It is possible to automatise the whole procedure obtaining a general Toom-n function, and to extend the method to polynomials in any characteristic except two.