Simplification of polynomials in n variables

Abstract

The object of this paper was to find an algorithm decreasing either the degree of a given polynomial P or the sum of the degrees of the monomials of P (this last algorithm being easier to perform).

We can also find other algorithms for the simplifications given at II, b. and c. In particular we can transform a given polynomial into a monic polynomial whose degree is minimum (without increasing the number of the monomials).

We can also define another simplification in order to decrease as much as possible the number of factors of all the monomials of a given polynomial. The simplified polynomial has a constant monomial and several monomials with only one factor.

Further information about such simplifications are given in [3]. But all these simplifications are limited by the size of the integer program we have to solve.