Let F = ( f 1 , … … , f k ) = ( p 1 / q 1 , … … , p k / q k ) be a finite set of rational functions over the field R where p i and q i are polynomials in R [ Z ] i.e. in variables Z = ( z 1 , … … , z n ) with coefficients in R . An algebraic system associated to F is defined by the following equalities and inequalities: