On solutions and Waring’s formulas for systems of $n$ algebraic equations for $n$ unknowns
On solutions and Waring’s formulas for systems of $n$ algebraic equations for $n$ unknowns
A system of $n$ algebraic equations for $n$ unknowns is considered, in which the collection of exponents is fixed, and the coefficients are variable. Since the solutions of such systems are $2n$-homogeneous, two coefficients in each equation can be fixed, which makes it possible to pass to the corresponding reduced …