Now one may change the point of view, by taking the roots rather than the coefficients as basic parameters for describing "P", and considering them as indeterminates rather than as constants in an appropriate field; the coefficients "a""i" then become just the particular symmetric polynomials given by the above equations. Those polynomials, without the sign formula_14, are known as the elementary symmetric polynomials in "x"1,…,"x""n". A basic fact, known as the fundamental theorem of symmetric polynomials states that "any" symmetric polynomial in "n" variables can be given by a polynomial expression in terms of these elementary symmetric polynomials. It follows that any symmetric polynomial expression in the roots of a monic polynomial can be expressed as a polynomial in the "coefficients" of the polynomial, and in particular that its value lies in the base field "k" that contains those coefficients. Thus, when working only with such symmetric polynomial expressions in the roots, it is unnecessary to know anything particular about those roots, or to compute in any larger field than "k" in which those roots may lie. In fact the values of the roots themselves become rather irrelevant, and the necessary relations between coefficients and symmetric polynomial expressions can be found by computations in terms of symmetric polynomials only. An example of such relations are Newton's identities, which express the sum of any fixed power of the roots in terms of the elementary symmetric polynomials.