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Reference.org
Power sum symmetric polynomial
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, specifically in <a href="/facts/Commutative_algebra/mKtUdPCT">commutative algebra</a>, the power sum symmetric polynomials are a type of basic building block for <a href="/facts/Symmetric_polynomial/GNhguVcn">symmetric polynomials</a>, in the sense that every symmetric polynomial with <a href="/facts/Rational_number/VJQmyY05">rational</a> <a href="/facts/Coefficient/5Hwq2Wuq">coefficients</a> can be expressed as a sum and difference of products of power sum symmetric polynomials with rational coefficients. However, not every symmetric polynomial with <a href="/facts/Integer/PUwwrawx">integral</a> coefficients is generated by integral combinations of products of power-sum polynomials: they are a generating set over the <i>rationals,</i> but not over the <i>integers.</i> </p>