RootSum

Sum of form[r] over the roots r of a polynomial; numeric-coefficient polynomial f with polynomial form gives an exact power-sum value via Newton identities; other shapes stay symbolic

形式

RootSum[f, form]

验证过的示例N[RootSum[# ^ 5 - 3# - 7&, Sin]] → 0.29218763022095307 D[RootSum[# ^ 5 + a # + 1&, Exp[#]&], a] → D[Exp[#1] & , a]*Derivative[0, 1][RootSum][#1^5 + a*#1 + 1 & , Exp[#1] & ] + D[#1^5 + a*#1 + 1 & , a]*Derivative[1, 0][RootSum][#1^5 + a*#1 + 1 & , Exp[#1] & ]D[RootSum[# ^ 5 + 11# + 1&, Exp[a #]&], a] → D[Exp[a*#1] & , a]*Derivative[0, 1][RootSum][#1^5 + 11*#1 + 1 & , Exp[a*#1] & ] + D[#1^5 + 11*#1 + 1 & , a]*Derivative[1, 0][RootSum][#1^5 + 11*#1 + 1 & , Exp[a*#1] & ]

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主题

Polynomial Algebra - Algebraic Number Fields »

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