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RootSum

  • RootSum[ f , form ] represents the sum of form [ x ] for all x that satisfy the polynomial equation f [ x ] == 0.
  • f must be a Function object such as (#^5 - 2 # + 1)&.
  • form need not correspond to a polynomial function.
  • Normal[ expr ] expands RootSum objects into explicit sums involving Root objects.
  • f and form can contain symbolic parameters.
  • RootSum[ f , form ] is automatically simplified whenever form is a rational function.
  • RootSum is often generated in computing integrals of rational functions.
  • See the Mathematica book: Section 3.4.3.
  • See also: Root.
  • Related package: Algebra`SymmetricPolynomials`.

    Further Examples

    This gives the sum of the seventh powers of the roots of the quintic.

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    Here is the sum of the logarithms.

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    The sum of exponentials is not evaluated explicitly, but we can get its numerical value with N.

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    In this polynomial the coefficients of the linear term is symbolic. We can get numerical results by substitution.

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