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RootSum

RootSum
represents the sum of for all x that satisfy the polynomial equation .
  • form need not correspond to a polynomial function.
  • f and form can contain symbolic parameters.
  • RootSum is automatically simplified whenever form is a rational function.
  • RootSum is often generated in computing integrals of rational functions.
Integrating a rational function of any order:
Evaluate numerically:
Automatic simplification of RootSum objects:
Integrating a rational function of any order:
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Evaluate numerically:
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Automatic simplification of RootSum objects:
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Compute a numerical approximation of a RootSum:
Evaluate to high precision:
Sums over roots of polynomials with inexact number coefficients:
Sums of numeric functions over roots of quadratics:
Sums of rational functions of roots:
Sums of logarithms of linear functions over roots of polynomials with rational coefficients:
Sums of numeric functions over roots of polynomials with multiple factors:
Represent a RootSum explicitly in terms of Root objects:
Derivatives:
Integrals:
Limits:
Series:
Integrate a rational function:
Sum a rational function:
Matrix exponential of any order:
Vieta's formulas:
The residue theorem:
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