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FunctionExpandRootSum

Root

FilledSmallSquareRoot[f, k] represents the k root of the polynomial equation f[x] == 0.

FilledSmallSquaref must be a Function object such as (#^5 - 2 # + 1)&.

FilledSmallSquareRoot[f, k] is automatically reduced so that f has the smallest possible degree and smallest integer coefficients.

FilledSmallSquare The ordering used by Root takes real roots to come before complex ones, and takes complex conjugate pairs of roots to be adjacent.

FilledSmallSquare The coefficients in the polynomial f[x] can involve symbolic parameters.

FilledSmallSquare For linear and quadratic polynomials f[x], Root[f, k] is automatically reduced to explicit rational or radical form.

FilledSmallSquareN finds the approximate numerical value of a Root object.

FilledSmallSquare Operations such as Abs, Re, Round and Less can be used on Root objects.

FilledSmallSquareRoot[f, k] is treated as a numeric quantity if f contains no symbolic parameters.

FilledSmallSquareRoot by default isolates the roots of a polynomial using approximate numerical methods. No cases are known where this approach fails. SetOptions[Root, ExactRootIsolation->True] will however make Root use much slower but fully rigorous methods.

FilledSmallSquare See The Mathematica Book: Section 1.5.7 and Section 3.4.2.

FilledSmallSquare See also: Solve, RootReduce, ToRadicals, RootSum, Extension, Algebraics.

FilledSmallSquare Related package: Algebra`RootIsolation`.

Further Examples

FunctionExpandRootSum