exact roots of a polynomial with respect to one variable
roots(a, x, K)
polynomial (either univariate or in x)
(optional) algebraic number field extension
(optional) polynomial variable
The roots function computes the exact roots of a polynomial over the rationals or an algebraic number field. The roots are returned as a list of pairs of the form [[r1,m1],...,[rn,mn]] where ri is a root of the polynomial a with multiplicity mi, that is, x−rimi divides a.
The call roots(a) returns roots over the field implied by the coefficients present. For example, if all the coefficients are rational, then the rational roots are computed. If a has no roots in the implied coefficient field, then an empty list is returned. This assumes that a is a univariate polynomials.
The call roots(a, K) computes the roots of a over the algebraic number field defined by K. Here K must be a single RootOf, or a list or set of RootOfs, or a single radical, or a list or set of radicals. For example, if I is given as the second argument, then roots looks for the roots of a over the complex rationals.
The calls roots(a, x) and roots(a, x, K) are equivalent to the above if a is univariate in x. Otherwise, it treats the other indeterminates in a as parameters, and finds all roots as above and ignoring symbolic roots.
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