Built-in Mathematica Symbol

IsolatingInterval

IsolatingInterval[a]
gives a rational isolating interval for the algebraic number a.

IsolatingInterval[a, dx]
gives an isolating interval of width at most dx.

IsolatingInterval[a] gives an interval that does not contain any other root with the same minimal polynomial as a.

If a is complex, IsolatingInterval[a] gives a pair of Gaussian rationals defining an isolating rectangle in the complex plane.

Find an isolating interval of

:

Find an isolating interval of

with width less than

:

Check that

belongs to [a, b] and the width of [a, b] is less than

:

Find an isolating interval of

:

Find an isolating interval of

with width less than

:

Check that

belongs to [a, b] and the width of [a, b] is less than

:

Isolating interval of a rational number:

Isolating interval of a Gaussian rational number:

Isolating interval of a radical:

Isolating interval of a Root object:

Isolating interval of an AlgebraicNumber object:

Isolating interval of an algebraic combination of algebraic numbers:

Isolating interval with width less than

:

Use RootIntervals to find isolating intervals for all real roots of a polynomial:

Find isolating intervals for all complex roots of a polynomial:

Find an isolating interval of a real algebraic number:

Use MinimalPolynomial to find the minimal polynomial of the algebraic number:

Use FindRoot to find an approximation of the root of poly in [a, b]:

Compute an approximation of alg directly: