IsolatingInterval
gives a rational isolating interval for the algebraic number a.
IsolatingInterval[a,dx]
gives an isolating interval of width at most dx.
Details
- 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.
Examples
open all close allBasic Examples (2)
Find an isolating interval of 
:
IsolatingInterval[Sqrt[2]]Find an isolating interval of 
with width less than 
:
{a, b} = IsolatingInterval[Sqrt[2], 10 ^ -10]Check that 
belongs to [a,b] and the width of [a,b] is less than 
:
a ≤ Sqrt[2] ≤ b && b - a < 10 ^ -10Scope (7)
Isolating interval of a rational number:
IsolatingInterval[1 / 2]Isolating interval of a Gaussian rational number:
IsolatingInterval[1 / 2 + I]Isolating interval of a radical:
IsolatingInterval[(-2) ^ (2 / 3)]Isolating interval of a Root object:
IsolatingInterval[Root[# ^ 5 - 2# + 11&, 1]]Isolating interval of an AlgebraicNumber object:
IsolatingInterval[AlgebraicNumber[Root[# ^ 5 - 2# + 11&, 1], {1, 2, 3, 4, 5}]]Isolating interval of an algebraic combination of algebraic numbers:
IsolatingInterval[Sqrt[2] + Root[# ^ 5 - 2# + 11&, 1] ^ 2 / 7]Isolating interval with width less than 
:
IsolatingInterval[Sqrt[2] + Root[# ^ 5 - 2# + 11&, 1] ^ 2 / 7, 2 ^ -100]Properties & Relations (2)
Use RootIntervals to find isolating intervals for all real roots of a polynomial:
RootIntervals[x ^ 5 - 2x + 1]Find isolating intervals for all complex roots of a polynomial:
RootIntervals[x ^ 5 - 2x + 1, Complexes]Find an isolating interval of a real algebraic number:
alg = Sqrt[2 + Sqrt[3]];
{a, b} = IsolatingInterval[alg]Use MinimalPolynomial to find the minimal polynomial of the algebraic number:
poly = MinimalPolynomial[alg, x]Use FindRoot to find an approximation of the root of poly in [a,b]:
FindRoot[poly == 0, {x, a, b}, Method -> "Brent"]Compute an approximation of alg directly:
N[alg]Text
Wolfram Research (2007), IsolatingInterval, Wolfram Language function, https://reference.wolfram.com/language/ref/IsolatingInterval.html.
CMS
Wolfram Language. 2007. "IsolatingInterval." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/IsolatingInterval.html.
APA
Wolfram Language. (2007). IsolatingInterval. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IsolatingInterval.html