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.

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

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Basic Examples  (2)

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 :

Scope  (7)

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 :

Properties & Relations  (2)

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:

Wolfram Research (2007), IsolatingInterval, Wolfram Language function, https://reference.wolfram.com/language/ref/IsolatingInterval.html.

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

BibTeX

@misc{reference.wolfram_2024_isolatinginterval, author="Wolfram Research", title="{IsolatingInterval}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/IsolatingInterval.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_isolatinginterval, organization={Wolfram Research}, title={IsolatingInterval}, year={2007}, url={https://reference.wolfram.com/language/ref/IsolatingInterval.html}, note=[Accessed: 21-December-2024 ]}