gives a list of isolating intervals for the real roots of any of the polyi, together with a list of which polynomials actually have each successive root.
gives isolating intervals for real roots of a single polynomial.
gives bounding rectangles for complex roots.
- The coefficients of poly must be integers or rationals.
- An isolating interval for a root of a polynomial poly is an interval where the only root of poly contained in the interval is .
- If a root is real, the isolating interval is an open real interval, or a point. If a root is not real, the isolating interval is an open rectangle, disjoint from the real axis.
- Multiple roots give multiple entries in the second list generated by RootIntervals.
Examplesopen allclose all
Basic Examples (2)
Isolate the real roots of a polynomial:
Isolate the real roots of a list of polynomials:
Isolate the complex roots of a polynomial:
Isolate the complex roots of a list of polynomials:
Polynomials may have multiple roots; pairs of polynomials may have common roots:
Properties & Relations (1)
Find real and complex roots of polynomials:
Isolate the real roots; multiple roots are indicated in the second part of the output:
Use CountRoots to count the real roots; multiple roots are counted with multiplicities:
Use Reduce to find the real roots; multiple roots are given once:
Isolate the complex roots; multiple roots are indicated in the second part of the output:
Use Reduce to find the complex roots; multiple roots are given once:
Use Solve to find the complex roots with multiplicities:
Wolfram Research (2007), RootIntervals, Wolfram Language function, https://reference.wolfram.com/language/ref/RootIntervals.html.
Wolfram Language. 2007. "RootIntervals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RootIntervals.html.
Wolfram Language. (2007). RootIntervals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RootIntervals.html