BUILT-IN MATHEMATICA SYMBOL

RootIntervals

gives a list of isolating intervals for the real roots of any of the

, together with a list of which polynomials actually have each successive root.

RootIntervals[poly]
gives isolating intervals for real roots of a single polynomial.

RootIntervals[polys, Complexes]
gives bounding rectangles for complex roots.

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.

Get isolating intervals, together with a list of which polynomial has which root:

The isolating intervals are always specified by exact rationals:

Get isolating intervals, together with a list of which polynomial has which root:

Out[1]=

The isolating intervals are always specified by exact rationals:

Out[1]=

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:

Isolating intervals of rational roots may be single points:

Find numeric approximations of real roots of a polynomial:

Find isolating intervals:

Find root approximations:

Reduce uses a similar approach, but factoring the polynomial for Root objects takes time:

Compute approximations of the Root objects:

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: