isolating intervals for real roots of a polynomial - Maple Help

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realroot - isolating intervals for real roots of a polynomial

Calling Sequence

realroot(poly, widthgoal)

Parameters

poly

-

univariate polynomial with integer coefficients

widthgoal

-

(optional) maximal size of each isolating interval

Description

• 

The command realroot(poly, widthgoal) returns a list of isolating intervals for all real roots of the univariate polynomial poly. The width of the interval is less than or equal to the optional parameter widthgoal, a positive number.  If widthgoal is omitted, the most convenient width is used for each interval returned.

• 

Each interval is returned as a list of two rational numbers. The list a&comma;a represents the single point a.  The list a&comma;b with a<b represents the open real interval defined by a and b. Multiplicity information is not included. The denominators of a and b are integer powers of 2.

• 

The intervals are sorted in ascending order.

• 

The algorithm behind realroot uses Descartes' rule of signs.

Examples

realrootx8&plus;5x74x620x5&plus;4x4&plus;20x3&comma;11000

5&comma;5&comma;57934096&comma;115858192&comma;0&comma;0&comma;115858192&comma;57934096

(1)

See Also

fsolve, RootFinding[Isolate], roots, Roots, solve

References

  

Loos and Collins, Computer Algebra, B. Buchberger, ed.


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