realroot - Maple Programming Help

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 $\left[a,a\right]$ represents the single point $a$.  The list $\left[a,b\right]$ with $a 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

 > $\mathrm{realroot}\left({x}^{8}+5{x}^{7}-4{x}^{6}-20{x}^{5}+4{x}^{4}+20{x}^{3},\frac{1}{1000}\right)$
 $\left[\left[{-}{5}{,}{-}{5}\right]{,}\left[{-}\frac{{5793}}{{4096}}{,}{-}\frac{{11585}}{{8192}}\right]{,}\left[{0}{,}{0}\right]{,}\left[\frac{{11585}}{{8192}}{,}\frac{{5793}}{{4096}}\right]\right]$ (1)

References

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