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.

The intervals are specified as a list of two rational numbers. The list  represents the single point .  The list  with  represents the open real interval defined by  and . Multiplicity information is not included.

The function realroot uses Descartes' rule of signs (see Loos and Collins in Computer Algebra, B. Buchberger, ed.).