AllRoots

*To*: mathgroup at yoda.physics.unc.edu*Subject*: AllRoots*From*: akyildiz at maths.ox.ac.uk ( Yilmaz Akyildiz tel 2-73558)*Date*: Mon, 19 Oct 92 11:27:13 BST

(* The previous version of the programme does not work for the initial interval [0, 2 Pi]. It must be because of the limitations with RealInterval. One way to get around this problem is to fatten the initial interval a bit in case it involves symbolic numbers. The following version is OK now. akyildiz at maths.oxford.ac.uk *) lefthalf[RealInterval[{x_, y_}]] := RealInterval[{x,(x+y)/2.}]; righthalf[RealInterval[{x_, y_}]] := RealInterval[{(x+y)/2.,y}]; containszero[RealInterval[{x_,y_}]] := (x <= 0 <= y); bisect[int_RealInterval] := {lefthalf[int],righthalf[int]}; intbisec[f_, a_, b_, tol_] := With[ {step = Select[(bisect/@#)//Flatten, containszero[N[f[#]]]&]& }, Nest[step, {RealInterval[N[{a-tol/2.,b+tol/2.}]]}, Ceiling[Log[2,N[(b-a)]/tol]]] ];