|  |  D.15.30.10 rootIsolationNoPreprocessing Procedure from libraryrootisolation.lib(see  rootisolation_lib).
 
Example:Usage:
rootIsolationNoPreprocessing(I, B, eps);I ideal, B list of boxes, eps number;
Assume:
Iis a zero-dimensional radical ideal
Return:
(L1, L2), whereL1contains boxes smaller than eps which
may contain an element of V(I), i.e. a root andL2contains boxes which contain exactly one element of V(I)
Purpose:
Given input box(es) startwe try to find all roots ofIlying instartby computing boxes that contain exactly one root.
Ifeps> 0 then boxes that become smaller thanepswill
be returned.
Theory:
We first check for every box if it contains no roots by interval
arithmetic. If this is inconclusive we apply the Newton step which, as
outlined in [2] and [3], converges to a root lying in the starting box.
If the result of the Newton step is already contained in the interior
of the starting box, it contains a unique root.
Note:
While rootIsolationdoes,rootIsolationNoPreprocessingdoes not check input ideal for necessary conditions.
 |  | LIB "rootisolation.lib";
ring R = 0,(x,y),dp;
ideal I = 2x2-xy+2y2-2,2x2-3xy+3y2-2;  // V(I) has four elements
interval i = bounds(-3/2,3/2);
box B = list(i, i);
list result = rootIsolationNoPreprocessing(I, list(B), 1/512);
size(result[1]);
==> 0
size(result[2]);
==> 4
result;
==> [1]:
==>    empty list
==> [2]:
==>    [1]:
==>       [-9/16, -15/32] x [-129/128, -127/128]
==>    [2]:
==>       [15/32, 33/64] x [31/32, 129/128]
==>    [3]:
==>       [63/64, 33/32] x [-1/256, 1/32]
==>    [4]:
==>       [-129/128, -63/64] x [-1/256, 1/32]
 | 
 
 |