OpenXM_contrib2/asir2000/lib/sturm - diff

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Diff for /OpenXM_contrib2/asir2000/lib/sturm between version 1.3 and 1.4

-version 1.3, 2000/08/22 05:04:23
+version 1.4, 2001/04/03 04:41:24
 Line 45
 Line 45
 Line 45
   * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
   * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
   *
-  * $OpenXM: OpenXM_contrib2/asir2000/lib/sturm,v 1.2 2000/08/21 08:31:43 noro Exp $
+  * $OpenXM: OpenXM_contrib2/asir2000/lib/sturm,v 1.3 2000/08/22 05:04:23 noro Exp $
  */
  /* find intervals which include roots of a polynomial */
 Line 159  def numch0(S,V,A,T) {
 Line 159  def numch0(S,V,A,T) {
 Line 159  def numch0(S,V,A,T) {
                  T = T1;
          }
          return C;
+ }
+ def count_real_roots(F)
+ {
+         if ( type(F) == 1 )
+                 return 0;
+         V = var(F);
+         R = 0;
+         /* remove three roots : -1, 0, 1 */
+         if ( Q = tdiv(F,V) ) {
+                 F = Q; R++;
+                 while ( Q = tdiv(F,V) )
+                         F = Q;
+         }
+         if ( Q = tdiv(F,V-1) ) {
+                 F = Q; R++;
+                 while ( Q = tdiv(F,V-1) )
+                         F = Q;
+         }
+         if ( Q = tdiv(F,V+1) ) {
+                 F = Q; R++;
+                 while ( Q = tdiv(F,V+1) )
+                         F = Q;
+         }
+         if ( type(F) == 1 )
+                 return R;
+         S = sturm(F);
+         /* number of roots in [-1,1] */
+         R += numch(S,V,-1)-numch(S,V,1);
+         RS = sturm(ureverse(F));
+         /* number of roots in [-inf,-1] \cup [1,inf] */
+         R += numch(RS,V,-1)-numch(RS,V,1);
+         return R;
  }
  end;

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