===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/lib/sturm,v
retrieving revision 1.3
retrieving revision 1.4
diff -u -p -r1.3 -r1.4
--- OpenXM_contrib2/asir2000/lib/sturm	2000/08/22 05:04:23	1.3
+++ OpenXM_contrib2/asir2000/lib/sturm	2001/04/03 04:41:24	1.4
@@ -45,7 +45,7 @@
  * 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 */
 
@@ -159,5 +159,38 @@ 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;