OpenXM_contrib2/asir2000/lib/sturm - diff

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Diff for /OpenXM_contrib2/asir2000/lib/sturm between version 1.1.1.1 and 1.4

-version 1.1.1.1, 1999/12/03 07:39:11
+version 1.4, 2001/04/03 04:41:24
 Line 1
 Line 1
 Line 1
- /* $OpenXM: OpenXM/src/asir99/lib/sturm,v 1.1.1.1 1999/11/10 08:12:31 noro Exp $ */
+ /*
+  * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
+  * All rights reserved.
+  *
+  * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
+  * non-exclusive and royalty-free license to use, copy, modify and
+  * redistribute, solely for non-commercial and non-profit purposes, the
+  * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
+  * conditions of this Agreement. For the avoidance of doubt, you acquire
+  * only a limited right to use the SOFTWARE hereunder, and FLL or any
+  * third party developer retains all rights, including but not limited to
+  * copyrights, in and to the SOFTWARE.
+  *
+  * (1) FLL does not grant you a license in any way for commercial
+  * purposes. You may use the SOFTWARE only for non-commercial and
+  * non-profit purposes only, such as academic, research and internal
+  * business use.
+  * (2) The SOFTWARE is protected by the Copyright Law of Japan and
+  * international copyright treaties. If you make copies of the SOFTWARE,
+  * with or without modification, as permitted hereunder, you shall affix
+  * to all such copies of the SOFTWARE the above copyright notice.
+  * (3) An explicit reference to this SOFTWARE and its copyright owner
+  * shall be made on your publication or presentation in any form of the
+  * results obtained by use of the SOFTWARE.
+  * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
+  * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
+  * for such modification or the source code of the modified part of the
+  * SOFTWARE.
+  *
+  * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
+  * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
+  * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
+  * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
+  * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
+  * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
+  * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
+  * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
+  * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
+  * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
+  * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
+  * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
+  * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
+  * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
+  * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
+  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
+  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
+  *
+  * $OpenXM: OpenXM_contrib2/asir2000/lib/sturm,v 1.3 2000/08/22 05:04:23 noro Exp $
+ */
  /* find intervals which include roots of a polynomial */
  #include "defs.h"
-Line 111  def numch0(S,V,A,T) {
+Line 159  def numch0(S,V,A,T) {
 Line 111  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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