Changeset e4eea0e in git

Timestamp:

Jul 19, 1997, 10:09:28 AM (27 years ago)

Author:

Jens Schmidt <schmidt@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

66e0d201fa56526ea7c5fe49c469ed956b42d2db

Parents:

fb8518fe473cb4484cb222f067d3ccdaf909d892

Message:

	* cf_ops.cc (resultant): assertion added
	(resultant): new variable flipFactor
	(resultant): handling of trivial cases fixed
	(resultant): some other minor bug fixes

	* cf_ops.cc (resultant): doc fix


git-svn-id: file:///usr/local/Singular/svn/trunk@537 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• factory/cf_ops.cc (modified) (4 diffs)

factory/cf_ops.cc

@@ -1 +1 @@
 /* emacs edit mode for this file is -*- C++ -*- */
-/* $Id: cf_ops.cc,v 1.2 1997-06-19 12:24:13 schmidt Exp $ */
+/* $Id: cf_ops.cc,v 1.3 1997-07-19 08:09:28 schmidt Exp $ */
 
 #include <config.h>
@@ -203 +203 @@
 }
 
-CanonicalForm
-resultant( const CanonicalForm & f, const CanonicalForm& g, const Variable & x )
+//{{{ CanonicalForm resultant( const CanonicalForm & f, const CanonicalForm & g, const Variable & x )
+//{{{ docu
+//
+// resultant() - return resultant of f and g with respect to x.
+//
+// We calculate the resultant using a subresultant PSR.
+//
+// flipFactor: Res(f, g) = flipFactor * Res(g, f)
+// F, G: f and g with x as main variable
+// pi, pi1, pi2: used to compute PSR
+// delta:
+// bi, Hi:
+//
+//}}}
+CanonicalForm
+resultant( const CanonicalForm & f, const CanonicalForm & g, const Variable & x )
 {
     CanonicalForm Hi, bi, pi, pi1, pi2, F, G;
-    int delta;
-    Variable v = f.mvar();
-
-    if ( f.mvar() < x || g.mvar() < x )
-        return 1;
-
+    int delta, flipFactor;
+    Variable v;
+
+    ASSERT( x.level() > 0, "cannot calculate resultant in respect to algebraic variables" );
+
+    // some checks on triviality.  We will not use degree( v )
+    // here because this may involve variable swapping.
+    if ( f.isZero() || g.isZero() )
+        return 0;
+    if ( f.mvar() < x )
+        return power( f, g.degree( x ) );
+    if ( g.mvar() < x )
+        return power( g, f.degree( x ) );
+
+    // make x main variale
     if ( f.mvar() > x || g.mvar() > x ) {
         if ( f.mvar() > g.mvar() )
@@ -226 +249 @@
         G = g;
     }
-    if ( F.degree( v ) < 1 || G.degree( v ) < 1 )
-        return 1;
-
-    if ( f.degree( v ) >= g.degree( v ) ) {
+    // at this point, we have to calculate resultant( F, G, v )
+    // where v is equal to or greater than the main variables
+    // of F and G
+
+    // trivial case: F or G in R.  Swapping will not occur
+    // when calling degree( v ).
+    if ( F.degree( v ) < 1 )
+        return power( f, G.degree( v ) );
+    if ( G.degree( v ) < 1 )
+        return power( g, F.degree( v ) );
+
+    // start the pseudo remainder sequence
+    if ( F.degree( v ) >= G.degree( v ) ) {
         pi = F; pi1 = G;
-    }
-    else {
+        flipFactor = 1;
+    }
+    else {
+        if ( (F.degree( v ) * G.degree( v )) % 2 )
+            flipFactor = -1;
+        else
+            flipFactor = 1;
         pi = G; pi1 = F;
     }
+
     delta = degree( pi, v ) - degree( pi1, v );
     Hi = power( LC( pi1, v ), delta );
+
+    // Ist hier nicht if und else zweig vertauscht ???
     if ( (delta+1) % 2 )
         bi = 1;
     else
         bi = -1;
+
+    // Ist pi1.isZero vielleich schneller ???
     while ( degree( pi1, v ) >= 0 ) {
         pi2 = psr( pi, pi1, v );
@@ -247 +289 @@
         if ( degree( pi1, v ) >= 0 ) {
             delta = degree( pi, v ) - degree( pi1, v );
+
+            // Ist hier nicht if und else zweig vertauscht ???
             if ( (delta+1) % 2 )
                 bi = LC( pi, v ) * power( Hi, delta );
             else
                 bi = -LC( pi, v ) * power( Hi, delta );
+
+            // Was ist f"ur delta == 0 ???
             Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 );
         }
     }
+
+    // f and g have non-trivial common divisor
+    // if ( degree( pi, v ) > 0 )
+    // return 0;
+
+    // undo variable swap
     if ( v == x )
-        return Hi;
-    else
-        return swapvar( Hi, v, x );
-}
-
+        // Gibt man hier nicht den letzten Rest der PSR zur"uck
+        // und nicht den Korrekturterm Hi ???
+        return Hi * flipFactor;
+    else
+        return swapvar( Hi, v, x ) * flipFactor;
+}
+//}}}
 
 static CanonicalForm