Changeset c91ad1 in git

Timestamp:

Oct 30, 2007, 6:27:44 PM (16 years ago)

Author:

Motsak Oleksandr <motsak@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

0273dec39cc5a468a269edd6c08a5ba742e0fb14

Parents:

ae4b619fa9115e2df8467ef6e83ea5302280e402

Message:

*motsal:ncalgebra + commutative cases in SuperCommutative()


git-svn-id: file:///usr/local/Singular/svn/trunk@10354 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/nctools.lib (modified) (18 diffs)

Singular/LIB/nctools.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: nctools.lib,v 1.32 2007-10-30 17:17:43 Singular Exp $";
+version="$Id: nctools.lib,v 1.33 2007-10-30 17:27:44 motsak Exp $";
 category="Noncommutative";
 info="
@@ -116 +116 @@
   matrix D[4][4];
   D[1,4]=(q-1/q)*b*c;
-  def S=ncalgebra(C,D);
-  setring S;S;
+  def S = ncalgebra(C,D); setring S; S;
   Gweights(S);
   def D=fetch(r,D);
@@ -157 +156 @@
     execute (newringstring);
     def lnewring=imap(r,lr);
-    def S=ncalgebra(lnewring[1],lnewring[2]);
-    return(S);
+    return( ncalgebra(lnewring[1],lnewring[2]) ); 
   }
   else
@@ -174 +172 @@
   matrix D[4][4];
   D[1,4]=(q-1/q)*b*c;
-  def S=ncalgebra(C,D);setring S;
-  S;
+  def S = ncalgebra(C,D); setring S; S;
   def t=weightedRing(S);
   setring t; t;
@@ -380 +377 @@
   matrix D[3][3]=0,1,2y,0,0,-2x+y+1;
   print(D);
-  def S=ncalgebra(C,D);setring S;
-  S;
+  def S=ncalgebra(C,D);setring S; S;
   def l=ncRelations(S);
   print (l[1]);
@@ -441 +437 @@
     }
   }
-  def S=ncalgebra(C,D);
-  ideal fdQuot = I;
+  def save = basering;
+  def S = ncalgebra(C,D); setring S;
+  ideal fdQuot = fetch(save,D);
   export fdQuot;
 }
@@ -493 +490 @@
   D[1,3]=2*x;
   D[2,3]=-2*y;
-  ncalgebra(1,D); // this is U(sl_2)
+  def S = ncalgebra(1,D); setring S; 
+  S; // this is U(sl_2)
   poly c = 4*x*y+z^2-2*z;
   printlevel = 0;
@@ -530 +528 @@
   C[1,3]   = q;
   print(C);
-  ncalgebra(C,0);
-  r;
+  def S = ncalgebra(C,0); serring S;
+  S;
 }
 
@@ -596 +594 @@
   matrix D[3][3];
   D[1,2]=x; D[1,3]=z;
-  ncalgebra(C,D);
-  r;
+  def S = ncalgebra(C,D); setring S; 
+  S;
   ideal j=ndcond(); // the silent version
   j;
@@ -675 +673 @@
 proc makeHeisenberg(int N, list #)
 "USAGE:  makeHeisenberg(n, [p,d]); int n (setting 2n+1 variables), optional int p (field characteristic), optional int d (power of h in the commutator)
-RETURN: nothing
+RETURN: ring
 PURPOSE: create an n-th Heisenberg algebra in the variables x(1),y(1),...,x(n),y(n),h
 SEE ALSO: makeWeyl
@@ -706 +704 @@
     D[i,N+i]=h^@deg;
   }
-  ncalgebra(1,D);
-  return(@@r);
+  return(ncalgebra(1,D));
 }
 example
@@ -803 +800 @@
     if( fprot == 1)
     {
-      print("Warning: b==e means that the resulting ring will be commutative!");
+      print("Warning: (b==e) means that the resulting ring will be commutative!");
     }
     Q = std(Q + (var(b)^2));
@@ -818 +815 @@
 */
 
-  matrix @E = UpOneMatrix(N);
+  if (char(basering)==2) // commutative ring!!!
+  {
+    if( fprot == 1)
+    {
+      print("Warning: (char == 2) means that the resulting ring will be commutative!");
+    }
+    
+    int j = ncols(Q) + 1;
+    
+    for ( int i=e; i>=b; i--, j++ )
+    {
+      Q[j] = var(i)^2;
+    }
+    
+    Q = std(Q);
+    qring @EA = Q; // and it will be internally commutative as well!!!
+    return(@EA);      
+  }
+  
 
   int i, j;
-
-  for ( i = b; i < e; i++ )
-  {
-    for ( j = i+1; j <= e; j++ )
-    {
-      @E[i, j] = -1;
-    }
-  }
-
-  ncalgebra(@E, 0); // define ground G-algebra!
+  
+  if( (b == 1) && (e == N) ) // just an exterior algebra?
+  {  
+    def S = ncalgebra(-1, 0); // define ground G-algebra!
+    setring S;  
+  } else
+  {
+    matrix @E = UpOneMatrix(N);
+  
+    for ( i = b; i < e; i++ )
+    {
+      for ( j = i+1; j <= e; j++ )
+      {
+        @E[i, j] = -1;
+      }
+    }
+    def S = ncalgebra(@E, 0); // define ground G-algebra!
+    setring S;
+  }
 
   ideal @Q = fetch(saveRing, Q);
@@ -1109 +1133 @@
 /////////////////////////////////////////////////////////////////////
   ring R = 0,(x(1..4)),dp;
-  ncalgebra(1, 0); // still commutative!
+  def S = ncalgebra(1, 0); setring S; S; // still commutative!
   if(IsSCA())
     { "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
@@ -1133 +1157 @@
   }
 
-  ncalgebra(E,0);
+  def S = ncalgebra(E,0); setring S; S;
+  
   if(IsSCA())
     { "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
@@ -1177 +1202 @@
   matrix @E = UpOneMatrix(N);
   @E = -1*(@E);
-  def @@RR=ncalgebra(@E,0);
-  setring @@RR;
+  def @@RR = ncalgebra(@E,0); setring @@RR;
   int i;
   ideal Q;
@@ -1329 +1353 @@
 { "EXAMPLE:"; echo = 2;
   ring r = 0,(x,d),dp;
-  ncalgebra(1,1); // the first Weyl algebra
+  def S = ncalgebra(1,1); setring S; // the first Weyl algebra
   ideal I = x,d;
   module LS = syz(I);
@@ -1361 +1385 @@
   LIB "ncalg.lib";
   ring r = 0,(x,d),dp;
-  ncalgebra(1,1); // Weyl algebra
+  def S = ncalgebra(1,1); setring S; // Weyl algebra
   ideal I = x; I = std(I);
   poly  p = x*d+1;