Changeset c591ad0 in git

Timestamp:

Feb 1, 2007, 12:56:34 AM (16 years ago)

Author:

Motsak Oleksandr <motsak@…>

Branches:

(u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')

Children:

bad2940b7a43a19da887b39672e04919a2b3a28c

Parents:

86016dc267659b0c4d7155a4accd5fb595c04de7

Message:

*motsak:
 !+!: support for factors of SCA!
  * : unified NC setup.


git-svn-id: file:///usr/local/Singular/svn/trunk@9793 2c84dea3-7e68-4137-9b89-c4e89433aadc

Location:

Singular

Files:

• LIB/nctools.lib (modified) (9 diffs)
• ipassign.cc (modified) (2 diffs)

Singular/LIB/nctools.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////////
-version="$Id: nctools.lib,v 1.22 2007-01-23 15:03:36 Singular Exp $";
+version="$Id: nctools.lib,v 1.23 2007-01-31 23:56:33 motsak Exp $";
 category="Noncommutative";
 info="
@@ -19 +19 @@
 Exterior();               return qring, the exterior algebra of a basering,
 findimAlgebra(M,[r]);     create finite dimensional algebra structure from the basering and the multiplication matrix M,
-SuperCommutative([b,e]);  return qring, the super-commutative algebra over a basering,
+SuperCommutative([b,e, Q]);  return qring, the super-commutative algebra over a basering,
 rightStd(I);              compute a right Groebner basis of an ideal,
 
@@ -716 +716 @@
 ///////////////////////////////////////////////////////////////////////////////
 proc SuperCommutative(list #)
-"USAGE:   SuperCommutative([b,[e]]);
+"USAGE:   SuperCommutative([b,[e, [Q]]]);
 RETURN:  qring
 PURPOSE:  create the super-commutative algebra over a basering,
 NOTE:  activate this qring with the \"setring\" command
 THEORY: given a basering, this procedure introduces the anticommutative relations x(j)x(i)=-x(i)x(j) for all e>=j>i>=b,
-@* moreover, creates a factor algebra modulo the two-sided ideal, generated by x(b)^2, ..., x(e)^2
+@* moreover, creates a factor algebra modulo the two-sided ideal, generated by x(b)^2, ..., x(e)^2[ + Q]
 EXAMPLE: example SuperCommutative; shows examples
 "
 {
-
   string rname=nameof(basering);
   if ( rname == "basering") // i.e. no ring has been set yet
@@ -737 +736 @@
   int e = N;
 
+        def saveRing = basering;
+  ideal Q = 0;
+
   if(size(#)>0)
   {
     if(typeof(#[1]) != "int")
     {
-      ERROR("First argument 'b' must be integter!");
+      ERROR("First argument 'b' must be an integer!");
       return();
     }
     b = #[1];
-
-
-    if(size(#)>1)
-    {
-      if(typeof(#[2]) != "int")
-      {
-        ERROR("Last argument 'e' must be integter!");
-        return();
-      }
-      e = #[2];
-    }
-  }
-
-
+  }
+
+        if(size(#)>1)
+        {
+          if(typeof(#[2]) != "int")
+          {
+            ERROR("Last argument 'e' must be an integer!");
+            return();
+          }
+          e = #[2];
+        }
+
+        if(size(#)>2)
+        {
+          if(typeof(#[3]) != "ideal")
+          {
+            ERROR("Last argument 'Q' must be an ideal!");
+            return();
+          }
+          Q = #[3];
+        }
+        
   list CurrRing = ringlist(basering);
   def @R = ring(CurrRing);
@@ -775 +785 @@
   }
 
-  ncalgebra(@E,0);
-
-  ideal Q;
-
-  for ( i=e; i>=b; i-- )
-  {
-    Q[i-b+1] = var(i)^2;
+  ncalgebra(@E, 0);
+
+        ideal Q = fetch(saveRing, Q);  
+        j = ncols(Q) + 1;
+
+  for ( i=e; i>=b; i--, j++ )
+  {
+    Q[j] = var(i)^2;
   }
   Q = twostd(Q);
@@ -815 +826 @@
 "
 {
-  def rRing = basering;
-  list L = ringlist(rRing);
+  def saveRing = basering;
+  list L = ringlist(saveRing);
 
   if( size(L)!=6 )
@@ -831 +842 @@
 
   int i, j;
-  int N = nvars(rRing);
+  int N = nvars(saveRing);
 
   int b = N+1;
-  int e = 0;
-
-  poly p;
-
-  ideal I = sort(L[4])[1];
-
-//   "Q = ", string(I);
-
-  intvec exp;
-  int d;
-  int n = 0;
-
-  for( i = size(I); i > 0; i-- )
-  {
-    p = I[i];
-//     p;
-
-    if( size(p) != 1 )
-    {
-      return("The current ring is not SCA! (Wrong quotient ideal, not monomial)");
-    }
-
-    exp = leadexp(p);
-//     exp;
-    d = 0;
-    for( j = size(exp); j >= 1; j-- )
-    {
-      d = d + exp[j];
-//       d;
-
-      if( (d!=2) && (d!=0) )
+  int e =  -1;
+
+  matrix C = L[5];
+  poly c;
+
+  for( i = 1; i < N; i++ )
+  {
+    for( j = i+1; j <= N; j++ )
+    {
+      c = C[i, j];
+      
+      if( c == -1 )
       {
-        return("The current ring is not SCA! (Wrong quotient ideal, wrong leading exponent)");
-      }
-
-      if(exp[j] == 2)
-      {
-        if(b > j)
+        if(i < b)
+        {
+                b = i;          
+        }
+        
+        if(j > e)
+        {
+                e = j;          
+        }
+      } else
+      { // should commute
+        if( c!=1 )
         {
-          b = j; // min
-          n = n + 1;
-        }
-        if(e < j)
-        {
-          e = j; // max
-          n = n + 1; // => n = n + 1 twice for the 1st one
+          return("The current ring is not SCA! (C["+ string(i)+"," + string(j)+"]!=1)");
         }
       }
     }
-
-    if( d!=2 )
-    {
-      return("The current ring is not SCA! (Wrong quotient ideal, wrong leading exponent)");
-    }
-  }
-
-//   b, e, n;
-
-  if(size(I) == 0)
-  {
-    b = N+1;
-    e = N+1;
-    n = 2;
-  }
-
-//   if( (e < 1) || (b > N) )
-//   {
-//     ERROR("The current ring is not SCA! (wrong quotient ideal, bad squares)");
-//     return();
-//   }
-
-  if( (e - b + 2) != n ) // +2 instead of +1!
-  {
-    return("The current ring is not SCA! (wrong quotient ideal, bad range)");
-  }
-
-
-  matrix C = L[5];
-  poly c;
-
+  }
+
+  if( (b > N) || (e < 1))
+  {
+    return("The current ring is commutative!");
+  }
+  
   for( i = 1; i < N; i++ )
   {
@@ -935 +903 @@
     }
   }
-
-  if( (b > N) || (e > N))
-  {
-    return("The current ring is commutative!");
-  }
-
-  return(list(b, e));
+  
+  list LL = list(L[1], L[2], L[3], ideal(0), L[5], L[6]);
+  ideal Q = L[4];
+//  "Q = ", string(Q);
+  
+  def  E = ring(LL);
+  setring E; // not a qring!
+//  E;
+
+        ideal Q = fetch(saveRing, Q); // should belong to E!
+        Q = twostd(Q);
+
+//  "Q = ", string(Q);
+
+  for( i = b; i <= e; i++ )
+  {
+    if( NF(var(i)^2, Q) != 0 )
+    {
+        setring saveRing;
+      return("The current ring is not SCA! (Wrong quotient ideal)");
+    }
+  }
+
+        ////////////////////////////////////////////////////////////////////////  
+  // ok. it is a SCA!!!
+  
+  ideal QQ;
+  
+  for( i = e; i >= b; i-- )
+  {
+    QQ[i - b + 1] = var(i)^2;
+  }
+  
+  QQ = twostd(QQ);
+  Q = simplify(NF(Q, QQ),  1 + 2 + 4);
+  
+  setring saveRing;
+  
+  ideal QQ = fetch(E, Q);
+
+  return(list(b, e, QQ));
 }
 
@@ -1069 +1071 @@
   setring ER; ER;
   if(IsSCA())
-    { "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
+    { "This is a SCA! Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
   else
     { "Not a supercommutative algebra!!!"; }

Singular/ipassign.cc

@@ -2 +2 @@
 *  Computer Algebra System SINGULAR     *
 ****************************************/
-/* $Id: ipassign.cc,v 1.87 2007-01-29 18:34:45 Singular Exp $ */
+/* $Id: ipassign.cc,v 1.88 2007-01-31 23:56:34 motsak Exp $ */
 
 /*
@@ -587 +587 @@
     }
 
-    // is this an exterior algebra or a commutative polynomial ring \otimes exterior algebra?
-    // we should check whether qr->qideal is of the form: y_i^2, y_{i+1}^2, \ldots, y_j^2 (j > i)
-    //.if yes, setup qr->nc->type, etc.
-    sca_SetupSCA(qr, currRing); 
+    nc_SetupQuotient(qr, currRing); 
   }
   #endif