Changeset e9478b in git for Singular

Timestamp:

Jul 9, 2015, 12:28:29 PM (9 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '2a584933abf2a2d3082034c7586d38bb6de1a30a')

Children:

38301d00726a0671f6dbc3f82923b5c9f6964c5d8af20e00f50d423ec4162319c3d9f63fdc7e796f

Parents:

ba52f58eed2a6367c0d09410b064a3fdc2c7170f

Message:

format

Location:

Singular

Files:

• LIB/gradedModules.lib (modified) (88 diffs)
• LIB/surf.lib (modified) (4 diffs)
• dyn_modules/singmathic/singmathic.cc (modified) (1 diff)
• dyn_modules/syzextra/mod_main.cc (modified) (3 diffs)
• extra.cc (modified) (1 diff)

Singular/LIB/gradedModules.lib

@@ -31 +31 @@
     grsum(M,N)      direct sum of two graded modules coker(M) + coker(N)
     grpower(M,p)    direct p-th power of graded module coker(M)
-    grtranspose(M)  un-ordered graded transpose of map M        
+    grtranspose(M)  un-ordered graded transpose of map M
     grgens(M)       try to compute submodule generators of coker(M)
     grpres(F)       presentation of submodule generated by columns of F
@@ -51 +51 @@
     mappingcone(M,N)   mapping cone?
     grlifting3(A,B)    RND! chain lifting? probably wrong one
-    mappingcone3(A,B)  mapping cone3? 
+    mappingcone3(A,B)  mapping cone3?
     grrange(M)         get the row-weightings
     grneg(A)           graded object given by -A
     matrixpres(a)      matrix presentation of direct sum of Omega^{a[i]}(i)
 ";
-    
+
 //    grisequal(A,B)  check whether A is exactly eqal to B? TODO: isomorphic!
 
@@ -86 +86 @@
 
   v = -v; // NOTE: due to Mathematical meanings of Singular data
-  
+
 
   int lst = v[1];
-  int cnt = 1; 
+  int cnt = 1;
 
   string p = R;
@@ -95 +95 @@
 
   int k, d;
-  for (k = 2; k <= n; k++ ) 
+  for (k = 2; k <= n; k++ )
   {
     d = v[k];
     if( d == lst ) { cnt = cnt + 1; }
-    else 
+    else
     {
       if (cnt > 1){ p = p + "^" + string(cnt); }
@@ -120 +120 @@
   def E = grtwist(2, 0);
   def v = grrange(E); // grdeg(E);
-  grsumstr("", v );  
+  grsumstr("", v );
 }
 
@@ -180 +180 @@
   {
     int n = size(N); ASSUME(0, n > 0);
-    
+
     string msg1 = "";
     if( size(R) >= 2 )
@@ -186 +186 @@
       msg1 = msg1 + "(let R:="+R+")";
       R = "R"; // !!!
-    }    
+    }
     msg1 = msg1 + ": " ;
 
-    
+
 
     list arr; arr[n] = list();
     int exact = (1==1);
-    
+
     int i = 1;
-    
+
     ASSUME(1, grtest(N[i]));
-    
+
     string dst = grsumstr(R, grrange(N[i]));
     string src = grsumstr(R, grdeg(N[i]));
-    
+
     arr[i] = list(dst,  src);
 
     i = i + 1;
-    
+
     while( i <= n )
     {
       ASSUME(1, grtest(N[i]));
-      
+
       dst = grsumstr(R, grrange(N[i]));
-      
+
       if( exact && (src != dst) )
       {
@@ -218 +218 @@
 
       src = grsumstr(R, grdeg(N[i]));
-      
+
       arr[i] = list(dst,  src);
 
@@ -236 +236 @@
         msg = msg + newline + arr[i][1] + " <-- "+o+"_" + string(i) + " --";
       };
-      
+
       msg =  msg + newline + arr[n][2];
-      msg = msg + ", given by maps: "; 
+      msg = msg + ", given by maps: ";
     } else
     {
 //      print(arr);
 
-      msg = msg + "-object collection";      
+      msg = msg + "-object collection";
       o = "o";
-      
+
 //      for( i = 1; i <= n; i++ )
 //      {
 //        msg = msg + newline + arr[i][1] + " <-- "+o+"_" + string(i) + " -- " + arr[i][2];
-//      };      
-      msg = msg + ", given by the following maps (named here as "+o+"_[1 .. "+string(n)+"]): "; 
+//      };
+      msg = msg + ", given by the following maps (named here as "+o+"_[1 .. "+string(n)+"]): ";
     }
 
@@ -257 +257 @@
 
     for( i = 1; i <= size(N); i++ )
-    { 
+    {
       print( o+"_" + string(i) + " :" );
-      grview( N[i] ); 
+      grview( N[i] );
     };
 
@@ -268 +268 @@
 
   ASSUME(1, grtest(N) );
-  
+
   msg = msg + " homomorphism";
   if( size(R) >= 2 )
@@ -280 +280 @@
   intvec gr = grrange(N); // grading weights?
   string dst = grsumstr(R, gr);
-  
+
   intvec G = grdeg(N);
   string src = grsumstr(R, G);
-  
+
   if( ncols(N) == 0 )
   {
     src = "0";
-  } 
+  }
 
   lst = msg;
 
-  if( (size(lst) + size(dst) + size(src) + 4) > 80 ) 
-  { 
+  if( (size(lst) + size(dst) + size(src) + 4) > 80 )
+  {
     if( (size(lst) + size(dst)) > 80 ) { msg = msg + newline; lst = ""; }
 
@@ -312 +312 @@
 //  lst = lst + ", given by ";
 
-  
+
   int nc = ncols(N); int nr = nrows(N);
 
@@ -323 +323 @@
   {
     ASSUME(0, nc > 0);
-    
+
     matrix M = module(N);
-    
+
     int r,c;
     int d = 1; // number of extra cols/rows for extra info around the central degree(N) block in D
@@ -361 +361 @@
       }
 
-    } else 
-    { 
+    } else
+    {
       msg = msg + "a matrix";
     }
 
-    print(msg + ", with degrees: " );    
-    draw(D, d); // print it nicely!    
+    print(msg + ", with degrees: " );
+    draw(D, d); // print it nicely!
   }
 }
@@ -462 +462 @@
 "
 {
-  ASSUME(1, grtest(M) ); 
-  
+  ASSUME(1, grtest(M) );
+
   if ( typeof(attrib(M, "degHomog")) == "intvec" )
   {
@@ -469 +469 @@
 
     if( size(t) == 0 ){ return (t); } // ZERO!
-    
+
     ASSUME(2, ncols(M) == size(t) );
     return (t);
@@ -629 +629 @@
   "Input degrees: "; grview(I);
 
-  def RR = grres(I, 0, 1); list L = RR; 
+  def RR = grres(I, 0, 1); list L = RR;
 
   " = Non-minimal betti numbers: "; print(betti(L, 0), "betti");
@@ -830 +830 @@
 
   ring r=32003,(x,y,z),dp;
-  
+
   grview( grtwists ( intvec(-4, 1, 6 )) );
 
@@ -843 +843 @@
 "
 {
-  ASSUME(0, a > 0);  
+  ASSUME(0, a > 0);
   def Z = grtwists( intvec(d:a) ); // will set the rank as well
 //  ASSUME(2, grisequal(Z, grpower( grshift(grzero(), d), a ) )); // optional check
@@ -931 +931 @@
 
   def SS = grobj(S, c, dc);
-  
+
   ASSUME(0, size( grrange(SS) ) == (size(a) + size(b)) );
   ASSUME(0, size( grdeg(SS) ) == (size(da) + size(db)) );
   ASSUME(0, ncols( SS ) == size( grdeg(SS) ) );
   ASSUME(0, nrows( SS ) == size( grrange(SS) ) );
-  
+
   return(SS);
 }
@@ -984 +984 @@
 {
   ASSUME(1, grtest(M) );
-           
-           
+
+
 
   intvec a = grrange(M);
@@ -993 +993 @@
   {
     "!! Warning: shifting '0 <- 0' leaves it as it unchanged!";
-    return (M);    
-  }
-  
+    return (M);
+  }
+
   a = a - intvec(d:size(a));
   t = t - intvec(d:size(t));
@@ -1056 +1056 @@
 {
   ASSUME(0, size(w) >= nrows(A) );
-  
+
   module M = module(A);
 
@@ -1063 +1063 @@
 
   intvec @ww = 0:0;
-  
+
   if( size(#) > 0 )
   {
     ASSUME(0, typeof(#[1]) == "intvec" );
-    
+
     @ww = intvec( #[1] );
 
@@ -1077 +1077 @@
       }
     }
-    
+
     ASSUME(0, size(@ww) == ncols(M) );
   }
@@ -1091 +1091 @@
         M = freemodule(0);
       }
-      
+
       attrib( M, "rank", size(w) );
       attrib( M, "isHomog", w );
-      
+
 //      ASSUME(0, /* PROBLEM WITH ZERO COLUMNS / THEIR DEGREES! */ (ncols(M) == 0) );
     }
   }
-  
+
 //  type(@ww);  type(M);
-  
+
   ASSUME(0, size(@ww) == ncols(M) ); // ?!
-  
+
   attrib(M, "degHomog", @ww);
 
@@ -1132 +1132 @@
   grview( grobj( freemodule(0), intvec(1,2,3) ) );
 
-  matrix z1[0][3]; grview( grobj( z1, 0:0, intvec(1,2,3) ) ); 
+  matrix z1[0][3]; grview( grobj( z1, 0:0, intvec(1,2,3) ) );
   grview( grobj( freemodule(0), 0:0, intvec(1,2,3) ) );
 
   matrix z0[0][0]; grview( grobj( z0, 0:0 ) );
   grview( grobj( freemodule(0), 0:0 ) );
-  
-  
+
+
 
 }
@@ -1145 +1145 @@
 "USAGE:  grtest(M[,b]), anyting M, optionally int b
 RETURN:  1 if M is a valid graded object, 0 otherwise
-PURPOSE: validate a graded object. Print an invalid object message if b is not given 
+PURPOSE: validate a graded object. Print an invalid object message if b is not given
 NOTE: M should be an ideal or module or matrix, with weighting attribute
    'isHomog' and optionally total graded degrees attribute 'degHomog'.
@@ -1169 +1169 @@
   if ( nrows(N) != size(gr) )
   {
-    if(b) { "   ? grtest: Input has wrong number of rows!"; };    
+    if(b) { "   ? grtest: Input has wrong number of rows!"; };
     return (0);
   };
@@ -1177 +1177 @@
     return(1);
   }
-  
+
 //  if( attrib(N, "rank") != size(gr) ){ return (0); } // wrong rank :(
 
@@ -1189 +1189 @@
       return (1);
     }
-    
+
     if ( ncols(N) != size(T) )
     {
-      if(b) { "   ? grtest: Input has wrong number of cols!"; };    
+      if(b) { "   ? grtest: Input has wrong number of cols!"; };
       return (0);
     };
-    
+
     int k = nvars(basering) + 1; // index of mod. column in the leadexp
 
@@ -1259 +1259 @@
 {
   ASSUME(0, d >= 0 );
-  
+
   if( d == 0 ) { return (A); }
-  
+
   if( ncols(A) == 0 )
   {
     matrix B[nrows(A) + d][0];
-    return (B);    
-  }
-  
+    return (B);
+  }
+
   module T; T[d] = 0;
   T = T, module(transpose(A));
@@ -1281 +1281 @@
   matrix m[0][2];
   type( align(m, 3) );
-}  
+}
 
 
@@ -1302 +1302 @@
   module A = grobj( module([x+y, x, 0, 0], [0, x+y, y, 0]), intvec(0,0,0,1) );
   grview(A);
-  
+
   module B = grgroebner(A);
   grview(B);
@@ -1324 +1324 @@
   ring r=32003,(x,y,z),dp;
 
-  module A = grgroebner( grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) ) ); 
+  module A = grgroebner( grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) ) );
   grview(A);
-  
+
   grview(grsyz(A));
-  
-  module X = grgroebner( grobj( module([x]), intvec(2) ) ); 
+
+  module X = grgroebner( grobj( module([x]), intvec(2) ) );
   grview(X);
 
   // syzygy module should be zero!
   grview(grsyz(X));
-  
-  
+
+
 }
 
@@ -1351 +1351 @@
   intvec a = grdeg(A);
   intvec b = grrange(B);
-  
+
   ASSUME(0, (size(a) == size(b)) && (a == b));  // == for intvec :(
 
@@ -1361 +1361 @@
   ring r=32003,(x,y,z),dp;
 
-  module A = grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) ); 
+  module A = grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) );
   grview(A);
-  
+
   A = grgroebner(A);
   grview(A);
-  
+
   module B = grsyz(A);
   grview(B);
   print(B);
-  
+
   module D = grprod( A, B );
   grview(D);
@@ -1384 +1384 @@
 "USAGE:  grres(M, l[, b]), graded object M, int l, int b
 RETURN:  graded resolution = list of graded objects
-PURPOSE: compute graded resolution of M (of length l) and minimise it if b was given                             
+PURPOSE: compute graded resolution of M (of length l) and minimise it if b was given
 EXAMPLE: example grres; shows an example
 "
@@ -1392 +1392 @@
 
   intvec v = grrange(A);
-  
+
   int b = (size(#) > 0);
   if(b) { list r = res(A, l, #[1]); } else { list r = res(A, l); }
 
   l = size(r);
-  
+
   int i;
-  
+
   for ( i = 1; i <= l; i++ )
   {
@@ -1411 +1411 @@
     r[i] = grobj(r[i], v); v = grdeg(r[i]);
   }
-  
+
   i = i-1;
 
@@ -1421 +1421 @@
   ring r=32003,(x,y,z),dp;
 
-  module A = grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) ); 
+  module A = grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) );
   grview(A);
-  
+
   module B = grgroebner(A);
   grview(B);
@@ -1438 +1438 @@
 RETURN:  graded object
 PURPOSE: graded transpose of M
-NOTE:    no reordering is performend by this procedure   
+NOTE:    no reordering is performend by this procedure
 EXAMPLE: example grtranspose; shows an example
 "
@@ -1457 +1457 @@
 
   module K = grsyz( L ); grview(K);
-  
+
 
   // Corner cases: 0 <- 0!
@@ -1463 +1463 @@
   grview( grtranspose( Z ) );
 
-  
+
   // Corner cases: * <- 0
   matrix M1[3][0];
-  
+
   module Z1 = grobj( M1, intvec(-1, 0, 1) ); grview(Z1);
   grview( grtranspose( Z1 ) );
-  
-  
+
+
   // Corner cases: 0 <- *
   matrix M2[0][3];
@@ -1476 +1476 @@
   module Z2 = grobj( M2, 0:0, intvec(-1, 0, 1) ); grview(Z2);
   grview( grtranspose( Z2 ) );
-  
+
 }
 
@@ -1482 +1482 @@
 proc grgens(def M)
 "USAGE:   grgens(M), graded object M (map)
-RETURN:  graded object  
+RETURN:  graded object
 PURPOSE: try compute graded generators of coker(M) and return them as columns
          of a graded map.
@@ -1492 +1492 @@
 
   module N = grtranspose( grsyz( grtranspose(M) ) );
-  
+
 //  ASSUME(3, grisequal( grgroebner(M), grgroebner( grpres( N ) ) ) ); // FIXME: not always true!?
-  
+
   return ( N );
 }
@@ -1505 +1505 @@
 
   module N = grgens(M);
-  
+
   grview( N ); print(N); // fine == M
 
 
-  module A = grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) ); 
+  module A = grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) );
 
   A = grgroebner(A); grview(A);
@@ -1518 +1518 @@
 
   grview( grgens( grzero() ) );
-  
+
 }
 
@@ -1534 +1534 @@
 
 //  ASSUME(3, grisequal( M, grgens( N ) ) );
-  
+
   return ( N );
 }
@@ -1545 +1545 @@
   grview(A);
 
-  "graded transpose: "; def B = grtranspose(A); grview( B ); print(B); 
+  "graded transpose: "; def B = grtranspose(A); grview( B ); print(B);
 
   "... syzygy: "; def C = grsyz(B); grview(C);
@@ -1553 +1553 @@
   "... and back to presentation: "; def E = grsyz( D ); grview(E); print(E);
 
-  def F = grgens( E ); grview(F); print(F); 
+  def F = grgens( E ); grview(F); print(F);
   def G = grpres( F ); grview(G); print(G);
 
 
   def M = grtwists( intvec(-2, 0, 4, 4) ); grview(M);
-  
+
   def N = grgens(M); grview( N ); print(N);
-  
-  def L = grpres( N ); grview( L ); print(L);  
+
+  def L = grpres( N ); grview( L ); print(L);
 }
 
@@ -1652 +1652 @@
   module N;
 
-  if(i>n) 
+  if(i>n)
     { // no middle part
       if(a[1]>0)
@@ -1659 +1659 @@
 
           if(a[n+1]>0)
-            { N=grsum(N,grtwist(a[n+1],-1));}        
-        }  
+            { N=grsum(N,grtwist(a[n+1],-1));}
+        }
       else
         { N=grtwist(a[n+1],-1);}
-      
-      return (N); // grorder(N)); 
+
+      return (N); // grorder(N));
     }
-  else // i <= n: middle part is present, a_i != 0 
+  else // i <= n: middle part is present, a_i != 0
     { // a = a1  ... |  i:2, a_2 ..... i: n, a_n | .... i: n+1a_(n+1)
       j = i - 1;
@@ -1697 +1697 @@
 
 
-      return ((N)); //      return (grorder(N)); 
+      return ((N)); //      return (grorder(N));
     }
 }
@@ -1704 +1704 @@
   ring r = 32003,(x(0..4)),dp;
 
-  def N1 = KeneshlouMatrixPresentation(intvec(2,0,0,0,0)); 
+  def N1 = KeneshlouMatrixPresentation(intvec(2,0,0,0,0));
   grview(N1);
 
@@ -1738 +1738 @@
   ASSUME(1, grtest(B));
   ASSUME(0, grrange(A)==grrange(B));
- 
+
   intvec v = grrange(A);
   intvec w=grdeg(A),grdeg(B);
@@ -1746 +1746 @@
 { "EXAMPLE:"; echo = 2;
   ring r;
-  
+
   module R=grobj(module([x,y,z]),intvec(0:3));
   grview(R);
@@ -1771 +1771 @@
 //  matrix U;
   matrix L =lift(A,B/*,U*/);  //  module(B*U) = module(matrix(A)*L)
-  
+
   return(grobj(L, grdeg(A), grdeg(B)));
 }
@@ -1782 +1782 @@
 
 
-  module D=grobj(module([y,0,z],[x2+y2,z,0]),intvec(0,1,0)); 
+  module D=grobj(module([y,0,z],[x2+y2,z,0]),intvec(0,1,0));
   grview(D);
 
@@ -1788 +1788 @@
   grview(G);
 
-  ASSUME(0, grisequal( grprod(D, G), P) );  
+  ASSUME(0, grisequal( grprod(D, G), P) );
 }
 
@@ -1807 +1807 @@
 
   module Z = grobj(freemodule(0),intvec(0:0),intvec(0:0));
-  
+
   grrange(Z);
   grdeg(Z);
-  
+
   grview(Z);
 
@@ -1838 +1838 @@
        grtranspose( grprod( N,  alpha1 ) ) )
        ) ); // alpha0!
-    
+
 }
 example
@@ -1899 +1899 @@
 
   ASSUME(0, t >= 2);
-  
+
   list P;
 
   "t: ", t;
-  
+
   P[1]= grrndmap( rM[1], rN[1] ); // alpha1
 
-  if(t==2){return(P[1]);}  
-    
+  if(t==2){return(P[1]);}
+
   for(k=2; k<=t; k++)
   {
-    P[k] = grlift( grprod(P[k-1],rM[k]), rN[k] ); 
-     grview(P[k]);  
-    
-  }
-      
+    P[k] = grlift( grprod(P[k-1],rM[k]), rN[k] );
+     grview(P[k]);
+
+  }
+
   return(P);
-    
+
 }
 example
@@ -1923 +1923 @@
   ring r=32003,(x,y,z),dp;
 
-  module P=grobj(module([xy,0,xz]),intvec(0,1,0)); 
+  module P=grobj(module([xy,0,xz]),intvec(0,1,0));
   grview(P);
 
-  module D=grobj(module([y,0,z],[x2+y2,z,0]),intvec(0,1,0)); 
+  module D=grobj(module([y,0,z],[x2+y2,z,0]),intvec(0,1,0));
   grview(D);
 
@@ -1937 +1937 @@
   module D=grobj(module([y,0,z],[x2+y2,z,0], [z3, xy, xy2]),intvec(0,1,0));
   D = grgroebner(D);
-  grview( grres(D, 0)); 
+  grview( grres(D, 0));
 
   def G=grlifting(D, D);
@@ -1951 +1951 @@
   def M = KeneshlouMatrixPresentation(intvec(0,0,1,0));
   grview( grres(M, 0) );
-  
+
 //   module N = grshift(kos[3], 1); // psi, Syz_2(K(1))
   def N = KeneshlouMatrixPresentation(intvec(0,1,0,0));
@@ -1966 +1966 @@
 proc mappingcone(M,N)
 "USAGE: mappingcone(M,N), M,N graded objects
-RETURN: chain complex (as a list) 
+RETURN: chain complex (as a list)
 PURPOSE: construct a free resolution of the cokernel of a random map between Img(M), and Img(N).
 EXAMPLE: example mappingcone; shows an example
@@ -2026 +2026 @@
 
 // correct
-proc grrndmap(def S, def D, list #) 
+proc grrndmap(def S, def D, list #)
 "USAGE: grrndmap(S,D), graded objects S and D
 RETURN: graded object
@@ -2092 +2092 @@
 // 0<---M<----F0<----F1<----F2<----F3<----
 //              |p1   |p2
-// 
+//
 // 0<---N<----G0<----G1<----G2<----G3<----
 //                B(g1)      g2     g3
-// 
+//
 proc grlifting2(A,B)
 "USAGE: grlifting2(A,B), graded objects A and B (matrices defining maps)
-RETURN: map of chain complexes (as a list) 
+RETURN: map of chain complexes (as a list)
 PURPOSE: construct a map of chain complexes between free resolution of
 M=coker(A) and N=coker(B).
@@ -2127 +2127 @@
   P[1]=grrndmap2(A,B);
 
-  // A(or B)=0 
+  // A(or B)=0
   if(t==1){return(P[1])};
- 
+
   for(k=2;k<=t;k++)
   {
@@ -2161 +2161 @@
 def T=grlifting2(DD,PP); T;
 
-// def Z=grlifting2(P,D); Z; // WRONG!!!  
-             
+// def Z=grlifting2(P,D); Z; // WRONG!!!
+
 }
 
@@ -2171 +2171 @@
 proc mappingcone2(A,B)
 "USAGE: mappingcone2(A,B), graded objects A and B (matrices defining maps)
-RETURN: chain complex (as a list) 
+RETURN: chain complex (as a list)
 PURPOSE: construct the free resolution of a cokernel of a random map between M=coker(A), and N=coker(B)
 EXAMPLE: example mappingcone2;
@@ -2234 +2234 @@
 */
 
-proc grlifting3(A,B) 
+proc grlifting3(A,B)
 "TODO: grlifting4 was newer and had more documentation than this proc, but was removed... Please verify and update!
 "
@@ -2247 +2247 @@
   list rN = grres(B,0,1);
   print( betti(rN), "betti");
-  
+
   int i,j,k;
 
@@ -2260 +2260 @@
   }
   int t=min(i,j);
-  
+
   list P;
 
   "t: ", t;
 //  grview(rM[t]);  grview(rN[t]);
-  
+
   P[t]= grrndmap2(rM[t],rN[t]);
   grview(P[t]);
@@ -2312 +2312 @@
 //def I=KeneshlouMatrixPresentation(intvec(2,3,0,6,2));
 //def J=KeneshlouMatrixPresentation(intvec(4,0,1,2,1));
-//def N=grlifting3(I,J); grview(N); 
+//def N=grlifting3(I,J); grview(N);
 }
 
@@ -2318 +2318 @@
 "USAGE: grneg(A), graded object A
 RETURN: graded object
-PURPOSE: graded map defined by -A 
+PURPOSE: graded map defined by -A
 EXAMPLE: example grneg; shows an example
 "
@@ -2341 +2341 @@
 proc mappingcone3(A,B)
 "USAGE: mappingcone3(A,B), graded objects A and B (matrices defining maps)
-RETURN: chain complex (as a list) 
+RETURN: chain complex (as a list)
 PURPOSE: construct a free resolution of the cokernel of a random map between M=coker(A), and N=coker(B)
 EXAMPLE: example mappingcone3; shows an example
@@ -2376 +2376 @@
 
     T[i]=grtranspose(D);
-    
+
     kill A, B, C, D, v, w, r, s, zero;
   }
@@ -2394 +2394 @@
 def F=grlifting3(A,T); grview(F);
 
-// BUG in the proc  
+// BUG in the proc
 def G=mappingcone3(A,T); grview(G);
 
@@ -2403 +2403 @@
 ideal P=groebner(flatten(U[2]));
 resolution L=mres(P,0);
-print(betti(L),"betti");    
+print(betti(L),"betti");
 */
 
@@ -2421 +2421 @@
 def I=KeneshlouMatrixPresentation(intvec(2,3,0,6,2));
 def J=KeneshlouMatrixPresentation(intvec(4,0,1,2,1));
-// def N=grlifting3(I,J); 
+// def N=grlifting3(I,J);
 // 2nd module does not lie in the first:
 // def NN=mappingcone3(I,J); // ????????
@@ -2458 +2458 @@
   module N;
 
-  if(i>n) 
+  if(i>n)
     { // no middle part
       if(a[1]>0)
@@ -2465 +2465 @@
 
           if(a[n+1]>0)
-            { N=grsum(N,grtwist(a[n+1],0));}         
-        }  
+            { N=grsum(N,grtwist(a[n+1],0));}
+        }
       else
         { N=grtwist(a[n+1],0);}
-      
-      return (N); // grorder(N)); 
+
+      return (N); // grorder(N));
     }
 
-else // i <= n: middle part is present, a_i != 0 
+else // i <= n: middle part is present, a_i != 0
     { // a = a1  ... |  i:2, a_2 ..... i: n, a_n | .... i: n+1a_(n+1)
       module I = maxideal(1);
@@ -2505 +2505 @@
 
 
-      return ((N)); //      return (grorder(N)); 
+      return ((N)); //      return (grorder(N));
     }
 }
@@ -2518 +2518 @@
 grview(S);
 
-def N1 = matrixpres(intvec(2,0,0,0,0)); 
+def N1 = matrixpres(intvec(2,0,0,0,0));
 grview(N1);
 

Singular/LIB/surf.lib

@@ -274 +274 @@
 
   string surf_call; i = 0;
-  
+
   if (isWindows())
   {
@@ -303 +303 @@
   else
   {
-    surf_call = "surfer";    
+    surf_call = "surfer";
     surf_call = surf_call + " " + l + " >/dev/null 2>&1";
     "Close window to exit from `surfer`.";
     i = system("sh", surf_call);
-    
-    if ( (i != 0) && isMacOSX() ) 
+
+    if ( (i != 0) && isMacOSX() )
     {
       "*!* Sorry: calling `surfer` failed ['"+surf_call+"']" + newline
       + " (The shell returned the error code " + string(i) + "." + newline
-      + "But since we are on Mac OS X, let us try to open SURFER.app instead..." + newline 
+      + "But since we are on Mac OS X, let us try to open SURFER.app instead..." + newline
       + "Appropriate SURFER.app is available for instance at http://www.mathematik.uni-kl.de/~motsak/files/SURFER.dmg";
-      
+
       // fallback, will only work if SURFER.app is available (e.g. in /Applications)
       // get SURFER.app e.g. from http://www.mathematik.uni-kl.de/~motsak/files/SURFER.dmg
       // note that the newer (Java-based) variant of Surfer may not support command line usage yet :(
-      
+
       surf_call = "open -a SURFER -W --args -t -s";
       surf_call = surf_call + " " + l + " >/dev/null 2>&1";
@@ -324 +324 @@
       i = system("sh", surf_call);
     }
-    
-    
-    
+
+
+
   }
   system("sh", "/bin/rm " + l);
@@ -381 +381 @@
 {
   string s = system("uname");
-  
+
   for (int i = 1; i <= size(s)-2; i = i + 1)
   {

Singular/dyn_modules/singmathic/singmathic.cc

@@ -468 +468 @@
   result->rtyp=NONE;
 
-  if (arg == NULL || arg->next != NULL || 
+  if (arg == NULL || arg->next != NULL ||
   ((arg->Typ() != IDEAL_CMD) &&(arg->Typ() != MODUL_CMD))){
     WerrorS("Syntax: mathicgb(<ideal>/<module>)");

Singular/dyn_modules/syzextra/mod_main.cc

@@ -82 +82 @@
     for (int j=0; j<l; j++)
       if (id->m[j] != NULL && p_GetComp(id->m[j], r) > 0)
-        return TRUE;    
+        return TRUE;
 
     return FALSE; // rank: 1, only zero or no entries? can be an ideal OR module... BUT in the use-case should better be an ideal!
@@ -91 +91 @@
 
 
-   
+
 
 static inline void NoReturn(leftv& res)
@@ -1550 +1550 @@
   const int iLimit = r->typ[pos].data.is.limit;
   const ideal F = r->typ[pos].data.is.F;
-  
+
   ideal FF = id_Copy(F, r);
 

Singular/extra.cc

@@ -3769 +3769 @@
     }
     else
-#endif    
+#endif
 /*==================== Error =================*/
       Werror( "(extended) system(\"%s\",...) %s", sys_cmd, feNotImplemented );