Changeset 7b4fc8 in git

Timestamp:

Apr 22, 2015, 7:17:40 PM (8 years ago)

Author:

Oleksandr Motsak <motsak@…>

Branches:

(u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')

Children:

04b3ef1b32a87e188ccba4b8a4308a0e75f9b895

Parents:

d088e2c2f2336235f058b94a17c4d3453de98df5

git-author:

Oleksandr Motsak <motsak@mathematik.uni-kl.de>2015-04-22 19:17:40+02:00

git-committer:

Oleksandr Motsak <motsak@mathematik.uni-kl.de>2015-04-29 18:04:56+02:00

Message:

Edited  by Hanieh Keneshlou<hkeneshlou@yahoo.com> on 22 Apr. 2015

File:

• Singular/LIB/gradedModules.lib (modified) (15 diffs)

Singular/LIB/gradedModules.lib

@@ -53 +53 @@
     mappingcone2(M,N)  mapping cone2?
     grlifting3(A,B)    RND! chain lifting? probably wrong one
-    grlifting4(A,B)    RND! chain lifting? newer from #hani# for mappingcone3
     mappingcone3(A,B)  mapping cone3? (using grlifting4 at the moment)
     grrange(M)         get the row-weightings
+    grneg(A)           graded object given by -A
+    matrixpres(intvec a)   matrix presentation of direct sum of Omega^a[i](i)
 ";
 
@@ -1458 +1459 @@
 
 proc KeneshlouMatrixPresentation(intvec a)
-"
-PURPOSE: Direct sum of all omegas_i(i) with powers a[i]
-NOTE: Please document/name this proc properly
-"
+"USAGE:  intvec a.
+RETURN: matrix 
+PURPOSE:matrix presentation for direct sum of omega^a[i](i) 
+EXAMPLE: example KeneshlouMatrixPresentation; shows an example
 {
   int n = size(a)-1;
@@ -1685 +1686 @@
 
 proc grlifting(M,N)
-"generic random alpha : coker(M) -> coker(N) "
+"USAGE:  graded objects M and N
+RETURN: map of chain complexes (as a list)
+PURPOSE: construct a map of chain complexes between free resolution of
+M=Img(M) and N=Img(N).
+EXAMPLE: example grlift; shows an example
+"
 {  ASSUME(1, grtest(M));
    ASSUME(1, grtest(N));
@@ -1712 +1718 @@
   P[1]= grrndmap( rM[1], rN[1] ); // alpha1
 
-  grview(P[1]); print(P[1]);  
-
-//   return();
-  
-  
+  if(t==2){return(P[1]);}  
+    
   for(k=2; k<=t; k++)
   {
-    "k: ", k;
-    grview(rN[k-1]);
-    grview(P[k-1]);
-
-//    grprod( grtranspose(P[k-1]), grtranspose(rN[k-1])  );
-//    grprod( grtranspose(rN[k-1]), grtranspose(P[k-1])  );
-
-//     grprod( P[k-1], rN[k-1] );
-    
-//    grview( _ );
-    
-//    rM[k];
-    grview(rM[k-1]);
-
-    P[k] =  grtranspose( grlift( grtranspose( rM[k-1] ),
-       grtranspose( grprod( rN[k-1],  P[k-1] ) ) ) ); // alpha0!
-    
-//    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]);  
     
   }
@@ -1791 +1777 @@
 
 proc mappingcone(M,N)
-"??"
+"USAGE:M,N graded objects
+RETURN: chain complex (as a list) 
+PURPOSE: construct a free resolution of the cokernel of a random map between
+M=Img(M), and N=Img(N).
+EXAMPLE: example mappingcone; shows an example
+
 {
   ASSUME(1, grtest(M));
@@ -1824 +1815 @@
 example
 { "EXAMPLE:"; echo = 2;
+//Veronese surface
 
 ring r=32003, (x(0..4)),dp;
-def I=maxideal(1);
-module R=grobj(module(I), intvec(0));
-resolution FR=mres(R,0);
-print(betti(FR,0),"betti");
-module K=grobj(module(FR[1]),intvec(-1),intvec(0,0,0,0,0));
-module S=grsyz(K);
-grview(S);
-module B=grobj(module([1,0,0],[0,1,0],[0,0,1]),intvec(1,1,1),intvec(1,1,1));
-grview(B);
-
-def Z=grlifting(B,S);
-Z;
-
-def G=mappingcone(B,S);
-G;
-
-
-resolution E=grres(G[1],0);
-print(betti(E,0),"betti");
-module W=grtranspose(G[1]);
-resolution U=grres(W,0);
-ideal P=groebner(flatten(U[2])); // flatten???
-resolution L=mres(P,0);
-print(betti(L),"betti");
+def A=KeneshlouMatrixPresentation(intvec(0,0,0,0,3));
+def M=grgens(A);
+grview(M);
+
+def B=KeneshlouMatrixPresentation(intvec(0,1,0,0,0));
+def N=grgens(B);
+grview(N);
+
+def R=grlifting(M,N);
+grview(R);
+def T=mappingcone(M,N);
+grview(T);
+
+def U=grtranspose(T[1]);
+resolution G=mres(U,0);
+print(betti(G),"betti");
+ideal I=groebner(flatten(G[2]));
+resolution GI=mres(I,0);
+print(betti(GI),"betti");
 }
 
@@ -2028 +2015 @@
     int r=size(v);
     int s=size(w);
-    module zero = (0:s);
+    matrix zero[r][s];
 
     module A=grconcat(P[i],rN[i]);
     module B=grobj(zero,v,w);
-    module C=grconcat(-rM[i-1],B);
+    ASSUME( 0, grtest( grneg( rM[i-1]) ) );
+    module C=grconcat( grneg( rM[i-1] ) ,B); // FIXME: '-' is wrong! need a graded-enabled minus (e.g. grneg?)
     module D=grconcat(grtranspose(C), grtranspose(A));
 
@@ -2039 +2027 @@
   return(T);
 }
+
+
+
 example
 { "EXAMPLE:"; echo = 2;
@@ -2065 +2056 @@
 def G=mappingcone2(SS,BB);G;
 }
-*/
-
-
-
-
-/*
-             -f1 0        -f2 0
-  (p1 g1)     p2 g2        p3 g3
-G0<-----F0+G1<------F1+G2<-------F2+G3<-----
-
-*/
-
-proc mappingcone2(A,B)
-"USAGE: (A,B), graded objects A and B (matrices defining maps)
-RETURN: chain complex (as a list) 
-PURPOSE: construct the free resolution of cokernel of a random map between
-M=coker(A), and N=coker(B)
-EXAMPLE: example ????????
-"
-
-{
-  ASSUME(1, grtest(A));
-  ASSUME(1, grtest(B));
-
-  list P=grlifting3(A,B);
-  list rM=grres(A,0,1);
-  list rN=grres(B,0,1);
-
-  int i;
-  list T;
-
-  T[1]=grconcat(P[1],rN[1]);
-
-  for(i=2;i<=size(P);i++)
-  {
-    intvec v=grrange(rM[i-1]);
-    intvec w=grdeg(rN[i]);
-    int r=size(v);
-    int s=size(w);
-    matrix zero[r][s]; 
-
-    module A=grconcat(P[i],rN[i]);
-    module B=grobj(zero,v,w);
-    module C=grconcat(-rM[i-1],B);
-    module D=grconcat(grtranspose(C), grtranspose(A));
-
-    T[i]=grtranspose(D);
-  }
-   return(T);
-}
+
+
 
 
@@ -2171 +2114 @@
 
 }
+
+
+
 example
 {"EXAMPLE:"; echo = 2;
@@ -2200 +2146 @@
 }
 
+
+proc grneg(A)
+"USAGE: A graded object
+RETURN: -A as graded object
+PURPOSE: graded map defined by -A. 
+EXAMPLE: example grneg; shows an example
+"
+{
+  ASSUME(0, grtest(A));
+return(grobj(-A,grrange(A), grdeg(A) ));
+}
+
+example
+{ "EXAMPLE:"; echo = 2;
+ring r=0,(x,y,z),dp;
+def A=grobj([x2,yz,xyz],intvec(1,1,0));
+grview(A);
+def F=grneg(A);
+grview(A);
+}
+
+
+
+
 /*
              -f1 0        -f2 0
   (p1 g1)     p2 g2        p3 g3
 G0<-----F0+G1<------F1+G2<-------F2+G3<-----
+
 */
 
-proc grneg(M)
-"negative map
-TODO for Hanieh: please document this and find good motivating examples for this proc!!
-"
-{
-  return ( grobj(-M, grrange(M), grdeg(M) ) );
-}
-
-// note: not clear which grlifting3 should be used by the following
-// procedure!!?
+
 proc mappingcone3(A,B)
 "USAGE: (A,B), graded objects A and B (matrices defining maps)
@@ -2262 +2224 @@
    return(T);
 }
+
+
+
 example
 { "EXAMPLE:"; echo = 2;
@@ -2273 +2238 @@
 grview(T);
 
-def F=grlifting4(A,T); grview(F);
+def F=grlifting3(A,T); grview(F);
 
 /* BUG in the proc */ 
@@ -2294 +2259 @@
 grview(S);
 
-def H=grlifting4(R,S); grview(H);
+def H=grlifting3(R,S); grview(H);
 
 /* BUG in the proc */ 
-def G=mappingcone3(R,S); // ????????
+def G=mappingcone3(R,S);
 
 
 def I=KeneshlouMatrixPresentation(intvec(2,3,0,6,2));
 def J=KeneshlouMatrixPresentation(intvec(4,0,1,2,1));
-// def N=grlifting4(I,J); 
+// def N=grlifting3(I,J); 
 /* 2nd module does not lie in the first: */ // def NN=mappingcone3(I,J); // ????????
 
@@ -2308 +2273 @@
 
 
-// this is grlifting3 from #hani# (NOTE that this version is different
-// to the grlifting3 that came within this library!!!
-proc grlifting4(A,B)
-"USAGE: (A,B), graded objects A and B (matrices defining maps)
-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). 
-EXAMPLE: example grlifting4; shows an example
-"
-{
-           ASSUME(1, grtest(A));
-           ASSUME(1, grtest(B));
-
-
-           list rM=grres(A,0,1);
-           list rN=grres(B,0,1);
-           int i,j,k;
-
-           for(i=1;i<=size(rM);i++)
-           {
-             if(size(rM[i])==0){break;}
-           }
-
-           for(j=1;j<=size(rN);j++)
-           {
-             if(size(rN[j])==0){break;}
-           }
-           int t=min(i,j);
-
-           list P;
-
-           P[t]= grrndmap2( rM[t],rN[t] );
-
-           if(t==1){return(P)};
-
-           for(k=t-1; k>=1; k--)
-           {
-             def C = grtranspose(rM[k]);
-             def T= grprod(rN[k],P[k+1]);
-             def tT = grtranspose(T);
-
-             P[k]= grtranspose(grlift(C,tT));
-
-           }
-           return(P);
-}
+
+
+
+
+proc matrixpres(intvec a)
+"USAGE:  intvec a.
+RETURN: matrix. 
+PURPOSE:matrix presentation for direct sum of omega^a[i](i) 
+EXAMPLE: example matrixpres; shows an example
+{  
+  int n = size(a)-1;
+  //  ring r = 32003,(x(0..n)),dp;
+  ASSUME(0, nvars(basering)==(n+1));
+  int i,j;
+
+  // find first nonzero exponent a_i
+  for(i=1;i<=size(a);i++)
+    {
+      if(a[i]!=0) {break; };
+    }
+
+  // all zeroes?
+  if(i>size(a)) {return (grzero()); };
+   for(i=2;i<=n;i++)
+    {
+      if(a[i]!=0) {break; };
+    }
+
+  module N;
+
+  if(i>n) 
+    { // no middle part
+      if(a[1]>0)
+        {
+          N=grtwist(a[1],-1);
+
+          if(a[n+1]>0)
+            { N=grsum(N,grtwist(a[n+1],0));}         
+        }  
+      else
+        { N=grtwist(a[n+1],0);}
+      
+      return (N); // grorder(N)); 
+    }
+
+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);
+      attrib(I,"isHomog", intvec(0));
+      list L = mres(I, 0);
+      list kos = grorder(L);
+      // make sure that graded maps  are represented by blocks corresponding to the betti diagram?
+      int j=size(a)-i;
+      def S = grpower(grshift(grobj( kos[j+2], attrib(kos[j+2], "isHomog")),j ), a[i]);
+
+      i++;
+
+      for(; i <= n; i++)
+        {
+          if(a[i]==0) { i++; continue; }
+          int j=size(a)-i;
+          S = grsum( S, grpower(grshift( grobj( kos[j+2], attrib(kos[j+2], "isHomog")), j), a[i])  );
+        }
+
+      // S is the middle (non-zero) part
+
+      if(a[1] > 0 )
+        {
+          N=grsum(grtwist(a[1],-1), S);
+        }
+      else
+        { N = S;}
+
+      if(a[n+1] > 0 )
+        { N=grsum(N, grtwist(a[n+1],0)); }
+
+
+      return ((N)); //      return (grorder(N)); 
+    }
+}
+
 example
 {"EXAMPLE:"; echo = 2;
 
-ring r=32003,x(0..4),dp;
-
-def A=KeneshlouMatrixPresentation(intvec(0,0,0,0,3));
-grview(A);
-
-def T= KeneshlouMatrixPresentation(intvec(0,1,0,0,0));
-grview(T);
-
-def F=grlifting4(A,T);
-grview(F);
-
-def G=mappingcone3(A,T);grview(G);
-/*
-module W=grtranspose(G[1]);
-resolution U=mres(W,0);
-print(betti(U,0),"betti"); // ?
-ideal P=groebner(flatten(U[2]));
-resolution L=mres(P,0);
-print(betti(L),"betti");
-*/
-
-
-def R=KeneshlouMatrixPresentation(intvec(0,0,0,2,0));
-def S=KeneshlouMatrixPresentation(intvec(1,2,0,0,0));
-
-def H=grlifting4(R,S); grview(H);
-
-def G=mappingcone3(R,S); // ????????
-
-def I=KeneshlouMatrixPresentation(intvec(2,3,0,6,2));
-def J=KeneshlouMatrixPresentation(intvec(4,0,1,2,1));
-/* 2nd module does not lie in the first: */ //def N=grlifting4(I,J);
-
-}
+def R=matrixpres(intvec(1,4,0,0,0));
+def S=matrixpres(intvec(0,0,3,0,0));
+}