Changeset 04b3ef in git

Timestamp:

Apr 22, 2015, 7:36:03 PM (9 years ago)

Author:

Oleksandr Motsak <motsak@…>

Branches:

(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')

Children:

5ae475019ef08f2c881ab47459777123fc5ee74a

Parents:

7b4fc83ac3b56ec34dfb40d2265468850bfcd0c7

git-author:

Oleksandr Motsak <motsak@mathematik.uni-kl.de>2015-04-22 19:36:03+02:00

git-committer:

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

Message:

Corrections  (and documentation improvements) for the edited gradedModules.lib from Hanie

File:

• Singular/LIB/gradedModules.lib (modified) (16 diffs)

Singular/LIB/gradedModules.lib

@@ -53 +53 @@
     mappingcone2(M,N)  mapping cone2?
     grlifting3(A,B)    RND! chain lifting? probably wrong one
-    mappingcone3(A,B)  mapping cone3? (using grlifting4 at the moment)
+    mappingcone3(A,B)  mapping cone3? 
     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)
+    matrixpres(a)      matrix presentation of direct sum of Omega^{a[i]}(i)
 ";
 
@@ -1460 +1460 @@
 proc KeneshlouMatrixPresentation(intvec a)
 "USAGE:  intvec a.
-RETURN: matrix 
-PURPOSE:matrix presentation for direct sum of omega^a[i](i) 
+RETURN: graded object
+PURPOSE: matrix presentation for direct sum of omega^a[i](i) in form of a graded object
 EXAMPLE: example KeneshlouMatrixPresentation; shows an example
 {
@@ -1688 +1688 @@
 "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
+PURPOSE: construct a map of chain complexes between free resolutions of Img(M) and Img(N).
+EXAMPLE: example grlifting; shows an example
 "
 {  ASSUME(1, grtest(M));
@@ -1779 +1778 @@
 "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).
+PURPOSE: construct a free resolution of the cokernel of a random map between Img(M), and Img(N).
 EXAMPLE: example mappingcone; shows an example
-
+"
 {
   ASSUME(1, grtest(M));
@@ -1815 +1813 @@
 example
 { "EXAMPLE:"; echo = 2;
-//Veronese surface
 
 ring r=32003, (x(0..4)),dp;
@@ -1904 +1901 @@
 }
 
+
+//                A     f2     f3
+// 0<---M<----F0<----F1<----F2<----F3<----
+//              |p1   |p2
+// 
+// 0<---N<----G0<----G1<----G2<----G3<----
+//                B(g1)      g2     g3
+// 
 proc grlifting2(A,B)
 "USAGE: (A,B), graded objects A and B (matrices defining maps)
@@ -1909 +1914 @@
 PURPOSE: construct a map of chain complexes between free resolution of
 M=coker(A) and N=coker(B).
-NOTE:
-               A     f2     f3
-0<---M<----F0<----F1<----F2<----F3<----
-             |p1   |p2
-
-0<---N<----G0<----G1<----G2<----G3<----
-               B(g1)      g2     g3
-
 EXAMPLE: example grlifting2; shows an example
 "
@@ -1983 +1980 @@
 
 /*
+//              -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 a cokernel of a random map between
-M=coker(A), and N=coker(B)
-NOTE: 
-             -f1 0       -f2 0
-  (p1 g1)     p2 g2       p3 g3
-G0<-----F0+G1<------F1+G2<-------F2+G3<-----
-
+PURPOSE: construct the free resolution of a cokernel of a random map between M=coker(A), and N=coker(B)
 EXAMPLE: example mappingcone2;
 "
@@ -2019 +2013 @@
     module A=grconcat(P[i],rN[i]);
     module B=grobj(zero,v,w);
-    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 C=grconcat( grneg( rM[i-1] ) ,B);
     module D=grconcat(grtranspose(C), grtranspose(A));
 
@@ -2056 +2050 @@
 def G=mappingcone2(SS,BB);G;
 }
-
-
-
-
-
-
-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!
+"
 {
   ASSUME(1, grtest(A));
@@ -2136 +2133 @@
 def H=grlifting3(R, S);
 // grview(H);
-def H=grlifting3(S, R);
-
-/*
-// ???
-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); // ???
-*/
-}
-
+
+// 2nd module does not lie in the first:
+// def H=grlifting3(S, R);
+
+
+//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); 
+}
 
 proc grneg(A)
-"USAGE: A graded object
-RETURN: -A as graded object
-PURPOSE: graded map defined by -A. 
+"USAGE: grneg(A), graded object A
+RETURN: 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<-----
-
-*/
-
-
+  ASSUME(1, 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(F);
+}
+
+//             -f1 0        -f2 0
+//  (p1 g1)     p2 g2        p3 g3
+//G0<-----F0+G1<------F1+G2<-------F2+G3<-----
 proc mappingcone3(A,B)
 "USAGE: (A,B), graded objects A and B (matrices defining maps)
 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)
+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
-
+"
 {
   ASSUME(1, grtest(A));
   ASSUME(1, grtest(B));
 
-  list P=grlifting4(A,B);
+  list P=grlifting3(A,B);
   list rM=grres(A,0,1);
   list rN=grres(B,0,1);
@@ -2212 +2201 @@
     module B=grobj(zero,v,w);
 
-//    ASSUME( 0, grtest(B) );
-//    ASSUME( 0, grtest(-rM[i-1]) );    
-    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 C=grconcat( grneg( rM[i-1] ) ,B);
     module D=grconcat(grtranspose(C), grtranspose(A));
 
@@ -2240 +2226 @@
 def F=grlifting3(A,T); grview(F);
 
-/* BUG in the proc */ 
+// BUG in the proc  
 def G=mappingcone3(A,T); grview(G);
 
@@ -2261 +2247 @@
 def H=grlifting3(R,S); grview(H);
 
-/* BUG in the proc */ 
+// BUG in the proc
 def G=mappingcone3(R,S);
 
@@ -2268 +2254 @@
 def J=KeneshlouMatrixPresentation(intvec(4,0,1,2,1));
 // def N=grlifting3(I,J); 
-/* 2nd module does not lie in the first: */ // def NN=mappingcone3(I,J); // ????????
-
-}
-
-
-
-
-
-
+// 2nd module does not lie in the first:
+// def NN=mappingcone3(I,J); // ????????
+
+}
+
+
+
+
+
+
+// TODO: Please decide between KeneshlouMatrixPresentation and matrixpres, and replace one with the other!
 proc matrixpres(intvec a)
-"USAGE:  intvec a.
-RETURN: matrix. 
-PURPOSE:matrix presentation for direct sum of omega^a[i](i) 
+"USAGE:  intvec a
+RETURN:  graded object
+PURPOSE: matrix presentation for direct sum of omega^a[i](i) in form of a graded object
 EXAMPLE: example matrixpres; shows an example
-{  
+"
+{
   int n = size(a)-1;
   //  ring r = 32003,(x(0..n)),dp;
@@ -2356 +2345 @@
 example
 {"EXAMPLE:"; echo = 2;
+ring r = 32003,(x(0..4)),dp;
 
 def R=matrixpres(intvec(1,4,0,0,0));
+grview(R);
 def S=matrixpres(intvec(0,0,3,0,0));
-}
+grview(S);
+
+def N1 = matrixpres(intvec(2,0,0,0,0)); 
+grview(N1);
+
+def N2 = matrixpres(intvec(0,0,0,0,3));
+grview(N2);
+
+def N = matrixpres(intvec(2,0,0,0,3));
+grview(N);
+
+
+def M1 = matrixpres(intvec(0,1,0,0,0));
+grview(M1);
+
+def M2 = matrixpres(intvec(0,1,1,0,0));
+grview(M2);
+
+def M3 = matrixpres(intvec(0,0,0,1,0));
+grview(M3);
+
+def M = matrixpres(intvec(1,1,1,0,0));
+grview(M);
+}
+