Changeset 0b59f5 in git for Singular/LIB/homolog.lib

Timestamp:

Dec 13, 1999, 4:33:50 PM (24 years ago)

Author:

Olaf Bachmann <obachman@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

82ed244cff3158b7a79a6eed4e0548d485960cfe

Parents:

925cab8e04ecb2f3c2e451b913c11bcac28b2374

Message:

* GMG's changes


git-svn-id: file:///usr/local/Singular/svn/trunk@4006 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/homolog.lib (modified) (8 diffs)

Singular/LIB/homolog.lib

@@ -1 @@
-// $Id: homolog.lib,v 1.9 1999-08-03 11:43:06 obachman Exp $
+// $Id: homolog.lib,v 1.10 1999-12-13 15:33:47 obachman Exp $
 //(BM/GMG)
 ///////////////////////////////////////////////////////////////////////////////
 
-version="$Id: homolog.lib,v 1.9 1999-08-03 11:43:06 obachman Exp $";
+version="$Id: homolog.lib,v 1.10 1999-12-13 15:33:47 obachman Exp $";
 info="
 LIBRARY:  homolog.lib   PROCEDURES FOR HOMOLOGICAL ALGEBRA
@@ -554 +554 @@
          0<--M'<-- F0 <-M-- F1 <-- F2 <--...  resp. 0<--N'<-- G0 <--N- G1 be
          a free resolution of M' resp. a presentations of N'. Consider
+@format
                       0                  0                  0
                       |^                 |^                 |^
@@ -562 +563 @@
                                          |C                 |B
                                       Hom(Fk,G1) -----> Hom(Fk+1,G1)
+@end format
          (Ak,Ak+1 induced by M and B,C induced by N).
          Let K=modulo(Ak+1,B), J=module(Ak)+module(C) and Ext=modulo(K,J),
@@ -568 +570 @@
          R^q -Ext-> R^p --K->Hom(Fk,G0)/im(Ak)+im(C) --Ak+1->Hom(Fk+1,G0)/im(B)
          Hence Ext presents Ext^k(M',N')
-RETURN:  Ext, of type module, a presentation of Ext^k(M',N') if v is of type
+RETURN:  
+         Ext, of type module, a presentation of Ext^k(M',N') if v is of type
          int, resp. a list of Ext^k (k=v[1],v[2],...) if v is of type intvec.
          In case of a third argument of any type return a list:
@@ -715 +718 @@
          Let ...-->F1 --M-> F0-->M'-->0 and ...-->G1 --N-> G0-->N'-->0  be
          presentations of M' and N'. Consider
+@format
                                          0               0
                                          |^              |^
@@ -728 +732 @@
               R^q -Hom-> R^p --D-> Hom(F0,G0)/im(C) --A-> Hom(F1,G0)/im(B).
          Hence Hom presents Hom(M',N')
+@end format
 RETURN:  Hom, of type module, presentation of Hom(M',N') or,
          in case of 3 arguments, a list:
@@ -845 +850 @@
          (R=basering) and let A:R^m-->R^n a matrix inducing a map A':M'-->N'.
          Compute a presentation K of ker(A') as in the commutative diagram:
+@format
                        ker(A') --->  M' --A'--> N'
                            |^        |^         |^
@@ -853 +859 @@
                            |         |          |
                           R^s  ---> R^p -----> R^q
+@end format
 RETURN:  module K, a presentation of ker(A')
 EXAMPLE: example kernel; shows examples