===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/complex.sm1,v
retrieving revision 1.2
retrieving revision 1.3
diff -u -p -r1.2 -r1.3
--- OpenXM/src/kan96xx/Doc/complex.sm1	2000/03/23 11:54:08	1.2
+++ OpenXM/src/kan96xx/Doc/complex.sm1	2000/06/08 08:35:01	1.3
@@ -1,10 +1,11 @@
-% $OpenXM$
+% $OpenXM: OpenXM/src/kan96xx/Doc/complex.sm1,v 1.2 2000/03/23 11:54:08 takayama Exp $
 %% lib/complex.sm1  [ functions for complex ], 1999, 9/9
 %% cf.  yama:1999/Int/uli.sm1
 %%%%%%%%%%%%%%%%%%%   commands %%%%%%%%%%%%%%%%%%%%%%%%%
 %%%  res-div, res-solv, res-kernel-image, res-dual
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 [(complex.sm1 : 1999, 9/28, res-div, res-solv, res-kernel-image, res-dual )
+ (              2000, 6/8,  isExact_h, isExact )
  (In this package, complex is expressed in terms of matrices.) 
 ] {message} map
 /uli.verbose 0 def
@@ -902,5 +903,96 @@
  $                     [[(y1) 1 (y2) 1 (y3) 1 (y4) 1]]] pgb $
  $            0 get [(y1) (y2) (y3) (y4)] eliminatev ::$
  $Example 2: [[(x2^2) (x2 x4) (x2) (x4^2)] [(x2) (x4)] (x2,x4)] saturation$
+]] putUsages
+
+
+%% 2000, 6/8,  at Fernando Colon, 319,  Sevilla
+
+
+/isExact.verbose 1 def  %% should be changed to gb.verbose
+/isExact_h {
+  /arg1 set
+  [/in-isExact_h  /vv /comp /i /j /n /kernel.i /ans] pushVariables
+  [
+    /comp arg1 0 get def
+    /vv arg1 1 get def
+    /n comp length def
+    /ans 1 def
+    0 1 n 2 sub {
+      /i set
+      /j i 1 add def
+      isExact.verbose { (Checking ker ) messagen i messagen ( = im of ) messagen
+                     j message } {   } ifelse
+      [comp i get vv] syz_h 0 get /kernel.i set
+      [ kernel.i comp j get vv] isSameIdeal_h /ans set
+      ans 0 eq {
+        (image != kernel at ) messagen i messagen ( and ) messagen j message
+         /LLL.isExact_h goto
+      } {  } ifelse
+      isExact.verbose { (OK) message } {  } ifelse
+    } for
+    /LLL.isExact_h
+    /arg1 ans def
+  ] pop
+  arg1
+} def
+
+[(isExact_h)
+[( complex isExact_h bool )
+ (It returns 1 when the given complex is exact. All computations are done)
+ (in D<h>, the ring of homogenized differential operators.)
+ (cf. syz_h, isSameIdeal_h )
+ $Example1: [ [[1 2 3]] [0]] gkz /ff set $
+ $         [ff 0 get (x1,x2,x3) [[(x2) -1 (Dx2) 1]]] resol1 /gg set $
+ $         [gg (x1,x2,x3)] isExact_h :: $
+ $         gg 1 get 0 get /pp set $
+ $         gg [1 1] pp put $
+ $         [gg (x1,x2,x3)] isExact_h :: $
+]] putUsages
+
+/isExact {
+  /arg1 set
+  [/in-isExact  /vv /comp /i /j /n /kernel.i /ans] pushVariables
+  [
+    /comp arg1 0 get def
+    /vv arg1 1 get def
+    /n comp length def
+    /ans 1 def
+    0 1 n 2 sub {
+      /i set
+      /j i 1 add def
+      isExact.verbose { (Checking ker ) messagen i messagen ( = im of ) messagen
+                     j message } {   } ifelse
+      [comp i get vv] syz 0 get /kernel.i set
+      [ kernel.i comp j get vv] isSameIdeal /ans set
+      ans 0 eq {
+        (image != kernel at ) messagen i messagen ( and ) messagen j message
+         /LLL.isExact goto
+      } {  } ifelse
+      isExact.verbose { (OK) message } {  } ifelse
+    } for
+    /LLL.isExact
+    /arg1 ans def
+  ] pop
+  arg1
+} def
+
+[(isExact)
+[( complex isExact bool )
+ (It returns 1 when the given complex is exact. All computations are done)
+ (in D, the ring of differentialoperators. Inputs are dehomogenized.)
+ (cf. syz, isSameIdeal )
+ $Example1: [ [[1 2 3]] [0]] gkz /ff set $
+ $         [ff 0 get (x1,x2,x3) [[(x2) -1 (Dx2) 1]]] resol1 /gg set $
+ $         [gg (x1,x2,x3)] isExact :: $
+ $         gg 1 get 0 get /pp set $
+ $         gg [1 1] pp put $
+ $         [gg (x1,x2,x3)] isExact :: $
+ $Example2: [ [[1 2 3]] [0]] gkz /ff set $
+ $         [ff 0 get (x1,x2,x3) [[(x2) -1 (Dx2) 1]]] resol1 /gg set $
+ $         gg dehomogenize /gg set $
+ $         [gg (x1,x2,x3)] isExact :: $
+ (       The syzygies of f_i^h in D<h> do not always give generators of )
+ (       the corresponding syzygy of f_i in D.)
 ]] putUsages