===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/complex.sm1,v
retrieving revision 1.5
retrieving revision 1.9
diff -u -p -r1.5 -r1.9
--- OpenXM/src/kan96xx/Doc/complex.sm1	2000/08/01 07:26:23	1.5
+++ OpenXM/src/kan96xx/Doc/complex.sm1	2004/09/10 13:20:22	1.9
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/src/kan96xx/Doc/complex.sm1,v 1.4 2000/07/30 09:55:39 takayama Exp $
+% $OpenXM: OpenXM/src/kan96xx/Doc/complex.sm1,v 1.8 2002/08/11 08:39:50 takayama Exp $
 %% lib/complex.sm1  [ functions for complex ], 1999, 9/9
 %% cf.  yama:1999/Int/uli.sm1
 %%%%%%%%%%%%%%%%%%%   commands %%%%%%%%%%%%%%%%%%%%%%%%%
@@ -267,12 +267,19 @@
 %% [M d] res-solv c'/r  ;   M : matrix,  d, c' : vectors, r : scalar, c'/r =c
 /res-solv {
   /arg1 set
-  [/in-res-solv /M /d /ans /B /vv /G /rr /rng] pushVariables
+  [/in-res-solv /M /d /ans /B /vv /G /rr /rng /nn] pushVariables
   [(CurrentRingp) (KanGBmessage)] pushEnv
   [
+     /nn arg1 length def
      /M arg1  0 get def
      /d arg1  1 get def
-     M getRing /rng set
+     nn 3 eq {
+       /rng arg1 2 get def
+     }{
+       M getRing /rng set
+       rng tag RingP eq {  }
+       { d getRing /rng set } ifelse
+     }ifelse
      rng res-getx /vv set
      uli.verbose { (res-solv : vv = ) messagen vv message } { } ifelse
      uli.verbose { } { [(KanGBmessage) 0] system_variable } ifelse
@@ -298,7 +305,7 @@
      d G 0 get reduction-noH  /rr set
      rr 0 get (0). eq {
        [rr 2 get] B mul 0 get /ans set
-       /ans [ ans { toString rng ,, (-1) rng ,, mul} map  
+       /ans [ ans { toString rng __ (-1) rng __ mul} map  
               rr 1 get toString .. ] def
      } {
        /ans null def
@@ -318,6 +325,9 @@
  (Note that M and d are not treated as an element of the homogenized Weyl)
  (algebra. If M or d contains the homogenization variable h, it automatically)
  (set to 1. If you need to use h, use the command res-solv-h)
+ $[M d rng] res-solv [c' r] $ 
+ $ rng is a ring object. $
+ $ res-solv extracts variables names from rng, but defines a new ring. $
  $Example 1:  [(x,y) ring_of_differential_operators [[(x) -1 (Dx) 1]] weight_vector 0] $
  $              define_ring $
  $ [ [ [(x Dx + 2).] [ (Dx (x Dx + 3) - (x Dx + 2) (x Dx -4)).]]   [(1).]] $
@@ -359,12 +369,19 @@
 %% M : matrix,  d, c' : vectors, r : scalar, c'/r =c
 /res-solv-h {
   /arg1 set
-  [/in-res-solv-h /M /d /ans /B /vv /G /rr /rng] pushVariables
+  [/in-res-solv-h /M /d /ans /B /vv /G /rr /rng /nn] pushVariables
   [(CurrentRingp) (KanGBmessage)] pushEnv
   [
+     /nn arg1 length def
      /M arg1  0 get def
      /d arg1  1 get def
-     M getRing /rng set
+     nn 3 eq {
+       /rng arg1 2 get def
+     }{
+       M getRing /rng set
+       rng tag RingP eq {  }
+       { d getRing /rng set } ifelse
+     }ifelse
      rng res-getx /vv set
      uli.verbose { (res-solv-h : vv = ) messagen vv message } { } ifelse
      uli.verbose { } { [(KanGBmessage) 0] system_variable } ifelse
@@ -394,7 +411,7 @@
      d G 0 get reduction  /rr set
      rr 0 get (0). eq {
        [rr 2 get] B mul 0 get /ans set
-       /ans [ ans { toString rng ,, (-1) rng ,, mul} map  
+       /ans [ ans { toString rng __ (-1) rng __ mul} map  
               rr 1 get toString .. ] def
      } {
        /ans null def
@@ -792,6 +809,9 @@
 
 [(intersection)
 [(Ideal intersections in the ring of differential operators.)
+ ([ I1 I2 V-list ] intersection  : I1 and I2 are ideals, and V-list)
+ (is a list of variables.  It returns the ideal intersection of I1 and I2.)
+ (Intersection is computed in the ring of differential operators.)
  $Example 1: [[[(x1) (x2)] [(x2) (x4)] (x1,x2,x3,x4)] intersection$
  $             [(x2) (x4^2)] (x1,x2,x3,x4)] intersection :: $
  $Example 2: [[[(x1) (x2)] [(x2) (x4)] (x1,x2,x3,x4)] intersection$
@@ -862,6 +882,9 @@
     /vlist ff 2 get  def
     /mm slist length def
 
+    vlist tag ArrayP eq {
+      vlist { toString } map from_records /vlist set
+    } {  } ifelse
     [vlist to_records pop] [(_z) (_y)] join /vlist2 set
     [vlist2 from_records ring_of_polynomials 
      [[(_z) 1 (_y) 1]] weight_vector