===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/usage.sm1,v
retrieving revision 1.3
retrieving revision 1.9
diff -u -p -r1.3 -r1.9
--- OpenXM/src/kan96xx/Kan/usage.sm1	2000/06/08 08:35:03	1.3
+++ OpenXM/src/kan96xx/Kan/usage.sm1	2004/09/11 01:00:42	1.9
@@ -1,4 +1,4 @@
-%% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.2 2000/01/16 07:55:42 takayama Exp $
+%% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.8 2004/09/10 22:21:27 takayama Exp $
 %% usage.sm1
 %%  [(key word)
 %%    [(   )
@@ -103,6 +103,16 @@
    (The user cannot use the variable names h, e, H and E.)
    (cf. show_ring, system_variable --- CurrentRing)
    (    print_switch_status, switch_function)
+   (Example: [(x,y) ring_of_differential_operators [[(Dx) 1 (Dy) 1]])
+   (           weight_vector 0] define_ring)
+   (   Define the ring of differential operators Q<x,y,Dx,Dy> with the order)
+   (   obtained by refining the partial order defined by the weight vector)
+   (   [x,y,Dx,Dy] = [0,0,1,1] ) 
+   (Example: [(x,y) ring_of_differential_operators 0 [(weightedHomogenization) 1]])
+   (          define_ring )
+   (Example: [(x,y) ring_of_differential_operators [[(x) -1 (Dx) 1]] weight_vector)
+   (          0 [(degreeShift) [[1 0 1]]] ])
+   (          define_ring )
    (Example: [(x,y,z) ring_of_differential_operators (Dx,Dy) elimination_order 0] define_ring)
    (         Dx,Dy, and Dz are corresponding differential operators to the )
    (         space variables x, y and z.)
@@ -111,6 +121,7 @@
 
 [(ring_of_difference_operators)
  [ (string ring_of_difference_operators)
+   (!!! OBSOLETE !!!)
    (  )
    (This command has not been maintained since 1996. So, there may be)
    (troubles if it is used with new features of kan/sm1.)
@@ -146,6 +157,22 @@
  ]
 ] putUsages
 
+[(ring_of_differential_difference_operators)
+ [ ([string1 string2]  ring_of_differential_difference operators)
+   (This command is used to define a ring of differential-difference operators )
+   (with the macros define_ring, weight_vector and elimination_order.)
+   (string1 is a set of variables for differential operators.)
+   (string2 is a set of variables for difference operators.)
+   (The user cannot use the variable names h, e, H and E.)
+   (cf. show_ring, system_variable --- CurrentRing)
+   (    print_switch_status, switch_function)
+   (Example: [[(x,y) (s)] ring_of_differential_difference_operators )
+   (          [[(Es) 1] [(s) 1]] weight_vector 0] define_ring)
+   (         Dx and Dy are corresponding differential operators to the )
+   (         space variables x and y.  Try show_ring to see the commutation)
+   (         relations.)
+ ]
+] putUsages
 
 [(define_ring)
   [( [varlist ring_of_??? order characteristic options] define_ring)
@@ -158,7 +185,7 @@
    (    <<ring_of_???>> ring_of_polynomials, ring_of_differential_operators, )
    (    ring_of_difference_operators)
    (    <<order>> elimination_order, weight_vector)
-   (    ring_def,ring , << ,, >>)
+   (    ring_def,ring , << __ >>)
   ]
 ] putUsages
 
@@ -246,6 +273,9 @@ def
 [(join) 
  [(list1 list2 join list3)
   (Ex.  [1 2] [3 [4 (ab)]] join  [1 2 3 [4 (ab)]])
+  (Note: Join should use for arrays. It works for list too,)
+  (      but it does not copy cells. cf. cons)
+  (      So, it might generate looped lists or destroy other lists.)
  ]
 ] putUsages