===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/usage.sm1,v
retrieving revision 1.2
retrieving revision 1.15
diff -u -p -r1.2 -r1.15
--- OpenXM/src/kan96xx/Kan/usage.sm1	2000/01/16 07:55:42	1.2
+++ OpenXM/src/kan96xx/Kan/usage.sm1	2013/09/22 01:06:20	1.15
@@ -1,4 +1,4 @@
-%% $OpenXM$
+%% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.14 2013/09/20 06:02:19 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.)
@@ -146,7 +157,34 @@
  ]
 ] 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.)
+   (Example: contiguity of 1F1. Eb b = (b-1) Eb)
+   ( [ [(x) (a,b)] ring_of_differential_difference_operators )
+   (  [[(Dx) 1]] weight_vector 0] define_ring )
+   ( [ ( x Dx (x Dx+b-1) -x (x Dx+a) ). )
+   ( ( (x Dx +b-1) - (b-1) Eb ). ] /ff set )
+   ( ff {dehomogenize homogenize} map /ff2 set )
+   ( [ff2] groebner /gg set )
+   ( gg dehomogenize 0 get /gg set )
+   ( gg [(Dx)] eliminatev /gg2 set )
+   ( gg2 pmat )
 
+ ]
+] putUsages
+
 [(define_ring)
   [( [varlist ring_of_??? order characteristic options] define_ring)
    ( Pointer to the ring.)
@@ -158,7 +196,7 @@
    (    <<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 +284,9 @@ 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
 
@@ -278,6 +319,7 @@ def
  [(obj toVectors vec)
   (Convert the internal expression of vector into the array <<vec>>.)
   (obj can be  [n [g1 ... gm]] where n is the length of the vector.)
+  $cf. [(toe_) array_of_poly] gbext $
   $Example 1: [(x) ring_of_polynomials 0] define_ring  $
   $           (e_ + 2).  toVectors :: $
   (        --->  [2  , 1] )
@@ -292,3 +334,23 @@ def
  [(Remained for the compatibility. cf. toVectors)
 ]] putUsages
 
+[(extension-examples)
+ [
+   $putAttributeList$
+   $  [(putAttributeList) [[(x+y-1) (x-y-2)] (x,y)]  $
+   $                      [(needSyz) 1 (sugar) 1]] extension /myarg set $
+   $  [(getAttributeList) myarg] extension :: $
+   $  [(getAttribute) myarg (sugar)] extension :: $
+]] putUsages
+
+[(note-class)
+[ 
+  $Example 1: [(object) [ ] [1,2]] [(class) (tree)] dc /ff set $
+  $           ff (array) dc :: $
+  $cf. data_conversion, kan96xx/Kan/kclass.c (KclassDataConversion) $
+]] putUsages
+
+[(sm1log)
+[
+  $str sm1log outputs the str to the log file /tmp/sm1log.txt$
+]] putUsages