===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/usage.c,v
retrieving revision 1.18
retrieving revision 1.20
diff -u -p -r1.18 -r1.20
--- OpenXM/src/kan96xx/Kan/usage.c	2003/08/22 11:47:03	1.18
+++ OpenXM/src/kan96xx/Kan/usage.c	2003/08/24 05:19:43	1.20
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM/src/kan96xx/Kan/usage.c,v 1.17 2003/08/21 04:45:40 takayama Exp $ */
+/* $OpenXM: OpenXM/src/kan96xx/Kan/usage.c,v 1.19 2003/08/23 02:28:39 takayama Exp $ */
 #include <stdio.h>
 #include "datatype.h"
 #include "stackm.h"
@@ -177,6 +177,7 @@ void Kusage2(fp,s)
     fppp(fp,"  [(isReducible) poly1 poly2 ] gbext integer \n");
     fppp(fp,"  [(lcm) poly1 poly2] gbext poly \n");
     fppp(fp,"  [(grade) poly1 ] gbext integer \n");
+    fppp(fp,"  [(ord_ws_all) fv wv] gbext integer \n");
     fppp(fp,"  [(mod) poly1 universalNumber] gbext poly \n");
     fppp(fp,"          poly = poly1 mod universalNumber where char=0 and \n"); 
     fppp(fp,"          poly and poly2 belong to a same ring.\n");
@@ -232,7 +233,23 @@ void Kusage2(fp,s)
   }else if (strcmp(s,"homogenize") == 0) {
     fppp(fp,"<< f homogenize g >>\n");
     fppp(fp,"poly f,g;\n");
-    fppp(fp,"array of poly f,g;\n");
+    fppp(fp,"array of poly f,g;\n\n");
+	fppp(fp,"[(degreeShift) (value)] homogenize [shiftD shiftUV]\n");
+	fppp(fp,"[(degreeShift) (reset)] homogenize [null null]\n");
+	fppp(fp,"[(degreeShift) shiftD ] homogenize [shiftD shiftUV]\n");
+	fppp(fp,"[(degreeShift) [shiftD shiftUV]] homogenize [shiftD shiftUV]\n");
+	fppp(fp,"[(degreeShift) [ ]     fv] homogenize   hfv\n");
+	fppp(fp,"[(degreeShift) shiftD  fv] homogenize   hfv\n");
+	fppp(fp,"[(degreeShift) [shiftD shiftUV] fv] homogenize hfv\n");
+    fppp(fp,"shiftD : degree shift vector for (0,1)-h homogenization\n");
+    fppp(fp,"shiftUV : degree shift vector for (-1,1)-s homogenization (internal for ecart.)\n");
+    fppp(fp,"fv : polynomial or vector of polynomials.\n");
+    fppp(fp,"Example:  [(x) ring_of_differential_operators 0] define_ring\n");
+	fppp(fp,"   [(degreeShift) [[1 0] [0 1]] [(x+1). (Dx+1).]] homogenize ::\n");
+	fppp(fp,"   [(degreeShift) (value)] homogenize ::\n");
+	fppp(fp,"Note. min of ord (-1,1)[0,1] is min {-1,1, 1+1,1+0} = -1 =m \n");
+    fppp(fp,"      Degree of H is b-a+v(i)-m where v=[0,1]\n");
+    fppp(fp,"DegreeShift is automatically reset when set_up_ring is called.\n");
   }else if (strcmp(s,"idiv") == 0) {
     fppp(fp,"<< a b idiv a/b >>\n");
     fppp(fp,"int a,b,a/b;\n");
@@ -257,7 +274,10 @@ void Kusage2(fp,s)
     fppp(fp,"Example: (x+1). [0 1 1 1] init ::    cf. weightv \n\n");
     fppp(fp,"<< fv weight_vector init h >>\n");
     fppp(fp,"<< fv [weight_vector shift_vector] init h >>\n");
+    fppp(fp,"<< fv init h >> or << hv [ ] init h >>\n");
     fppp(fp,"fv is a polynomial or a vector of polynomials.\n");
+    fppp(fp,"h is the initial term with respect to the weight vector and the shift vector\n");
+    fppp(fp,"if they are given.\n");
     fppp(fp,"Note: the last x variable is always assumed to be the vector index.\n");
     fppp(fp,"Example: [(x,y) ring_of_differential_operators 0] define_ring\n");
 	fppp(fp,"    [(x^2*Dx^2+2*x*Dx+x). (Dx+x).] [[(Dx) 1 (x) -1] weightv [0 -1]] init ::\n");