===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v
retrieving revision 1.3
retrieving revision 1.4
diff -u -p -r1.3 -r1.4
--- OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw	2010/02/06 00:50:32	1.3
+++ OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw	2012/06/11 05:23:52	1.4
@@ -1,4 +1,4 @@
-/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.2 2008/06/04 01:46:52 takayama Exp $ */
+/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.3 2010/02/06 00:50:32 takayama Exp $ */
 
 /*&C
 @c DO NOT EDIT THIS FILE   
@@ -2075,8 +2075,13 @@ not bihomogeneous.
 Algorithm:
 see "A.Assi, F.J.Castro-Jimenez and J.M.Granger,
 How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
-Note that the signs of the slopes are negative, but the absolute values
+Note that the signs of the slopes s' are negative, but the absolute values -s'
 of the slopes are returned.
+In other words, when pF+qV is the gap, -s'=q/p is returned.
+Note that s=1-1/s' is called the slope in recent literatures. Solutions belongs to O(s).
+The number s satisfies 1<= s.  
+We have r=s-1=-1/s', and kappa=1/r=-s', which is used 1/Gamma(1+m*r) factor and exp(-tau^kappa)
+in the Borel and Laplace transformations respectively.
 
 */
 
@@ -2119,8 +2124,14 @@ Algorithm:
 "A.Assi, F.J.Castro-Jimenez and J.M.Granger,
 How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
 をみよ.
-Slope の本来の定義では, 符号が負となるが, このプログラムは,
-Slope の絶対値を戻す.
+Slope s' の本来の定義では, 符号が負となるが, このプログラムは,
+Slope の絶対値 -s' を戻す.
+つまり pF+qV がmicro特性多様体のgapであるとき, -s'=q/p を戻す.
+最近の文献では s=1-1/s' を slope と呼んでいる. 解は O(s) に属する.
+数 s は 1<= s を満す.  
+r=s-1=-1/s' および kappa=1/r=-s' である.
+これらの数はBorel and Laplace 変換においてそれぞれ 1/Gamma(1+m*r) factor,
+exp(-tau^kappa) 項として使われる.
 */
 
 /*&C