===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v
retrieving revision 1.2
retrieving revision 1.4
diff -u -p -r1.2 -r1.4
--- OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw	2008/06/04 01:46:52	1.2
+++ 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 1.1 2005/04/13 23:50:17 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   
@@ -18,6 +18,10 @@
 計算代数幾何のいろいろな不変量の計算が微分作用素の計算に帰着する.
 @code{sm1} についての文書は @code{OpenXM/doc/kan96xx} にある.
 
+なお, sm1 server windows 版はバイナリ配布していない.
+cygwin 環境でソースコードからコンパイルし, OpenXM/misc/packages/Windows
+に従い変更を加えると sm1 サーバはwindows でも動作する.
+
 とこに断りがないかぎりこの節のすべての関数は,
 有理数係数の式を入力としてうけつけない.
 すべての多項式の係数は整数でないといけない.
@@ -49,6 +53,10 @@ to constructions in the ring of differential operators
 Documents on @code{sm1} are in
 the directory @code{OpenXM/doc/kan96xx}.
 
+The sm1 server for windows is not distributed in the binary form. 
+If you need to run it, compile it under the cygwin environment
+following the Makefile in OpenXM/misc/packages/Windows.
+
 All the coefficients of input polynomials should be
 integers for most functions in this section.
 Other functions accept rational numbers as inputs
@@ -2067,8 +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.
 
 */
 
@@ -2111,8 +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