===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/slope.sm1,v
retrieving revision 1.1
retrieving revision 1.4
diff -u -p -r1.1 -r1.4
--- OpenXM/src/kan96xx/Doc/slope.sm1	2000/11/01 01:57:55	1.1
+++ OpenXM/src/kan96xx/Doc/slope.sm1	2012/06/11 05:23:52	1.4
@@ -1,7 +1,12 @@
-% $OpenXM$
-(cohom.sm1) run (oxasir.sm1) run
+% $OpenXM: OpenXM/src/kan96xx/Doc/slope.sm1,v 1.3 2005/10/20 11:22:27 takayama Exp $
+(oxasir.sm1.loaded) boundp not {
+   [(parse) (oxasir.sm1)  pushfile] extension
+} { } ifelse
+(cohom.sm1.loaded) boundp not {
+   [(parse) (cohom.sm1)  pushfile] extension
+} { } ifelse
 $slope.sm1, computing the slopes of a D-ideal:  June 15, 2000$ message
-$                            (C) F.Castro-Jimenez, N.Takayama$ message
+$                            (C) N.Takayama, F.Castro-Jimenez$ message
 $Imported commands:  slope $ message
 /slope.verbose 1 def
 /gb.warning 0 def
@@ -577,8 +582,14 @@ $Imported commands:  slope $ message
  (When slope.geometric is one, it outputs the geometric slopes.)
  (As to the 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.)
+ $In other words, when pF+qV is the gap, -s'=q/p is returned.$
+ $Note that s=1-1/s' is called the slope in recent literatures. Solutions belongs to O(s).$
+ $The number s satisfies 1<= s.$  
+ $We have r=s-1=-1/s', and kappa=1/r=-s',$
+ $which is used 1/Gamma(1+m*r) factor and exp(-tau^kappa)$
+ $in the Borel and Laplace transformations respectively.$
  $Example 1: [ [(x^4 Dx + 3)] (x) [0 1] [-1 1]] slope :: $
  $          The solution is exp(x^(-3)). $
  $Example 2: [ [(x^3 Dx^2 + (x + x^2) Dx + 1)] [(x)] $
@@ -748,3 +759,4 @@ $Imported commands:  slope $ message
 
 } def
 
+/slope.sm1.loaded 1 def
\ No newline at end of file