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Diff for /OpenXM/src/kan96xx/Doc/slope.sm1 between version 1.2 and 1.4

version 1.2, 2001/06/18 03:12:21 version 1.4, 2012/06/11 05:23:52
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 % $OpenXM: OpenXM/src/kan96xx/Doc/slope.sm1,v 1.1 2000/11/01 01:57:55 takayama Exp $  % $OpenXM: OpenXM/src/kan96xx/Doc/slope.sm1,v 1.3 2005/10/20 11:22:27 takayama Exp $
 (oxasir.sm1.loaded) boundp not {  (oxasir.sm1.loaded) boundp not {
    [(parse) (oxasir.sm1)  pushfile] extension     [(parse) (oxasir.sm1)  pushfile] extension
 } { } ifelse  } { } ifelse
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    [(parse) (cohom.sm1)  pushfile] extension     [(parse) (cohom.sm1)  pushfile] extension
 } { } ifelse  } { } ifelse
 $slope.sm1, computing the slopes of a D-ideal:  June 15, 2000$ message  $slope.sm1, computing the slopes of a D-ideal:  June 15, 2000$ message
 $                            (C) F.Castro-Jimenez, N.Takayama$ message  $                            (C) N.Takayama, F.Castro-Jimenez$ message
 $Imported commands:  slope $ message  $Imported commands:  slope $ message
 /slope.verbose 1 def  /slope.verbose 1 def
 /gb.warning 0 def  /gb.warning 0 def
Line 582  $Imported commands:  slope $ message
Line 582  $Imported commands:  slope $ message
  (When slope.geometric is one, it outputs the geometric slopes.)   (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)   (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)   ( 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.)   (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 :: $   $Example 1: [ [(x^4 Dx + 3)] (x) [0 1] [-1 1]] slope :: $
  $          The solution is exp(x^(-3)). $   $          The solution is exp(x^(-3)). $
  $Example 2: [ [(x^3 Dx^2 + (x + x^2) Dx + 1)] [(x)] $   $Example 2: [ [(x^3 Dx^2 + (x + x^2) Dx + 1)] [(x)] $

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