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version 1.3, 2010/02/06 00:50:32

version 1.4, 2012/06/11 05:23:52

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/*$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

Line 2075 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.

Line 2119 Algorithm:

Line 2124 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"

$B$r$_$h(B.

Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B,

Slope s' $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B,

Slope $B$N@dBPCM$rLa$9(B.

Slope $B$N@dBPCM(B -s' $B$rLa$9(B.

$B$D$^$j(B pF+qV $B$,(Bmicro$BFC@-B?MMBN$N(Bgap$B$G$"$k$H$-(B, -s'=q/p $B$rLa$9(B.

$B:G6a$NJ88%$G$O(B s=1-1/s' $B$r(B slope $B$H8F$s$G$$$k(B. $B2r$O(B O(s) $B$KB0$9$k(B.

$B?t(B s $B$O(B 1<= s $B$rK~$9(B.

r=s-1=-1/s' $B$*$h$S(B kappa=1/r=-s' $B$G$"$k(B.

$B$3$l$i$N?t$O(BBorel and Laplace $BJQ49$K$*$$$F$=$l$>$l(B 1/Gamma(1+m*r) factor,

exp(-tau^kappa) $B9`$H$7$F;H$o$l$k(B.

/*&C