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Diff for /OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw between version 1.1 and 1.4

-version 1.1, 2005/04/13 23:50:17
+version 1.4, 2012/06/11 05:23:52
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- /*$OpenXM$ */
+ /*$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 18
 Line 18
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  $B7W;;Be?t4v2?$N$$$m$$$m$JITJQNL$N7W;;$,HyJ,:nMQAG$N7W;;$K5"Ce$9$k(B.
  @code{sm1} $B$K$D$$$F$NJ8=q$O(B @code{OpenXM/doc/kan96xx} $B$K$"$k(B.
+ $B$J$*(B, sm1 server windows $BHG$O%P%$%J%jG[I[$7$F$$$J$$(B.
+ cygwin $B4D6-$G%=!<%9%3!<%I$+$i%3%s%Q%$%k$7(B, OpenXM/misc/packages/Windows
+ $B$K=>$$JQ99$r2C$($k$H(B sm1 $B%5!<%P$O(Bwindows $B$G$bF0:n$9$k(B.
  $B$H$3$KCG$j$,$J$$$+$.$j$3$N@a$N$9$Y$F$N4X?t$O(B,
  $BM-M}?t78?t$N<0$rF~NO$H$7$F$&$1$D$1$J$$(B.
  $B$9$Y$F$NB?9`<0$N78?t$O@0?t$G$J$$$H$$$1$J$$(B.
-Line 49  to constructions in the ring of differential operators
+Line 53  to constructions in the ring of differential operators
 Line 49  to constructions in the ring of differential operators
 Line 53  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
-Line 102  Grobner Deformations of Hypergeometric Differential Eq
+Line 110  Grobner Deformations of Hypergeometric Differential Eq
 Line 102  Grobner Deformations of Hypergeometric Differential Eq
 Line 110  Grobner Deformations of Hypergeometric Differential Eq
  * sm1.mul::
  * sm1.distraction::
  * sm1.gkz::
+ * sm1.mgkz::
  * sm1.appell1::
  * sm1.appell4::
  * sm1.rank::
-Line 1657  List
+Line 1666  List
 Line 1657  List
 Line 1666  List
  */
+ /*&en
+ @node sm1.mgkz,,, SM1 Functions
+ @subsection @code{sm1.mgkz}
+ @findex sm1.mgkz
+ @table @t
+ @item sm1.mgkz([@var{A},@var{W},@var{B}]|proc=@var{p})
+ ::  Returns the modified GKZ system (A-hypergeometric system) associated to the matrix
+ @var{A} and the weight @var{w} with the parameter vector @var{B}.
+ @end table
+ @table @var
+ @item return
+ List
+ @item p
+ Number
+ @item A, W, B
+ List
+ @end table
+ @itemize @bullet
+ @item Returns the modified GKZ hypergeometric system
+ (A-hypergeometric system) associated to the matrix
+ @item http://arxiv.org/abs/0707.0043
+ @end itemize
+ */
+ /*&ja
+ @node sm1.mgkz,,, SM1 Functions
+ @subsection @code{sm1.mgkz}
+ @findex sm1.mgkz
+ @table @t
+ @item sm1.mgkz([@var{A},@var{W},@var{B}]|proc=@var{p})
+ ::  $B9TNs(B @var{A}, weight @var{W} $B$H%Q%i%a!<%?(B @var{B} $B$KIU?o$7$?(B modified GKZ $B7O(B (A-hypergeometric system) $B$r$b$I$9(B.
+ @end table
+ @table @var
+ @item return
+ $B%j%9%H(B
+ @item p
+ $B?t(B
+ @item A, W, B
+ $B%j%9%H(B
+ @end table
+ @itemize @bullet
+ @item  $B9TNs(B @var{A}, weight vector @var{W} $B$H%Q%i%a!<%?(B @var{B} $B$KIU?o$7$?(B modified GKZ $B7O(B (A-hypergeometric system) $B$r$b$I$9(B.
+ @item http://arxiv.org/abs/0707.0043
+ @end itemize
+ */
+ /*&C
+ @example
+ [280] sm1.mgkz([ [[1,2,3]], [1,2,1], [a/2]]);
+ [[6*x3*dx3+4*x2*dx2+2*x1*dx1-a,-x4*dx4+x3*dx3+2*x2*dx2+x1*dx1,
+   -dx2+dx1^2,-x4^2*dx3+dx1*dx2],[x1,x2,x3,x4]]
+ Modified A-hypergeometric system for
+ A=(1,2,3), w=(1,2,1), beta=(a/2).
+ @end example
+ */
  /*&en
  @node sm1.appell1,,, SM1 Functions
  @subsection @code{sm1.appell1}
-Line 2002  not bihomogeneous.
+Line 2075  not bihomogeneous.
 Line 2002  not bihomogeneous.
 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 2046  Algorithm:
+Line 2124  Algorithm:
 Line 2046  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

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