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version 1.1, 2000/02/06 06:39:48 version 1.4, 2002/08/23 08:16:12
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 /* $OpenXM$ */  /* $OpenXM: OpenXM/src/asir-contrib/packages/doc/dsolv.oxweave,v 1.3 2002/08/08 08:56:32 takayama Exp $ */
 /* dsolv.oxweave */  /* dsolv.oxweave */
 /*&eg-texi  /*&C-texi
 @node DSOLV Functions,,, Top  @node DSOLV Functions,,, Top
   */
   
   /*&eg-texi
   
 @chapter DSOLV Functions  @chapter DSOLV Functions
   
 This section is a collection of functions to solve regular holonomic  This section is a collection of functions to solve regular holonomic
 systems in terms of series.  systems in terms of series.
 Algorithms are explained in the book [SST].  Algorithms are explained in the book [SST].
 You can load this package by the command  You can load this package by the command
 @code{load("dsolv");}  @code{load("dsolv")$}
 This package requires @code{Diff} and @code{dmodule}.  This package requires @code{Diff} and @code{dmodule}.
   
   To use the functions of the package @code{dsolv} in OpenXM/Risa/Asir,
   executing the command @code{load("dsolv")$}
   is necessary at first.
   
   
 This package uses @code{ox_sm1}, so the variables you can use  This package uses @code{ox_sm1}, so the variables you can use
 is as same as those you can use in the package @code{sm1}.  is as same as those you can use in the package @code{sm1}.
   
Line 20  is as same as those you can use in the package @code{s
Line 28  is as same as those you can use in the package @code{s
 */  */
   
 /*&jp-texi  /*&jp-texi
 @node DSOLV $BH!?t(B,,, Top  
   
 @chapter DSOLV $BH!?t(B  @chapter DSOLV $BH!?t(B
   
Line 29  is as same as those you can use in the package @code{s
Line 36  is as same as those you can use in the package @code{s
 $B%"%k%4%j%:%`$K$D$$$F$O(B [SST] $B$K@bL@$,$"$k(B.  $B%"%k%4%j%:%`$K$D$$$F$O(B [SST] $B$K@bL@$,$"$k(B.
 $B$3$N%Q%C%1!<%8$O<!$N%3%^%s%I(B @code{load("dsolv");}  $B$3$N%Q%C%1!<%8$O<!$N%3%^%s%I(B @code{load("dsolv");}
 $B$G%m!<%I$G$-$k(B.  $B$G%m!<%I$G$-$k(B.
 $B$3$N%Q%C%1!<%8$O(B @code{Diff} $B$*$h$S(B @code{dmodule} $B$r;HMQ$9$k(B.  $B$3$N%Q%C%1!<%8$O(B @code{Diff} $B$*$h$S(B @code{Dmodule} $B$r;HMQ$9$k(B.
   
   OpenXM/Risa/Asir $B$G$NMxMQ$K$"$?$C$F$O(B,
   @example
   load("dsolv");$
   @end example
   $B$,;O$a$KI,MW(B.
   
 $B$3$N%Q%C%1!<%8$O(B @code{ox_sm1} $B$rMxMQ$7$F$$$k(B.  $B$3$N%Q%C%1!<%8$O(B @code{ox_sm1} $B$rMxMQ$7$F$$$k(B.
 $B$7$?$,$C$F;HMQ$G$-$kJQ?t$O(B @code{sm1} $B%Q%C%1!<%8$HF1MM$NJQ?t$7$+$D$+$($J$$(B.  $B$7$?$,$C$F;HMQ$G$-$kJQ?t$O(B @code{sm1} $B%Q%C%1!<%8$HF1MM$NJQ?t$7$+$D$+$($J$$(B.
   
 @section Functions  @section $BH!?t0lMw(B
   
 */  */
   
 /*&eg-texi  /*&c-texi
 @menu  @menu
 * dsolv_dual::  * dsolv_dual::
   * dsolv_starting_term::
 @end menu  @end menu
   */
   
   
   /*&eg-texi
 @node dsolv_dual,,, DSOLV Functions  @node dsolv_dual,,, DSOLV Functions
 @subsection @code{dsolv_dual}  @subsection @code{dsolv_dual}
 @findex dsolv_dual  @findex dsolv_dual
Line 64  with variables @var{v}.
Line 82  with variables @var{v}.
 generated by @var{v}.  generated by @var{v}.
 If it is not primary to the maximal ideal, then this function falls into  If it is not primary to the maximal ideal, then this function falls into
 an infinite loop.  an infinite loop.
 @item This is an implementation of Algorithm 2.3.14 of the book [SST].  @end itemize
   
   
   @noindent
   Algorithm:
   This is an implementation of Algorithm 2.3.14 of the book [SST].
 If we replace variables x, y, ... in the output by log(x), log(y), ...,  If we replace variables x, y, ... in the output by log(x), log(y), ...,
 then these polynomials in log are solutions of the system of differential  then these polynomials in log are solutions of the system of differential
 equations @code{map(subst,@var{f},x,x*dx, y,y*dy, ...)}.  equations @var{f}@code{_(x->x*dx, y->y*dy, ...)}.
 @end itemize  
 */  */
   
 /*&jp-texi  /*&jp-texi
 @menu  @node dsolv_dual,,, DSOLV Functions
 * dsolv_dual::  
 @end menu  
 @node dsolv_dual,,, DSOLV $BH!?t(B  
 @subsection @code{dsolv_dual}  @subsection @code{dsolv_dual}
 @findex dsolv_dual  @findex dsolv_dual
 @table @t  @table @t
Line 96  equations @code{map(subst,@var{f},x,x*dx, y,y*dy, ...)
Line 116  equations @code{map(subst,@var{f},x,x*dx, y,y*dy, ...)
 @item @var{f} $B$G@8@.$5$l$k%$%G%"%k$O(B, @var{v} $B$G@8@.$5$l$k6KBg%$%G%"%k$K(B  @item @var{f} $B$G@8@.$5$l$k%$%G%"%k$O(B, @var{v} $B$G@8@.$5$l$k6KBg%$%G%"%k$K(B
 $BBP$7$F(B, primary $B$G$J$$$H$$$1$J$$(B.  $BBP$7$F(B, primary $B$G$J$$$H$$$1$J$$(B.
 primary $B$G$J$$>l9g(B, $B$3$NH!?t$OL58B%k!<%W$K$*$A$$$k(B.  primary $B$G$J$$>l9g(B, $B$3$NH!?t$OL58B%k!<%W$K$*$A$$$k(B.
 @item $B$3$NH!?t$OK\(B [SST] $B$N(B Algorithm 2.3.14  $B$N<BAu$G$"$k(B.  @end itemize
   
   @noindent
   Algorithm:
   $B$3$NH!?t$OK\(B [SST] $B$N(B Algorithm 2.3.14  $B$N<BAu$G$"$k(B.
 $B=PNOCf$NJQ?t(B x, y, ... $B$r$=$l$>$l(B log(x), log(y), ..., $B$G$*$-$+$($k$H(B,  $B=PNOCf$NJQ?t(B x, y, ... $B$r$=$l$>$l(B log(x), log(y), ..., $B$G$*$-$+$($k$H(B,
 $B$3$l$i$N(B log $BB?9`<0$O(B,  $B$3$l$i$N(B log $BB?9`<0$O(B,
 @code{map(subst,@var{f},x,x*dx, y,y*dy, ...)} $B$G@8@.$5$l$kHyJ,J}Dx<07O(B  @var{f}@code{_(x->x*dx, y->y*dy, ...)}
   $B$G@8@.$5$l$kHyJ,J}Dx<07O(B
 $B$N2r$H$J$C$F$$$k(B.  $B$N2r$H$J$C$F$$$k(B.
 @end itemize  
 */  */
   
 /*&C-texi  /*&C-texi
Line 132  primary $B$G$J$$>l9g(B, $B$3$NH!?t$OL58B%k!<%W$K$*$
Line 156  primary $B$G$J$$>l9g(B, $B$3$NH!?t$OL58B%k!<%W$K$*$
   
 /*&eg-texi  /*&eg-texi
   
 @menu  
 * dsolv_starting_term::  
 @end menu  
 @node dsolv_starting_term,,, DSOLV Functions  @node dsolv_starting_term,,, DSOLV Functions
 @subsection @code{dsolv_starting_term}  @subsection @code{dsolv_starting_term}
 @findex dsolv_starting_term  @findex dsolv_starting_term
Line 169  then this function outputs messages during the computa
Line 190  then this function outputs messages during the computa
   
 /*&jp-texi  /*&jp-texi
   
 @menu  @node dsolv_starting_term,,, DSOLV Functions
 * dsolv_starting_term::  
 @end menu  
 @node dsolv_starting_term,,, DSOLV $BH!?t(B  
 @subsection @code{dsolv_starting_term}  @subsection @code{dsolv_starting_term}
 @findex dsolv_starting_term  @findex dsolv_starting_term
 @table @t  @table @t
Line 200  Staring terms $B$r7W;;$9$k(B. $B$3$3$G(B, @var{v} 
Line 218  Staring terms $B$r7W;;$9$k(B. $B$3$3$G(B, @var{v} 
 $B$3$NH!?t$O7W;;$NESCf$K$$$m$$$m$H%a%C%;!<%8$r=PNO$9$k(B.  $B$3$NH!?t$O7W;;$NESCf$K$$$m$$$m$H%a%C%;!<%8$r=PNO$9$k(B.
 @end itemize  @end itemize
   
   
 */  */
   
 /*&C-texi  /*&C-texi
   
   @noindent
   Algorithm: Saito, Sturmfels, Takayama, Grobner Deformations of Hypergeometric
   Differential Equations ([SST]), Chapter 2.
   
   
 @example  @example
 [1076]   F = sm1_gkz( [ [[1,1,1,1,1],[1,1,0,-1,0],[0,1,1,-1,0]], [1,0,0]]);  [1076]   F = sm1_gkz( [ [[1,1,1,1,1],[1,1,0,-1,0],[0,1,1,-1,0]], [1,0,0]]);
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