=================================================================== RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/Attic/dsolv.oxweave,v retrieving revision 1.1 retrieving revision 1.6 diff -u -p -r1.1 -r1.6 --- OpenXM/src/asir-contrib/packages/doc/Attic/dsolv.oxweave 2000/02/06 06:39:48 1.1 +++ OpenXM/src/asir-contrib/packages/doc/Attic/dsolv.oxweave 2004/03/05 15:30:50 1.6 @@ -1,17 +1,25 @@ -/* $OpenXM$ */ +/* $OpenXM: OpenXM/src/asir-contrib/packages/doc/dsolv.oxweave,v 1.5 2003/07/27 13:18:45 takayama Exp $ */ /* dsolv.oxweave */ -/*&eg-texi +/*&C-texi @node DSOLV Functions,,, Top +*/ +/*&en + @chapter DSOLV Functions This section is a collection of functions to solve regular holonomic systems in terms of series. Algorithms are explained in the book [SST]. You can load this package by the command -@code{load("dsolv");} +@code{load("dsolv")$} This package requires @code{Diff} and @code{dmodule}. +To use the functions of the package @code{dsolv} in OpenXM/Risa/Asir, +executing the command @code{load("dsolv")$} +is necessary at first. + + This package uses @code{ox_sm1}, so the variables you can use is as same as those you can use in the package @code{sm1}. @@ -19,8 +27,7 @@ is as same as those you can use in the package @code{s */ -/*&jp-texi -@node DSOLV 函数,,, Top +/*&ja @chapter DSOLV 函数 @@ -29,19 +36,30 @@ is as same as those you can use in the package @code{s アルゴリズムについては [SST] に説明がある. このパッケージは次のコマンド @code{load("dsolv");} でロードできる. -このパッケージは @code{Diff} および @code{dmodule} を使用する. +このパッケージは @code{Diff} および @code{Dmodule} を使用する. +OpenXM/Risa/Asir での利用にあたっては, +@example +load("dsolv");$ +@end example +が始めに必要. + このパッケージは @code{ox_sm1} を利用している. したがって使用できる変数は @code{sm1} パッケージと同様の変数しかつかえない. -@section Functions +@section 函数一覧 */ -/*&eg-texi +/*&C-texi @menu * dsolv_dual:: +* dsolv_starting_term:: @end menu +*/ + + +/*&en @node dsolv_dual,,, DSOLV Functions @subsection @code{dsolv_dual} @findex dsolv_dual @@ -64,18 +82,20 @@ with variables @var{v}. generated by @var{v}. If it is not primary to the maximal ideal, then this function falls into 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), ..., then these polynomials in log are solutions of the system of differential -equations @code{map(subst,@var{f},x,x*dx, y,y*dy, ...)}. -@end itemize +equations @var{f}@code{_(x->x*dx, y->y*dy, ...)}. + */ -/*&jp-texi -@menu -* dsolv_dual:: -@end menu -@node dsolv_dual,,, DSOLV 函数 +/*&ja +@node dsolv_dual,,, DSOLV Functions @subsection @code{dsolv_dual} @findex dsolv_dual @table @t @@ -96,12 +116,16 @@ equations @code{map(subst,@var{f},x,x*dx, y,y*dy, ...) @item @var{f} で生成されるイデアルは, @var{v} で生成される極大イデアルに 対して, primary でないといけない. primary でない場合, この函数は無限ループにおちいる. -@item この函数は本 [SST] の Algorithm 2.3.14 の実装である. +@end itemize + +@noindent +Algorithm: +この函数は本 [SST] の Algorithm 2.3.14 の実装である. 出力中の変数 x, y, ... をそれぞれ log(x), log(y), ..., でおきかえると, これらの log 多項式は, -@code{map(subst,@var{f},x,x*dx, y,y*dy, ...)} で生成される微分方程式系 +@var{f}@code{_(x->x*dx, y->y*dy, ...)} +で生成される微分方程式系 の解となっている. -@end itemize */ /*&C-texi @@ -130,11 +154,8 @@ primary でない場合, この函数は無限ループにお��������⑮�繚∑纔���緕���㍉辣銛�⑩�糂闌�齡癇�鈑熹纈躡�㍉緕�辣銛��川閼�糂闌�齡癇�鈑熹纈蹶��柘鰐�弐釿�闔��栴�黼笏蜿�雪閼纛糂闌�齡癇�鈑熹纈逹��蝉蜴粤�糂闌�齡癇�鈑熹纈�誓�⑰況���幻��誓��緕��蜩�胚釿�闔�阨���辣齠瘍纉�糒鱸鈑���竢逅���������⑮�褓∑纔���裃���㍉辣銛�⑩�糂闌�齡癇�鈑熹纈躡�㍉緕�辣銛�㍉鈿粤�糂闌�齡癇�鈑熹纈蹶��柘鰐�函数 +@node dsolv_starting_term,,, DSOLV Functions @subsection @code{dsolv_starting_term} @findex dsolv_starting_term @table @t @@ -200,9 +218,15 @@ Staring terms を計算する. ここで, @var{v} この函数は計算の途中にいろいろとメッセージを出力する. @end itemize + */ /*&C-texi + +@noindent +Algorithm: Saito, Sturmfels, Takayama, Grobner Deformations of Hypergeometric +Differential Equations ([SST]), Chapter 2. + @example [1076] F = sm1_gkz( [ [[1,1,1,1,1],[1,1,0,-1,0],[0,1,1,-1,0]], [1,0,0]]);