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Diff for /OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi between version 1.7 and 1.8

version 1.7, 2022/01/13 02:38:00 version 1.8, 2022/02/13 05:59:56
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 %% $OpenXM: OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v 1.6 2021/12/11 11:40:45 takayama Exp $  %% $OpenXM: OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v 1.7 2022/01/13 02:38:00 takayama Exp $
 %% xetex mt_gkz-en.texi   (.texi までつける. )  %% xetex mt_gkz-en.texi   (.texi までつける. )
 %% @math{tex形式の数式}  %% @math{tex形式の数式}
 %% 参考: http://www.fan.gr.jp/~ring/doc/texinfo/texinfo-ja_14.html#SEC183  %% 参考: http://www.fan.gr.jp/~ring/doc/texinfo/texinfo-ja_14.html#SEC183
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 @title GKZ hypergeometric system  @title GKZ hypergeometric system
 @subtitle Pfaffian system (Pfaff equation), contiguity relations, cohomology intersection  @subtitle Pfaffian system (Pfaff equation), contiguity relations, cohomology intersection
 @subtitle Version 1.0  @subtitle Version 1.0
 @subtitle December 21, 2021  @subtitle February 13, 2022
   
 @author  by S-J. Matsubara-Heo, N.Takayama  @author  by S-J. Matsubara-Heo, N.Takayama
 @page  @page
Line 125  systems, Linear Algebra and its Applications (LAA), 42
Line 125  systems, Linear Algebra and its Applications (LAA), 42
 * mt_gkz.rvec_to_fvec::  * mt_gkz.rvec_to_fvec::
 * mt_gkz.fvec_to_conn_mat::  * mt_gkz.fvec_to_conn_mat::
 * mt_gkz.contiguity::  * mt_gkz.contiguity::
   * mt_gkz.contiguity_by_fvec::
 @end menu  @end menu
   
 @node Pfaff equation for given cocycles,,, Pfaff equation  @node Pfaff equation for given cocycles,,, Pfaff equation
Line 569  obtains connection matrices.
Line 570  obtains connection matrices.
 @comment --- contiguity  @comment --- contiguity
 @comment --- section 名を正確に ---  @comment --- section 名を正確に ---
 @node mt_gkz.contiguity,,, Pfaff equation for given cocycles  @node mt_gkz.contiguity,,, Pfaff equation for given cocycles
 @subsection @code{mt_gkz.contiguity}  @node mt_gkz.contiguity_by_fvec,,, Pfaff equation for given cocycles
   @subsection @code{mt_gkz.contiguity}, @code{mt_gkz.contiguity_by_fvec}
 @comment --- 索引用キーワード  @comment --- 索引用キーワード
 @findex mt_gkz.contiguity  @findex mt_gkz.contiguity
   @findex mt_gkz.contiguity_by_fvec
   
 @table @t  @table @t
 @item mt_gkz.contiguity(@var{A},@var{Beta},@var{Ap},@var{Rvec1},@var{Rvec2})  @item mt_gkz.contiguity(@var{A},@var{Beta},@var{Ap},@var{Rvec1},@var{Rvec2})
 :: It returns the coefficient matrix P that satisfies  :: It returns the coefficient matrix P that satisfies
 @var{Rvec1} = P @var{Rvec2}.  @var{Rvec1} = P @var{Rvec2}.
   @item mt_gkz.contiguity_by_fvec(@var{A},@var{Beta},@var{Ap},@var{Fvec1},@var{Fvec2})
   :: It returns the coefficient matrix P that satisfies
   @var{Fvec1} = P @var{Fvec2}.
 @end table  @end table
   
 @comment --- 引数の簡単な説明 ---  @comment --- 引数の簡単な説明 ---
 @table @var  @table @var
 @item return  @item return
 The coefficient matrix P that satisfies @var{Rvec1} = P @var{Rvec2}.  The coefficient matrix P that satisfies @var{Rvec1} = P @var{Rvec2}
   or @var{Fvec1}=P @var{Fvec2}
 @item A Beta Ap Rvec1 Rvec2  @item A Beta Ap Rvec1 Rvec2
 Same with @ref{mt_gkz.pfaff_eq}.  Same with @ref{mt_gkz.pfaff_eq}.
 @end table  @end table
Line 605  Example:
Line 612  Example:
              Ap = [[1,1,0,0],[0,0,1,1],[0,0,0,0]],               Ap = [[1,1,0,0],[0,0,1,1],[0,0,0,0]],
              Rvec1 = [[1,0,0,0],[0,0,1,0]],               Rvec1 = [[1,0,0,0],[0,0,1,0]],
              Rvec2 = [[0,0,1,0],[1,0,0,0]]);               Rvec2 = [[0,0,1,0],[1,0,0,0]]);
   
   [3366] Fvec411=mt_gkz.rvec_to_fvec(Rvec411=[[1,1,0]],
                       A=[[1,1,1],[1,0,1],[0,1,1]],
                       Ap=[[1,1,1],[0,0,0],[0,0,0]],
                       Beta=[eps,-eps*del,-eps*del])$
   Fvec411d=[mt_gkz.dmul(dx1,Fvec411[0],[x1,x2,x3])];
    [(dx1^2*dx2)/(eps^2-eps)]
   [3367] mt_gkz.contiguity_by_fvec(A,Beta,Ap,Fvec411d,Fvec411);
    1 .ooo
   [ ((del+1)*eps-1)/(x1) ]
 @end example  @end example
   
 @comment --- 参照(リンク)を書く ---  @comment --- 参照(リンク)を書く ---
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