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 |
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@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 |
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Line 125 systems, Linear Algebra and its Applications (LAA), 42 |
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* 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:: |
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* mt_gkz.contiguity_by_fvec:: |
@end menu |
@end menu |
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@node Pfaff equation for given cocycles,,, Pfaff equation |
@node Pfaff equation for given cocycles,,, Pfaff equation |
Line 569 obtains connection matrices. |
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Line 570 obtains connection matrices. |
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@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 |
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@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 |
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@findex mt_gkz.contiguity_by_fvec |
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@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}. |
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@item mt_gkz.contiguity_by_fvec(@var{A},@var{Beta},@var{Ap},@var{Fvec1},@var{Fvec2}) |
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:: It returns the coefficient matrix P that satisfies |
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@var{Fvec1} = P @var{Fvec2}. |
@end table |
@end table |
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@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} |
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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 |
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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]]); |
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[3366] Fvec411=mt_gkz.rvec_to_fvec(Rvec411=[[1,1,0]], |
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A=[[1,1,1],[1,0,1],[0,1,1]], |
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Ap=[[1,1,1],[0,0,0],[0,0,0]], |
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Beta=[eps,-eps*del,-eps*del])$ |
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Fvec411d=[mt_gkz.dmul(dx1,Fvec411[0],[x1,x2,x3])]; |
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[(dx1^2*dx2)/(eps^2-eps)] |
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[3367] mt_gkz.contiguity_by_fvec(A,Beta,Ap,Fvec411d,Fvec411); |
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1 .ooo |
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[ ((del+1)*eps-1)/(x1) ] |
@end example |
@end example |
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@comment --- 参照(リンク)を書く --- |
@comment --- 参照(リンク)を書く --- |