OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi - diff

Return to mt_gkz-en.texi CVS log

Up to [local] / OpenXM / src / asir-contrib / packages / doc / mt_gkz

Diff for /OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi between version 1.5 and 1.6

version 1.5, 2021/10/27 06:13:24

version 1.6, 2021/12/11 11:40:45

Line 1

%% $OpenXM: OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v 1.4 2021/03/29 05:08:01 takayama Exp $

%% $OpenXM: OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v 1.5 2021/10/27 06:13:24 takayama Exp $

%% xetex mt_gkz-en.texi (.texi までつける. )

%% @math{tex形式の数式}

%% 参考: http://www.fan.gr.jp/~ring/doc/texinfo/texinfo-ja_14.html#SEC183

Line 38

@title GKZ hypergeometric system

@subtitle Pfaffian system (Pfaff equation), contiguity relations, cohomology intersection

@subtitle Version 1.0

@subtitle January 20, 2021

@subtitle December 21, 2021

@author by S-J. Matsubara-Heo, N.Takayama

@page

Line 123 systems, Linear Algebra and its Applications (LAA), 42

* mt_gkz.ff1::

* mt_gkz.ff2::

* mt_gkz.rvec_to_fvec::

* mt_gkz.fvec_to_conn_mat::

* mt_gkz.contiguity::

@end menu

@node Pfaff equation for given cocycles,,, Pfaff equation

Line 152 the parameter vector of the GKZ system.

Line 154 the parameter vector of the GKZ system.

@item Ap

See [MT2020].

@item Rvec

It is used to specify a basis of cocycles. See [MT2020]

It is used to specify a basis of cocycles as explained below. See also [MT2020].

@item DirX

a list of dxi's.

@end table

Line 169 the set of the cocycles standing for Av_1, Av_2, ...,

Line 171 the set of the cocycles standing for Av_1, Av_2, ...,

(see [MT2020])

is supposed

to be the basis to construct the Pfaffian system.

The exponents @math{(q_\ell, q)} of the integral representation

@math{\int \prod h_\ell^{-q_\ell} x^q {{dx} \over {x}}}

is shifted by Av_i@math{=:A_{v_i}} as @math{(q_\ell,q)+A_{v_i}}.

Let a_1, a_2, ..., a_n be the column vectors of the matrix A

and v be a column vector (x_1, x_2, ..., x_n)^T.

Av is defined as a_1 x_1 + a_2 x_2 + ... + a_n x_n.

Line 558 obtains connection matrices.

Line 563 obtains connection matrices.

@table @t

@item Refer to

@ref{mt_gkz.pfaff_eq}

@end table

@comment おわり.

@comment --- contiguity

@comment --- section 名を正確に ---

@node mt_gkz.contiguity,,, Pfaff equation for given cocycles

@subsection @code{mt_gkz.contiguity}

@comment --- 索引用キーワード

@findex mt_gkz.contiguity

@table @t

@item mt_gkz.contiguity(@var{A},@var{Beta},@var{Ap},@var{Rvec1},@var{Rvec2})

:: It returns the coefficient matrix P that satisfies

@var{Rvec1} = P @var{Rvec2}.

@end table

@comment --- 引数の簡単な説明 ---

@table @var

@item return

The coefficient matrix P that satisfies @var{Rvec1} = P @var{Rvec2}.

@item A Beta Ap Rvec1 Rvec2

Same with @ref{mt_gkz.pfaff_eq}.

@end table

@comment --- ここで関数の詳しい説明 ---

@comment --- @itemize〜@end itemize は箇条書き ---

@comment --- @bullet は黒点付き ---

@itemize @bullet

@item

It returns the contiguity relation between

@var{Rvec1} and @var{Rvec2}

@end itemize

@comment --- @example〜@end example は実行例の表示 ---

Example:

@example

[1883] import("mt_gkz.rr");

[3200] PP=mt_gkz.contiguity(A=[[1,1,0,0],[0,0,1,1],[0,1,0,1]],

Beta=[-g1,-g2,-c],

Ap = [[1,1,0,0],[0,0,1,1],[0,0,0,0]],

Rvec1 = [[1,0,0,0],[0,0,1,0]],

Rvec2 = [[0,0,1,0],[1,0,0,0]]);

@end example

@comment --- 参照(リンク)を書く ---

@table @t

@item Refer to

@ref{mt_gkz.pfaff_eq}

@ref{mt_gkz.fvec_to_conn_mat}

@end table

@comment おわり.

FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>