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Diff for /OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi between version 1.4 and 1.5

version 1.4, 2021/03/29 05:08:01

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

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%% $OpenXM: OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v 1.3 2021/03/02 10:57:17 takayama Exp $

%% $OpenXM: OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v 1.4 2021/03/29 05:08:01 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 134 systems, Linear Algebra and its Applications (LAA), 42

@subsection @code{mt_gkz.pfaff_eq}

@comment --- 索引用キーワード

@findex mt_gkz.pfaff_eq

@findex mt_gkz.use_hilbert_driven

@table @t

@item mt_gkz.pfaff_eq(@var{A},@var{Beta},@var{Ap},@var{Rvec},@var{DirX})

Line 225 Option @var{cg}. A constant matrix given by this optio

Line 226 Option @var{cg}. A constant matrix given by this optio

for the Gauge transformation of the Pfaffian system.

In other words, the basis of cocycles specified by @var{Rvec}

is transformed by the constant matrix given by this option.

@item

By mt_gkz.use_hilbert_driven(Rank), the rank of the GKZ system is assumed to be

Rank. It makes the computation of Groebner basis by yang.rr faster.

This option is disabled by mt_gkz.use_hilbert_driven(0);

@end itemize

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

Line 697 Example:

Line 702 Example:

* mt_gkz.get_check_fvec::

* mt_gkz.get_bf_step_up::

* mt_gkz.mytoric_ideal::

* mt_gkz.cbase_by_euler::

@end menu

@node some utility functions,,, utilities

Line 713 Example:

Line 719 Example:

@node mt_gkz.get_check_fvec,,, some utility functions

@node mt_gkz.get_bf_step_up,,, some utility functions

@node mt_gkz.mytoric_ideal,,, some utility functions

@node mt_gkz.cbase_by_euler,,, some utility functions

@findex mt_gkz.reduce_by_toric

@findex mt_gkz.tk_base_equal

Line 725 Example:

Line 732 Example:

@findex mt_gkz.get_check_fvec

@findex mt_gkz.get_bf_step_up

@findex mt_gkz.mytoric_ideal

@findex mt_gkz.cbase_by_euler

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

We only show examples on these functions. As for details, please see

Line 789 the source code.

Line 797 the source code.

[3192] mt_gkz.mytoric_ideal(0 | use_4ti2=0);

// A slower method is used to obtain a generator set of the toric ideal

// defined by the matrix A. 4ti2 is not needed. Default.

[3193] mt_gkz.cbase_by_euler(A=[[1,1,1,1],[0,1,3,4]]);

// Cohomology basis of the GKZ system defined by A for generic beta.

// Basis is given by a set of Euler operators.

// It is an implementation of the algorithm in http://dx.doi.org/10.1016/j.aim.2016.10.021

// beta is set by random numbers. Option: no_prob=1

@end example

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