===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v
retrieving revision 1.4
retrieving revision 1.5
diff -u -p -r1.4 -r1.5
--- OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi	2021/03/29 05:08:01	1.4
+++ OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi	2021/10/27 06:13:24	1.5
@@ -1,4 +1,4 @@
-%% $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
@@ -134,6 +134,7 @@ 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})
@@ -225,6 +226,10 @@ 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 ---
@@ -697,6 +702,7 @@ 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
@@ -713,6 +719,7 @@ 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
@@ -725,6 +732,7 @@ 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
@@ -789,6 +797,12 @@ 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