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Diff for /OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi between version 1.1 and 1.2

version 1.1, 2021/01/20 03:05:29 version 1.2, 2021/01/20 08:17:54
Line 1 
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 %% $OpenXM$  %% $OpenXM: OpenXM/src/asir-contrib/packages/doc/mt_gkz/mt_gkz-en.texi,v 1.1 2021/01/20 03:05:29 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
Line 696  Example: 
Line 696  Example: 
 * mt_gkz.ord_xi::  * mt_gkz.ord_xi::
 * mt_gkz.get_check_fvec::  * mt_gkz.get_check_fvec::
 * mt_gkz.get_bf_step_up::  * mt_gkz.get_bf_step_up::
   * mt_gkz.mytoric_ideal::
 @end menu  @end menu
   
 @node some utility functions,,, utilities  @node some utility functions,,, utilities
Line 711  Example: 
Line 712  Example: 
 @node mt_gkz.ord_xi,,, some utility functions  @node mt_gkz.ord_xi,,, some utility functions
 @node mt_gkz.get_check_fvec,,, some utility functions  @node mt_gkz.get_check_fvec,,, some utility functions
 @node mt_gkz.get_bf_step_up,,, some utility functions  @node mt_gkz.get_bf_step_up,,, some utility functions
   @node mt_gkz.mytoric_ideal,,, some utility functions
   
 @findex mt_gkz.reduce_by_toric  @findex mt_gkz.reduce_by_toric
 @findex mt_gkz.tk_base_equal  @findex mt_gkz.tk_base_equal
Line 722  Example: 
Line 724  Example: 
 @findex mt_gkz.ord_xi  @findex mt_gkz.ord_xi
 @findex mt_gkz.get_check_fvec  @findex mt_gkz.get_check_fvec
 @findex mt_gkz.get_bf_step_up  @findex mt_gkz.get_bf_step_up
   @findex mt_gkz.mytoric_ideal
   
 @comment --- @example〜@end example は実行例の表示 ---  @comment --- @example〜@end example は実行例の表示 ---
 We only show examples on these functions. As for details, please see  We only show examples on these functions. As for details, please see
Line 780  the source code.
Line 783  the source code.
      -s_2^3+(3*s_1+1)*s_2^2-3*s_1*s_2 s_2^3-3*s_2^2+2*s_2 ],       -s_2^3+(3*s_1+1)*s_2^2-3*s_1*s_2 s_2^3-3*s_2^2+2*s_2 ],
   [ x3^3*dx4^2+ ---snip---    [ x3^3*dx4^2+ ---snip---
     3*x3^2*x4*dx4^2+ --- snip---]]      3*x3^2*x4*dx4^2+ --- snip---]]
   [3191] mt_gkz.mytoric_ideal(0 | use_4ti2=1);
   // 4ti2 is used to obtain a generator set of the toric ideal
   // defined by the matrix A
   [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.
 @end example  @end example
   
   
Line 847  the source code.
Line 856  the source code.
 * mt_gkz.secondary_eq::  * mt_gkz.secondary_eq::
 * mt_gkz.generate_maple_file_IC::  * mt_gkz.generate_maple_file_IC::
 * mt_gkz.generate_maple_file_MR::  * mt_gkz.generate_maple_file_MR::
 * mt_gkz.normalizing_constant::  * mt_gkz.principal_normalizing_constant::
 @end menu  @end menu
   
   
Line 873  the source code.
Line 882  the source code.
 @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
 a matrix which is equal to the Kronecker product of @var{A} and @var{B} (https://en.wikipedia.org/wiki/Kronecker_product).  a matrix which is equal to the Kronecker product of @var{A} and @var{B} (@uref{https://en.wikipedia.org/wiki/Kronecker_product}).
 @item A,B  @item A,B
 list  list
 @end table  @end table
Line 886  list
Line 895  list
 [[a,b],[c,d]]  [[a,b],[c,d]]
 [2645] B=[[e,f],[g,h]];  [2645] B=[[e,f],[g,h]];
 [[e,f],[g,h]]  [[e,f],[g,h]]
 [2646] kronecker_prd(A,B);  [2646] mt_gkz.kronecker_prd(A,B);
 [ e*a f*a e*b f*b ]  [ e*a f*a e*b f*b ]
 [ g*a h*a g*b h*b ]  [ g*a h*a g*b h*b ]
 [ e*c f*c e*d f*d ]  [ e*c f*c e*d f*d ]
Line 941  Example:
Line 950  Example:
 [2650] A=[[1,1,0,0],[0,0,1,1],[0,1,0,1]]$  [2650] A=[[1,1,0,0],[0,0,1,1],[0,1,0,1]]$
 [2651] Ap=[[1,1,0,0],[0,0,1,1],[0,0,0,0]]$  [2651] Ap=[[1,1,0,0],[0,0,1,1],[0,0,0,0]]$
 [2652] Xrule=[[x2,1],[x3,1]]$  [2652] Xrule=[[x2,1],[x3,1]]$
 [2653] P=secondary_eq(A,Beta,Ap,Rvec,DirX|xrule=Xrule)$  [2653] P=mt_gkz.secondary_eq(A,Beta,Ap,Rvec,DirX|xrule=Xrule)$
 --snip--  --snip--
 [2654] length(P);  [2654] length(P);
 2  2
Line 1013  Example: 
Line 1022  Example: 
 [2684] A=[[1,1,0,0],[0,0,1,1],[0,1,0,1]]$  [2684] A=[[1,1,0,0],[0,0,1,1],[0,1,0,1]]$
 [2685] Ap=[[1,1,0,0],[0,0,1,1],[0,0,0,0]]$  [2685] Ap=[[1,1,0,0],[0,0,1,1],[0,0,0,0]]$
 [2687] Xrule=[[x2,1],[x3,1]]$  [2687] Xrule=[[x2,1],[x3,1]]$
 [2688] generate_maple_file_IC(A,Beta,Ap,Rvec,DirX|xrule=Xrule,filename="Test.ml")$  [2688] mt_gkz.generate_maple_file_IC(A,Beta,Ap,Rvec,DirX|xrule=Xrule,filename="Test.ml")$
   
   
 //A file named Test.ml is automatically generated as follows:  //A file named Test.ml is automatically generated as follows:
Line 1115  Example:
Line 1124  Example:
 [2672] Ap=[[1,1,0,0],[0,0,1,1],[0,0,0,0]]$  [2672] Ap=[[1,1,0,0],[0,0,1,1],[0,0,0,0]]$
 [2673] Xvar=[x1,x4]$  [2673] Xvar=[x1,x4]$
 [2674] Xrule=[[x2,1],[x3,1]]$  [2674] Xrule=[[x2,1],[x3,1]]$
 [2675] generate_maple_file_MR(A,Beta,Ap,Rvec,DirX,2,2|xrule=Xrule)$  [2675] mt_gkz.generate_maple_file_MR(A,Beta,Ap,Rvec,DirX,2,2|xrule=Xrule)$
   
   
 //A file "auto-generated-MR.ml" is automatically generated as follows:  //A file "auto-generated-MR.ml" is automatically generated as follows:
Line 1211  Example:
Line 1220  Example:
 [2677] Beta=[b1,b2,b3]$  [2677] Beta=[b1,b2,b3]$
 [2678] K=2$  [2678] K=2$
 [2679] T=[[1,2,3],[2,3,4]]$  [2679] T=[[1,2,3],[2,3,4]]$
 [2680] normalizing_constant(A,T,Beta,K);  [2680] mt_gkz.principal_normalizing_constant(A,T,Beta,K);
 (-b1-b2)/(b3*b1+b3*b2-b3^2)  (-b1-b2)/(b3*b1+b3*b2-b3^2)
 @end example  @end example
   
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