version 1.1, 2021/01/20 03:05:29 |
version 1.2, 2021/01/20 08:17:54 |
|
|
%% $OpenXM$ |
%% $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 |
|
|
* 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 |
|
|
@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 |
|
|
@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 |
|
|
[[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 ] |
|
|
[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 |
|
|
[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: |
|
|
[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: |
|
|
[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 |
|
|