Tigers OX Server マニュアル

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1 TIGERS 函数

この章では, tigers ox server ox_sm1_tigers にたいするインタフェース函数を説明する.


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1.0.1 tigers.tigers

tigers.tigers(a|proc=a)

:: この函数は識別子 p の tigers サーバに 行列 a に付随したトーリックイデアルのすべてのグレブナ基底を 計算してくれるようにたのむ.

戻り値

リスト

p

a

リスト

[395] A=[[1,1,1,1],[0,1,2,3]]$
[306] S=tigers.tigers(A)$
[307] length(S);
8
[308] S[0];
[[[1,0,1,0],[0,2,0,0]],[[1,0,0,1],[0,1,1,0]],[[0,1,0,1],[0,0,2,0]]]
[309] S[1];
[[[1,0,0,1],[0,1,1,0]],[[0,2,0,0],[1,0,1,0]],[[0,1,0,1],[0,0,2,0]]]

この例では, A に付随したアフィントーリックイデアルの すべてのグレブナ基底が S に格納される. この例では, 8 個のグレブナ基底がある. [[i_1, i_2, ...],[j_1, j_2, ...]] は二つのモノミアルの exponent をならべたものであり, 2 項式をあらわす. たとえば, S[0] は次の多項式の集合
x1 x3 - x2^2, x1 x4 - x2 x3, x2 x4 - x3^2
であり, <x1 x3, x1 x4, x2 x4> がその initial ideal である.


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