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An Application of Groebner Basis: computing the index of reducibility

By 姚盈孜


[[abstract]]對任意自然數n,令q_n是多項式環Q[x,y,z]中的理想< x^{2n},y^{2n},(xy+z)^n,z^n >。首先,我們找出q_n的一組Groebner basis,再利用這組Groebner basis計算(q_n:m),其中m=< x,y,z >。最後利用index of reducibility和socle dimension的關係給出這個結論: N_R(q_n)=<n 若 n is even, N_R(q_n)=<2n 若 n is odd。

Topics: 計算index of reducibility, [[classification]]37
Year: 2011
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