Admissible Orderings And Bounds for Grobner Basis Normal Form Algorithms
Admissible Orderings And Bounds for Grobner Basis Normal Form Algorithms
Thomas Dube
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To see that the Ujt, 's are non-negative, note that the weights in Wi are non-negative, and for fc > 1, we have for all j, "t, j = ^k, j + «*-!. , • max {^^l^k. I u;^^. + Ui_i, j(^^^^) >0. To get some intuitions, let us look at the resulting weight functions for the admissible orderings introduced in section 1. For each admissible ordering, let the variables Xi, . . . , x„ be ordered such that ii>X2> • • • >a:„ A A A The construction yields the following weight functions: Example 1 : Lexicogra...phic Ordering Example 2 : Total-Degree(Lex) Ordering {k = l, ... , n) [k = l, ... , n) ^lixv^r- ■ ■
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