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Math Help - Gröbner base for some lexicographic order

  1. #1
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    Gröbner base for some lexicographic order

    Let A(a_{ij}) a non null real matrix of dimension m \times n. Let I the ideal generated by the m polynomials \sum_i a_{ji}x_i. Show that this polynomials are a Gröbner base of the ideal I for some lexicographic order.


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  2. #2
    Super Member Rebesques's Avatar
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    Re: Gröbner base for some lexicographic order

    Consider the lexicographic order x_1<x_2<\ldots.

    Reduce the matrix in row echelon form using row operations; The polynomial set produces the same ideal, and cannot be reduced any further.
    Thus, this set (and equivalently the starting set) is a Groebner basis.
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