Let a non null real matrix of dimension . Let the ideal generated by the polynomials . Show that this polynomials are a Gröbner base of the ideal I for some lexicographic order.

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- Nov 7th 2008, 07:04 PMroporteGröbner base for some lexicographic order
Let a non null real matrix of dimension . Let the ideal generated by the polynomials . Show that this polynomials are a Gröbner base of the ideal I for some lexicographic order.

Thanks!! - Jan 13th 2015, 04:14 PMRebesquesRe: Gröbner base for some lexicographic order
Consider the lexicographic order .

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.