Let $I$ be an parametric polynomial ideal in $K[a_1,\cdots,a_m][x_1,\cdots,x_n]$ where $a_1,\cdots,a_m$ is a sequence of parameters and $x_1,\cdots,x_n$ is a sequence of variables. Is there any famous example or application which in it we must compute the reduced Groebner basis of $I$ w.r.t. lex ordering and w.r.t. some conditions on parameters?
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Depends on what you consider as "famous". But yes, there are "famous" examples, e.g., for the Auslander conjecture. – Dietrich Burde Nov 07 '15 at 18:48
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Your problem translated to a parametric polynomial ideal? Is there any conditions on parameters? – mahdi dehghani Nov 07 '15 at 18:54
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Yes, there is. In particular, one wants to find the "important" conditions on the parameters. – Dietrich Burde Nov 07 '15 at 18:56
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Could you please send it for me and determine the variables and parameters? – mahdi dehghani Nov 07 '15 at 18:58