> Here is the solution I came up with.

Is that the solution to this problem?

http://axiom-wiki.newsynthesis.org/ExampleGroebner

Actually, I wanted to computed a Groebner basis for that case, but that
simply give [1], saying, that for generic a, b, c, u, v, w, such m and n
cannot be found. So I conclude that your problem is most probably
something else.

Can you please edit the above site and state your problem as clearly as
possible?

Thanks
Ralf

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