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Thank you for your answer. There are a number of things that I don't understand yet. Can you please explain: Why can you saturate at X ("since X is indeterminate")? In Claim 1, are you saying that you want to choose f,g so that Claim 1 is satisfied? What do you mean by "then we replace"/why can you replace $f$? And then David Lamperts comment. It would be great if you could fill in some more detail. Thanks!
Oh, sorry. I did not see that you worked with the actual problem (because I did not see that it was linked). I was wondering where you numbers came from... :)
In this case it looks like it will use a general SQP approach, then. I somehow doubt that it will take only a few seconds to find a reasonable approximation to a global minimum of a long sum of squares in 12 variables, but I have not used Maple in a couple of years...
Judging from the result that you expect, I'm suspecting that you are after the variety of a commutative semigroup ring? Maybe one that satisfies $x_i^2 = x_i^3$ for each indeterminate $x_i$? Please rework this questions, at the moment it makes no sense.
