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01/30/07 02:57am

In a problem I'm working on I came up with the following underdetermined quadratic system.


where the [a's,b's and c's] are constants.

I need a general solution to the question "is there at least one solution for {x_i, y_i}"

to solve this I tried (see the attempts in the file):
Minimize[{x_1+y_1},{Sum[x_i^2+x_i,{i,1,5}]==(-Sum[y_i^2 y_i,{i,1,5}]),Sum[x_i^2+x_i,{i,1,5}]==(-Sum[y_i^2+y\i,{i,1,5}]), Sum[x_i^2+x_i,{i,1,5}]==(-Sum[y_i^2+y_i,{i,1,5}])}]\)

I know that in the general case this is NP-hard but I have (what I think is) a simple special case.

What am I doing wrong and can Mathematica help me?


Attachment: try_mini.nb, URL: ,
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