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Student Support Forum: 'Finding point in feasable regen' topicStudent Support Forum > General > Archives > "Finding point in feasable regen"

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Yoni
01/30/07 02:57am

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

[
x1^2+x2^2+x3^2+...+a1*x1+a2*x2+a3*x3=-(y1^2+y2^2+y3^2+...+a1*y1+a2*y2+a3*y3)
x1^2+x2^2+x3^2+...+b1*x1+b2*x2+b3*x3=-(y1^2+y2^2+y3^2+...+b1*y1+b2*y2+b3*y3)
x1^2+x2^2+x3^2+...+c1*x1+c2*x2+c3*x3=-(y1^2+y2^2+y3^2+...+c1*y1+c2*y2+c3*y3)
]

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?

Yoni

Attachment: try_mini.nb, URL: ,
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