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Suppose I have the following matrix equalities:

A=X, B=Y

where the left-hand side matrices are numeric and the right hand side contains non-linear combinations of unknowns. Since I have quite a few variables, it would be tiresome to rewrite the equations one by one. Is there any clever way to solve the system implicitly defined above in Mathematica? Or do I have to grab each of the equations? Is there any quick way to explicitly write the equations?

Thanks.

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1 Answer 1

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Something like this?

A = {{1, 1}, {1, 1}};
X = {{x x + y y, x x - w w}, {w w - z z, y y + z z z}};
Solve[And @@@ MapThread[Equal, {A, X}, 2], Variables@X]
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  • $\begingroup$ Thats something along the lines, but what if I have the same unknowns in X and Y? Would something like this work: Solve[And @@@ MapThread[Equal,{{A,X},{B,Y}},{Variables@X,Variables@Y}] $\endgroup$
    – user191919
    Dec 14, 2014 at 11:51
  • $\begingroup$ By the way, what are the chances it will solve a system of 45 variables? (numerically; I tried it here and obtained no response after running solve for about half an hour) $\endgroup$
    – user191919
    Dec 14, 2014 at 14:12
  • $\begingroup$ @user191919 Sorry, the chance depends strongly depends on your system. Impossible to say without understanding it. $\endgroup$
    – Dr. belisarius
    Dec 14, 2014 at 16:11
  • $\begingroup$ Do you have any hints in solving high dimensional systems? $\endgroup$
    – user191919
    Dec 14, 2014 at 16:47
  • $\begingroup$ @user191919 If you do a cursory search at this site you'll easily find that numerical methods are too complicated to give general answers to questions like that one. Sorry. $\endgroup$
    – Dr. belisarius
    Dec 14, 2014 at 16:51

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