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This is the first time I have used Mathematica, so please bear with me. I'm trying to solve a system of $10$ nonlinear polynomial equations in $10$ unknowns, which I denote by $a, b, c, d, e, f, g, h, j, t$, subject to $4$ quadratic constraint equations (so essentially $14$ equations in $10$ unknowns). Here is my code:

Solve[{a^2 - b^2 - c^2 - d^2 == 4 && b^2 - e^2 - f^2 - j^2 ==-2 &&
       c^2 - f^2 - g^2 - h^2 ==-2 && d^2 - j^2 - h^2 - t^2 ==-2 &&
       a b - b e - c f - d j - 1 ==0 && b c - e f - f g - j h - 1 ==0 && 
       c d - f j - g h - h t -1 ==0 && d-j-h-t-1 ==0 && a-b-c-d-1 ==0 &&
       d b - j e - h f - t j -1 ==0 && c a - f b - g c - h d - 1 ==0 && 
       c-f-g-h-1 ==0 && d a - j b - h c - t d - 1 ==0 && b-e-f-j-1 ==0}
,{a, b, c, d, e, f, g, h, j, t}, Reals]  

Every time I try to evaluate this, it returns a blank line. Is there something wrong with my code, that I'm not able to spot? Maybe I need to change the domain to rationals instead.

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closed as off-topic by Daniel Lichtblau, MarcoB, gwr, Hector, bbgodfrey Aug 22 '16 at 4:03

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Daniel Lichtblau, MarcoB, gwr, Hector, bbgodfrey
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ There appears to be 14 equations rather than 15 (just 4 quadratic constraints) and next to last equation has the && missing just before it. $\endgroup$ – JimB Aug 20 '16 at 18:40
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    $\begingroup$ I fixed the code in my question. $\endgroup$ – Libertron Aug 20 '16 at 18:51
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    $\begingroup$ Are you sure there is a solution to this system of equations? Most of the times, Mathematica alerts the user if it cannot find a way to solve a problem; having no messages means that Mathematica was successful in solving the equation (which in this case is "no solution"). $\endgroup$ – JungHwan Min Aug 20 '16 at 19:07
  • $\begingroup$ If you are not concerned about being exact, try NSolve (which seems to give no solution as well). $\endgroup$ – JungHwan Min Aug 20 '16 at 19:16
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    $\begingroup$ There is no solution. $\endgroup$ – Daniel Lichtblau Aug 20 '16 at 19:17
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I am also new MMA user. I think we don't need {} for the equations. EDIT: Deleted the redundant code to tidy-up.

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    $\begingroup$ The curly braces are optional. Thus, your code is identical to OP's code, except that it uses other symbols for equations and that it uses Reduce. $\endgroup$ – JungHwan Min Aug 20 '16 at 19:14

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