# Solving a system of simultaneous polynomial equations [closed]

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.

## closed as off-topic by Daniel Lichtblau, MarcoB, gwr, Hector, bbgodfreyAug 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
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• There appears to be 14 equations rather than 15 (just 4 quadratic constraints) and next to last equation has the && missing just before it. – JimB Aug 20 '16 at 18:40
• I fixed the code in my question. – Libertron Aug 20 '16 at 18:51
• 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"). – JungHwan Min Aug 20 '16 at 19:07
• If you are not concerned about being exact, try NSolve (which seems to give no solution as well). – JungHwan Min Aug 20 '16 at 19:16
• There is no solution. – Daniel Lichtblau Aug 20 '16 at 19:17

## 1 Answer

I am also new MMA user. I think we don't need {} for the equations. EDIT: Deleted the redundant code to tidy-up.

• 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. – JungHwan Min Aug 20 '16 at 19:14