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Polynomial system of 6 variables

  1. Jul 19, 2015 #1
    U = A a²
    V = 2 A a b
    W = A b²
    u = 2 A a c + B a
    v = 2 A b c + B b
    w = A c² + B c + C

    I'd like to solve this system for A, B, C, a, b, c. Is it possible!?
  2. jcsd
  3. Jul 19, 2015 #2

    Suraj M

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    Gold Member

    If you want those terms, in terms of all the other terms, then i dont think you can, if in terms of U,V,W,u,v,w included then ofcourse, it would be simple,
    the basic problem is you have only one equation with U in it, or were you trying to say ##U##instead of ##u##?
  4. Jul 19, 2015 #3


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    Unless i'm mistaken, there are 12 variables and not 6 which means the system cannot be solved.
  5. Jul 19, 2015 #4


    Staff: Mentor

    The system cannot be solved uniquely, which is different from saying that it can't be solved.
  6. Jul 19, 2015 #5


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    I stand corrected.
  7. Jul 19, 2015 #6


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    Science Advisor
    Gold Member

    Assuming U,V,W,u,v,w are known, it might be possible. As a first step, the last three equations in A,B,C are linear, so you can get A,B,C, in terms of u,v,w,a,b,c. Substitute the expression for A into the first three equations. You now have polynomial expressions for a,b,c - good luck!
  8. Jul 19, 2015 #7
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