1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.

System of 15 equations in 23 variables

Discussion in 'Mathematics' started by LCH, Aug 2, 2020 at 2:25 AM.

  1. LCH

    LCH Guest

    $$ 1-k_0^2=0, \frac{1}{2} \left(-7 \alpha ^2+38 \alpha +2 c_3 (\alpha +\beta-3)+2 c_6-2 k_1^2-2 k_5^2-48\right)=0, c_5-k_2^2-k_{10}^2=0, c_8(\alpha +\beta -5)+5 c_{10}-k_3^2-k_6^2-k_8^2-k_{11}^2-2 k_2 k_4=0, c_{11}(\alpha +\beta -7)-k_4^2-k_7^2-k_9^2-k_{12}^2=0, -2 \alpha +\beta +2 c_3-2k_0 k_1+4=0, c_2-2 k_0 k_2=0, c_6-2 k_0 k_3=0, c_9-2 k_0 k_4=0,-\frac{3}{2} (\alpha -2) (3 \alpha -11)+c_2 (\alpha +\beta -3)+3 c_5+2 c_6-2 k_1 k_2=0, (4-\alpha ) (\alpha -2) (2 \alpha -9)+c_6 (\alpha +\beta -4)+2c_8+4 c_9-2 k_1 k_3-2 k_5 k_6=0, -\frac{1}{8} (\alpha -6) (\alpha -5)(\alpha -4) (\alpha -2)+c_9 (\alpha +\beta -5)+c_{10}-2 k_1 k_4-2 k_5k_7=0, c_5 (\alpha +\beta -4)+3 c_8-2 k_2 k_3=0, c_8 (\alpha +\beta -5)+5 c_{10}-k_3^2-k_6^2-k_8^2-k_{11}^2-2 k_2 k_4=0, c_{10} (\alpha +\beta-6)+7 c_{11}-2 \left(k_3 k_4+k_6 k_7+k_8 k_9\right)=0 $$

    I use FindInstance to find a set of real parameters (here $\alpha$, $\beta>0$ and other parameters are real) which satisfy the above 15 equations. Perhaps there are lots of parameters, I didn't get any answer from Mathematica. Any reference, suggestion, idea, alternative solution or comment is welcome. Thank you! (the code I used is as follows.)

    FindInstance[10 - 5*\[Alpha] + 2*Subscript[c, 2] + Subscript[c, 3]==0 && 1 - Subscript[k, 0]^2 == 0 && (1/2)*(-48 + 38*\[Alpha] - 7*\[Alpha]^2 + 2*(-3 + \[Alpha] + \[Beta])*Subscript[c, 3] + 2*Subscript[c, 6] - 2*Subscript[k, 1]^2 - 2*Subscript[k, 5]^2) == 0 && Subscript[c, 5] - Subscript[k, 2]^2 - Subscript[k, 10]^2 == 0 && (-5 + \[Alpha] + \[Beta])*Subscript[c, 8] + 5*Subscript[c, 10] - Subscript[k, 3]^2 - 2*Subscript[k, 2]*Subscript[k, 4] - Subscript[k, 6]^2 - Subscript[k, 8]^2 - Subscript[k, 11]^2 == 0 && (-7 + \[Alpha] + \[Beta])*Subscript[c, 11] - Subscript[k, 4]^2 - Subscript[k, 7]^2 - Subscript[k, 9]^2 - Subscript[k, 12]^2 == 0 && 4 - 2*\[Alpha] + \[Beta] + 2*Subscript[c, 3] - 2*Subscript[k, 0]*Subscript[k, 1] == 0 && Subscript[c, 2] - 2*Subscript[k, 0]*Subscript[k, 2] == 0 && Subscript[c, 6] - 2*Subscript[k, 0]*Subscript[k, 3] == 0 && Subscript[c, 9] - 2*Subscript[k, 0]*Subscript[k, 4] == 0 && (-(3/2))*(-2 + \[Alpha])*(-11 + 3*\[Alpha]) + (-3 + \[Alpha] + \[Beta])*Subscript[c, 2] + 3*Subscript[c, 5] + 2*Subscript[c, 6] - 2*Subscript[k, 1]*Subscript[k, 2] == 0 && (-(-4 + \[Alpha]))*(-2 + \[Alpha])*(-9 + 2*\[Alpha]) + (-4 + \[Alpha] + \[Beta])*Subscript[c, 6] + 2*Subscript[c, 8] + 4*Subscript[c, 9] -2*Subscript[k, 1]*Subscript[k, 3] - 2*Subscript[k, 5]*Subscript[k, 6] == 0 && (-(1/8))*(-6 + \[Alpha])*(-5 + \[Alpha])*(-4 + \[Alpha])*(-2 + \[Alpha]) + (-5 + \[Alpha] + \[Beta])*Subscript[c, 9] + Subscript[c, 10] - 2*Subscript[k, 1]*Subscript[k, 4] - 2*Subscript[k, 5]*Subscript[k, 7] == 0 && (-4 + \[Alpha] + \[Beta])*Subscript[c, 5] + 3*Subscript[c, 8] - 2*Subscript[k, 2]*Subscript[k, 3] == 0 && (-5 + \[Alpha] + \[Beta])*Subscript[c, 8] + 5*Subscript[c, 10] - Subscript[k, 3]^2 - 2*Subscript[k, 2]*Subscript[k, 4] - Subscript[k, 6]^2 - Subscript[k, 8]^2 - Subscript[k, 11]^2 == 0 && (-6 + \[Alpha] + \[Beta])*Subscript[c, 10] + 7*Subscript[c, 11] - 2*(Subscript[k, 3]*Subscript[k, 4] + Subscript[k, 6]*Subscript[k, 7] + Subscript[k, 8]*Subscript[k, 9]) == 0, {\[Alpha], \[Beta], Subscript[k, 0], Subscript[k, 1], Subscript[k, 2], Subscript[k, 3], Subscript[k, 4], Subscript[k, 5], Subscript[k, 6], Subscript[k, 7], Subscript[k, 8], Subscript[k, 9], Subscript[k, 10], Subscript[k, 11], Subscript[k, 12], Subscript[c, 2], Subscript[c, 3], Subscript[c, 5], Subscript[c, 6], Subscript[c, 8], Subscript[c, 9], Subscript[c, 10], Subscript[c, 11]}, Reals]

    Login To add answer/comment
     

Share This Page