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Math Help - Discriminant of multi variable equations

  1. #1
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    Thumbs up Discriminant of multi variable equations

    Hi, please send me how find discriminant of a elliptic curve with two variable..


    urgent please send me any reference url' s
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  2. #2
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    Quote Originally Posted by vinodannu View Post
    Hi, please send me how find discriminant of a elliptic curve with two variable..


    urgent please send me any reference url' s
    I think this is what you mean. The method is similar for classifying PDE's as well.

    The general form of an ellipse is

    Ax^2+By^2+Cxy+Dx+Ey+F=0

    This is a quadratic form and can be written as a matrix as follows

    \begin{bmatrix}x & y \end{bmatrix}\begin{bmatrix}A & \frac{C}{2} \\ \frac{C}{2} & B \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}+\begin{bmatrix}D && E \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}+F=0

    The first matrix is always real symmetric and can be diagonalized and its discriminant is the sum of its eigenvalues.

    I hope this is what you were looking for!
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