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Results tagged with elimination-theory
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user 10898
Elimination theory is the study of necessary and sufficient conditions for polynomial equations (E) to have solutions.In the homogeneous case, if the number of variables is equal to the number of equations, this leads to the study of the Resultant (polynomial in the coefficients of (E), obtained by "eliminating" the variables ). In the general case, one get a Resultant ideal, generated by polynomial relations in the coefficients of the equations (E).
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Discriminant of a composition of binary forms
When $R = h(f,g)$ with $h,f,g$ quadratic forms, with coefficients $h_i, f_i, g_i$ respectively for $i = 0,1,2$, the $K$ polynomial is given explicitly as
$$\displaystyle K = g_1^4h_0^2 - 8 g_0 g_1^2 …
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