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Results tagged with elimination-theory
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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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Multiple root of resultant
This is one of the most important steps in the proof of Bézout theorem on plane curves by elimination theory.
Without loss of generality, let me work with resultants in $x$. Assume that the point $p=( …
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