# Questions tagged [elimination-theory]

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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### How did Hilbert prove the Nullstellensatz?

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### Abel-Ruffini theorem for systems of polynomial equations

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### Division of bivariate polynomials

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### Does positivstellensatz and SOS proof system help here?

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### Do many homogeneous polynomials help in faster integer root extraction?

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### Final step in Coppersmith?

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### Solving solutions to systems of polynomial equations over $\mathbb Z$

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### Counting real zeros of a polynomial

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### Question on the integral $\int_{-\infty}^{\infty} e^{a x^4+b x^3+c x^2+d x+f}\,dx$

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### Discriminant of a composition of binary forms

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### Computer algebra programs for dummies

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### Elimination theory for variables packaged in a matrix

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### Algebraic approach to showing trigonometric equations have no solution

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### Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky

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### Why A. Weil considered elimination theory to be eliminated?

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### Why is any maximal minor of the Bezoutian matrix divisible by the resultant?

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### Calculating the images of varieties under projections

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### Interpolating for particular coefficients

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### General hyperplane sections and projection from a point

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