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### What are some efficient algorithms for determining if a quadratic multivariate polynomial has a solution?

I know that in general, multivariate polynomial satisfiability is equivalent to 3-SAT; however, I'm wondering if there are any good techniques in the quadratic case, specifically if there is a ...
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### Checking whether two quadratic equations have a common zero

Given two quadratic equations (with integer coefficients): $x^T A_1 x+ b^T_1 x + c_1=0$ and $x^T A_2 x+ b^T_2 x + c_2=0$ The problem is to decide whether they have a common zero. Here $x$ is a ...
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### What are some efficient algorithms for finding the solutions to a quadratic multivariate polynomial?

Based on this question, there's an efficient algorithm to determine whether a quadratic multivariate polynomial has a root. What are some algorithms to enumerate these solutions? I'm interested in ...
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