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Search for numerical solutions of underdetermined systems of quadratic equations

This is a bit late for you, perhaps, but it might be worth looking at cylindrical algebraic decomposition. CAD takes a general statement in the real closed fields (i.e. an arbitrary boolean statement …
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Deciding whether an integer polynomial has an integer root

(Let's call the root $\xi$, because $n$ here means the degree of the polynomial. That's seriously bugging me about the question.) The secret is in noticing that it's easy to test if $\xi$ is a root, s …
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