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Optimal Polynomial Check

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I'm writing a program that checks for valid polynomials read from a file. Is checking if the polynomial is equal to zero enough?

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Need more info....

 

Surely everything is valid as a polynomial as long as it doesn't have negative powers of the free variables. Two or more values for a given power might be invalid as well I suppose...


Are you trying to check if a polynomial has a solution over the real numbers? You may want to start by looking here: http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs in that case.

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