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Solution set

From Biocrawler, the free encyclopedia.

In mathematics, a solution set for a collection of polynomials ${f i}$ over some ring $R$ is defined to be the set $\{x\in R:\forall i\in I, f_i(x)=0\}$ .

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Examples

1. The solution set of $f (x): = x$ over the real numbers is the set {0}.

2. For any non-zero polynomial $f$ over the complex numbers in one variable, the solution set is made up of finitely many points. However, for a complex polynomial in more than one variable the solution set has no isolated points.

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