Unisolvent point set
In approximation theory, a finite collection of points [math]\displaystyle{ X \subset R^n }[/math] is often called unisolvent for a space [math]\displaystyle{ W }[/math] if any element [math]\displaystyle{ w \in W }[/math] is uniquely determined by its values on [math]\displaystyle{ X }[/math].
[math]\displaystyle{ X }[/math] is unisolvent for [math]\displaystyle{ \Pi^m_n }[/math] (polynomials in n variables of degree at most m) if there exists a unique polynomial in [math]\displaystyle{ \Pi^m_n }[/math] of lowest possible degree which interpolates the data [math]\displaystyle{ X }[/math].
Simple examples in [math]\displaystyle{ R }[/math] would be the fact that two distinct points determine a line, three points determine a parabola, etc. It is clear that over [math]\displaystyle{ R }[/math], any collection of k + 1 distinct points will uniquely determine a polynomial of lowest possible degree in [math]\displaystyle{ \Pi^k }[/math].
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