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In algebra, the Vandermonde polynomial of an ordered set of n variables X 1 , … , X n {\displaystyle X_{1},\dots ,X_{n}} , named after Alexandre-Théophile Vandermonde, is the polynomial:
{\displaystyle } , which changes the sign {\displaystyle {\binom {n}{2}}} times: thus in some dimensions the two formulas agree in sign, while in others they have opposite signs.]
It is also called the Vandermonde determinant, as it is the determinant of the Vandermonde matrix.
The value depends on the order of the terms: it is an alternating polynomial, not a symmetric polynomial.
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