Talk:Polarization of an algebraic form

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The polar form of f is a polynomial

F(u⁽¹⁾, u⁽²⁾, ..., u^(d))

which is linear separately in each u⁽ⁱ⁾ (i.e., F is multilinear) and such that

F(u,u, ..., u)=f(u).

Is this supposed to be a definition of the polar form? In this case, I tend to believe that we need a condition more - namely, F should be symmetric in its d (vectorial) variables. Is this correct? - darij