= Product of Morse functions
{title2=$F(x,y)=f(x)+g(y)$}
The <critical points> of $F$ are exactly pairs of <critical points> of its factors. Its <Hessian matrix> is their block direct sum, so their <Morse indices> add and nondegeneracy is preserved. The critical-count polynomial is the product of those of the factors. This construction also gives products of arbitrary <smooth functions>, with the critical-point count still multiplying even when some <Hessians> are degenerate.
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