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authorJaron Kent-Dobias <jaron@kent-dobias.com>2023-11-28 17:23:20 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2023-11-28 17:23:20 +0100
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Added not about complicated saddle formula.
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diff --git a/2-point.tex b/2-point.tex
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@@ -642,7 +642,7 @@ $r^{11}_\mathrm d$, $r^{11}_0$, and $q^{11}_0$, is
It is possible to further extremize this expression over all the other
variables but $q_0^{11}$, for which the saddle point conditions have a unique
solution. However, the resulting expression is quite complicated and provides
-no insight. In practice, the complexity can be calculated in two ways. First,
+no insight. In fact, the numeric root-finding problem is more stable preserving these parameters, rather than analytically eliminating them. In practice, the complexity can be calculated in two ways. First,
the extremal problem can be done numerically, initializing from $q=0$ where the
problem reduces to that of the single-point complexity of points with energy
$E_1$ and stability $\mu_1$, and then taking small steps in $q$ or other