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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
commit01d47c182ce0c1ee01acaf79043a9ce40ecead56 (patch)
tree349398f71d4b3576ac77320cf702902ff55118af
parentcca6ae689762dd447a464be37a2b5229248235e1 (diff)
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Added not about complicated saddle formula.
-rw-r--r--2-point.tex2
1 files changed, 1 insertions, 1 deletions
diff --git a/2-point.tex b/2-point.tex
index ce2d1bc..860a6c7 100644
--- a/2-point.tex
+++ b/2-point.tex
@@ -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