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authorJaron Kent-Dobias <jaron@kent-dobias.com>2021-03-12 16:58:40 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2021-03-12 16:58:40 +0100
commit85002f83cae33123e568413f6c5b811d429431f2 (patch)
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parent875f996cd76d1c534beca1beb2e0e821e3ea84c6 (diff)
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Simplified constraint arguement somewhat.
-rw-r--r--bezout.tex4
1 files changed, 1 insertions, 3 deletions
diff --git a/bezout.tex b/bezout.tex
index 458b448..db14a52 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -106,9 +106,7 @@ First, we seek draw conclusions from our model that would be applicable to
generic holomorphic functions without any symmetry. Samples of $H_0$ nearly
provide this, save for a single anomaly: the value of the energy and its
gradient at any point $z$ correlate along the $z$ direction, with
-$\overline{H_0\partial_iH_0}\propto \overline{H_0(\partial_iH_0)^*}\propto z_i$. Besides being a
-spurious correlation, in each sample there is also a `radial' gradient of
-magnitude proportional to the energy, since $z\cdot\partial H_0=pH_0$. This
+$\overline{H_0\partial H_0}\propto \overline{H_0(\partial H_0)^*}\propto z$. This
anomalous direction must be neglected if we are to draw conclusions about
generic functions, and the constraint surface $z^Tz=N$ is the unique surface
whose normal is parallel to $z$ and which contains the configuration space of