From 85002f83cae33123e568413f6c5b811d429431f2 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 12 Mar 2021 16:58:40 +0100 Subject: Simplified constraint arguement somewhat. --- bezout.tex | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) (limited to 'bezout.tex') 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 -- cgit v1.2.3-54-g00ecf