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added comment 'symmetry axis'

Martin Thoma 11 yıl önce
ebeveyn
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+ 1 - 1
documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex

@@ -356,7 +356,7 @@ For all other points $P = (0, w)$, there are exactly two minima $x_{1,2} = \pm \
 So the solution is given by
 
 \begin{align*}
-x_S &:= - \frac{b}{2a}\\
+x_S &:= - \frac{b}{2a} \;\;\;\;\; \text{(the symmetry axis)}\\
 \underset{x\in\mdr}{\arg \min d_{P,f}(x)} &= \begin{cases}
      x_1 = +\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S \text{ and }   &\text{if } x_P = x_S \text{ and } y_p + \frac{b^2}{4a} - c >  \frac{1}{2a} \\
      x_2 = -\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S\\