tex-projects/LaTeX-examples
2
0
Fork 0
mirror of https://github.com/MartinThoma/LaTeX-examples.git synced 2025-04-26 06:48:04 +02:00
Code Activity

Remove trailing spaces

Browse source 
The commands

find . -type f -name '*.md' -exec sed --in-place 's/[[:space:]]\+$//' {} \+

and

find . -type f -name '*.tex' -exec sed --in-place 's/[[:space:]]\+$//' {} \+

were used to do so.
This commit is contained in:
Martin Thoma 2015-10-14 14:25:34 +02:00
parent c578b25d2f
commit 7740f0147f
538 changed files with 3496 additions and 3496 deletions
Download patch file Download diff file Expand all files Collapse all files

2
documents/math-minimal-distance-to-cubic-function/analyzing-t.tex
View file

@ -1,7 +1,7 @@
\begin{align}
t &:= \sqrt[3]{\sqrt{3 \cdot (4 \alpha^3 + 27 \beta^2)} -9\beta}\\
&= \sqrt[3]{\sqrt{3 \cdot \left (4 \left (\frac{1- 2 aw}{2 a^2} \right )^3 + 27 \left (\frac{-z}{2 a^2} \right )^2 \right )} -9 \frac{-z}{2 a^2}}\\
&= \sqrt[3]{\sqrt{3 \cdot \left (4 \left (\frac{1- 2 a (y_P+\frac{b^2}{4a}-c)}{2 a^2} \right )^3 + 27 \left (\frac{-(x_P+\frac{b}{2a})}{2 a^2} \right )^2 \right )}
&= \sqrt[3]{\sqrt{3 \cdot \left (4 \left (\frac{1- 2 a (y_P+\frac{b^2}{4a}-c)}{2 a^2} \right )^3 + 27 \left (\frac{-(x_P+\frac{b}{2a})}{2 a^2} \right )^2 \right )}
-9 \frac{-(x_P+\frac{b}{2a})}{2 a^2}}\\
&= \sqrt[3]{\sqrt{12a^4 \cdot \left (4 \frac{\left ( 1- 2 a (y_P+\frac{b^2}{4a}-c) \right )^3}{2 a^2} + 27 \left (x_P^2+2 x_P \frac{b}{2a} + \frac{b^2}{4a^2} \right )\right )}
+ 9 \frac{x_P+\frac{b}{2a}}{2 a^2}}\\