Difference between revisions of "Useful Examples"
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echo 'hello planeto world' | echo 'hello planeto world' | ||
</syntaxhighlight> | </syntaxhighlight> | ||
| + | |||
| + | == How to create a new page == | ||
| + | Look for it via the searh bar! | ||
| + | Advice: you should use CamelCase formating (and/or _ between words) | ||
== Link to the LMD Generic GCM user manual == | == Link to the LMD Generic GCM user manual == | ||
Revision as of 10:50, 13 April 2022
Contents
To Edit Sidebar (as admin only!!!)
Go to MediaWiki:Sidebar
To write some LateX
See e.g. LMDZPedia And check out this page in "edit" mode! $$\newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}$$
We consider, for various values of $$s$$, the $$n$$-dimensional integral \begin{align} \label{def:Wns} W_n (s) &:= \int_{[0, 1]^n} \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} \end{align} which occurs in the theory of uniform random walk integrals in the plane, where at each step a unit-step is taken in a random direction. As such, the integral \eqref{def:Wns} expresses the $$s$$-th moment of the distance to the origin after $$n$$ steps.
By experimentation and some sketchy arguments we quickly conjectured and strongly believed that, for $$k$$ a nonnegative integer \begin{align} \label{eq:W3k} W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. \end{align}
Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers. The reason for \eqref{eq:W3k} was long a mystery, but it will be explained at the end of the paper.
Miscellaneous
- HTML like syntax works! e.g. comments with
<!-- This is a comment in the page --> which you see because between "pre" tags
- Some special features:
Link to the internal page with all special features: Special:Version
- Examples of Syntax Highlighting:
Some Fortran Code:
1 program truc
2 implicit none
3 integer :: i
4 do i=1,10
5 write(*,*) "i=",i," for each hello planeto world"
6 end do
7 end program
Some Python Code:
1 import numpy
2 import matplotlib as plt
3 for i in range(0,5,1):
4 print('hello planeto world")
5 plt.show()
Some bash code:
1 echo 'hello planeto world'
How to create a new page
Look for it via the searh bar! Advice: you should use CamelCase formating (and/or _ between words)
Link to the LMD Generic GCM user manual
https://web.lmd.jussieu.fr/~lmdz/planets/LMDZ.GENERIC/ManualGCM_GENERIC.pdf
or even better, the one on the trac which is what is on svn and thus will always be up to date: https://trac.lmd.jussieu.fr/Planeto/browser/trunk/LMDZ.GENERIC/ManualGCM_GENERIC.pdf
