This is the famous equation ‹E=mc^2›. Or \(\diag (1,2,3)\)
«E=mc^2»
OK ‹a^2› \(/ \!\!\!\! P\)
This is \(a\lt b\) and \(b\gt a\)...
Here is an equation
\[
{\LARGE E = mc^2 } \tag{E.1}
\] OK too many spaces.
\[
{\Huge \sqrt{s}\not\in\ZZ}
\] Extended \(\NNN=4\) supersymmetry.
\[ a+3 \zav{\frac{c}{d}} \] in a bracket. Let's try a matrix
\[ \begin{pmatrix} 1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9 \end{pmatrix} \] See more matrix commands here or here. Array with lines
\[ \begin{array}{rlc} n & n^2 & n^3 \\ \hline 3 & 9 & 27 \\ 4 & 16 & 64 \\ 11 & 121 & 1331 \end{array} \] Fine, my simplified matrix command:
\[ \pmatrix{ 9 & 10 & 11 \\ 12 & 13 & 14 \\ 15 & 16 & 17}
\] OK?
\[ \eq{ c+d &= 4+3+5 \\ e&= 7+6+85+23}
\] Fine, one may press enter before backslash final bracket without problems.
\[ b=\cases {38+a\\ 48 + b + \pmatrix{2&3\\4&6} }
\] Funny. What about macros for derivatives
\[ \ddfrac{y}{x} \neq \pfrac{f}{x} + \pfrac{{}^2 g}{x^2} + \frac{\dd h}{\dd x} \] And backslash pmatrix without brackets
\[ \array{1&2&3 \\ 4& 5& 6 } \] A product of \(\ket\psi\) and \(\bra\lambda\) is \(\braket\lambda\psi\).
\[
\int_0^\infty \dd x\,\,f(x) = g(x)
\] With limits,
\[
\int\limits_0^\pi \dd x~\sin(x) = 2
\] Ordinary linebreaks with two backslashes,
\[
2+3
=5 \\ 4+6=10
\] OK? The mass is \(125\GeV\), isn't it? Text may be better than rm, respects spaces:
\[ A_{\text{spin matrix}} = \pmatrix{0&1\\ 1&0} \neq B_{\rm bush spin} \]
Test of my standardized macros, the full list to be updated:\[
\int \dd x\,x^2\in \CC\RR\ZZ\OO\HHH\NN\NNN\FF\HH\LL
\] and \(\eV\keV\MeV\GeV\TeV\) and \[
\diag (1,2,3)\pfrac{E_x}{y}\ddfrac{y}{x}\bold{ahoj}\cdot\zav{\frac 12+\frac 45}
\] and \[
\zzav{\frac 12+\frac 34}+\abs{x+y}+\braket{\phi}{\psi}+\ket\psi+\bra\phi+\iddots
\] and\[
\eq{
a+b&=c\\
c+d+e&=f
}
\]
Comments of the Week #132: from dark comets to alien searches

“Ships that could circumnavigate the galaxy in a few years, and count every
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