1. Test

$\displaystyle \int^\frac{\pi}{4} _0 \cos(4x)$

2. $\displaystyle \underset{\smile}{\text{. .}}$

3. Originally Posted by Drexel28
$\displaystyle \underset{\smile}{\text{. .}}$
. . . . . . . . . .$\displaystyle \setbox0=\hbox{$\text{o o} \atop\displaystyle \smile$}\dimen0=\wd0 \divide\dimen0 by 2 \advance\dimen0 by -12pt \lower2pt\hbox to0pt{\kern\dimen0\Huge$\bigcirc$\hss}\box0$

(A few years ago, I had to develop a macro for putting a circle round an expression, when I was teaching a course on games theory. The solutions sheets for the homework exercises had to include things like $\displaystyle \begin{bmatrix}1&\framebox[1.25em]{$-1$}&\setbox0=\hbox{$-3$}\dimen0=\wd0 \divide\dimen0 by 2 \advance\dimen0 by -8.5pt \lower0.6pt\hbox to0pt{\kern\dimen0\Large$\bigcirc$\hss}\box0\,\\ \,\fbox{2}&\setbox0=\hbox{$-2$}\dimen0=\wd0 \divide\dimen0 by 2 \advance\dimen0 by -8.5pt \lower0.6pt\hbox to0pt{\kern\dimen0\Large$\bigcirc$\hss}\box0&\fbox {3}\end{bmatrix}$.)

4. Haha the last 2 are nice ones !

Hmmm $\displaystyle \textcircled{L}\textcircled{e}\textcircled{t}\text circled{t}\textcircled{e}\textcircled{r} ~ \textcircled{b}\textcircled{y} ~\textcircled{l}\textcircled{e}\textcircled{t}\tex tcircled{t}\textcircled{e}\textcircled{r}$

5. Originally Posted by Moo
Haha the last 2 are nice ones !

Hmmm $\displaystyle \textcircled{L}\textcircled{e}\textcircled{t}\text circled{t}\textcircled{e}\textcircled{r} ~ \textcircled{b}\textcircled{y} ~\textcircled{l}\textcircled{e}\textcircled{t}\tex tcircled{t}\textcircled{e}\textcircled{r}$
If I had known about the \textcircled command, it would have saved me a lot of work! (I don't believe it featured in earlier versions of LaTeX.)

6. just testing

$\displaystyle \frac{\sin} {\cos} = \tan$

7. $\displaystyle \overset{\begin{array} {c} \color{red} \blacktriangle \end{array}}\sum^{\frac{dx}{dy}x^3}_{love}$$\displaystyle \frac{\left [ \left ( -1 \right ) x^{2n+1} \right ]}{\left ( 2n+1 \right )!}$

It is my summation of love...

8. $\displaystyle \prod_{n = 0}^{+\infty} \frac{\varphi{(n)}}{\ln{(n)}} + \epsilon$

Just messing around ...

9. $\displaystyle \begin{matrix}\Omega\times\Omega & \xrightarrow[\quad\quad\quad]{\alpha} & \Omega\\ ^{\pi\times\pi}\bigg\downarrow & & \bigg\downarrow ^{\pi} \\ \text{Top }\Omega\times\text{Top }\Omega & \xrightarrow[\quad\quad\quad]{\overset{\sim}{\alpha}} & \text{Top }\Omega\end{matrix}$

10. Originally Posted by Drexel28
$\displaystyle \begin{matrix}\Omega\times\Omega & \xrightarrow[\quad\quad\quad]{\alpha} & \Omega\\ ^{\pi\times\pi}\bigg\downarrow & & \bigg\downarrow ^{\pi} \\ \text{Top }\Omega\times\text{Top }\Omega & \xrightarrow[\quad\quad\quad]{\overset{\sim}{\alpha}} & \text{Top }\Omega\end{matrix}$
Nice! The only improvement I can suggest is a little tweak to lower the $\displaystyle \pi$ beside the right-hand vertical arrow:

$\displaystyle \begin{matrix}\Omega\times\Omega & \xrightarrow[\quad\quad\quad]{\alpha} & \Omega\\ ^{\pi\times\pi}\bigg\downarrow & & \bigg\downarrow {}^{\pi} \\ \text{Top }\Omega\times\text{Top }\Omega & \xrightarrow[\quad\quad\quad]{\overset{\sim}{\alpha}} & \text{Top }\Omega\end{matrix}$

11. Originally Posted by Drexel28
$\displaystyle \begin{matrix}\Omega\times\Omega & \xrightarrow[\quad\quad\quad]{\alpha} & \Omega\\ ^{\pi\times\pi}\bigg\downarrow & & \bigg\downarrow ^{\pi} \\ \text{Top }\Omega\times\text{Top }\Omega & \xrightarrow[\quad\quad\quad]{\overset{\sim}{\alpha}} & \text{Top }\Omega\end{matrix}$
Interesting diagram, although the horizontal lines look a bit jagged and blurred on my computer, anyone got the same artifact ?

12. Originally Posted by Opalg
Nice! The only improvement I can suggest is a little tweak to lower the $\displaystyle \pi$ beside the right-hand vertical arrow:

$\displaystyle \begin{matrix}\Omega\times\Omega & \xrightarrow[\quad\quad\quad]{\alpha} & \Omega\\ ^{\pi\times\pi}\bigg\downarrow & & \bigg\downarrow {}^{\pi} \\ \text{Top }\Omega\times\text{Top }\Omega & \xrightarrow[\quad\quad\quad]{\overset{\sim}{\alpha}} & \text{Top }\Omega\end{matrix}$
Yeah, I meant to lower it. Thanks for the tip!

Do you have any idea how to do triangular diagrams with this? I can't figure out how to make it nice. One of my main problems is that $$\bigg\searrow$$ produces $\displaystyle \bigg\searrow$

Originally Posted by Bacterius
Interesting diagram, although the horizontal lines look a bit jagged and blurred on my computer, anyone got the same artifact ?
Yeah, I'm not sure

13. $\displaystyle \varphi(x)=\prod_{z\in\mathbb{C}}(x-z)\overset{?}{=}0$

14. Originally Posted by Drexel28
$\displaystyle \begin{matrix}\Omega\times\Omega & \xrightarrow[\quad\quad\quad]{\alpha} & \Omega\\ ^{\pi\times\pi}\bigg\downarrow & & \bigg\downarrow ^{\pi} \\ \text{Top }\Omega\times\text{Top }\Omega & \xrightarrow[\quad\quad\quad]{\overset{\sim}{\alpha}} & \text{Top }\Omega\end{matrix}$
Looking at this again, I can see another way in which it needs tweaking. Ideally, the vertical arrow on the left should be aligned with the product signs above and below it; and the vertical arrow on the right should similarly be aligned under the $\displaystyle \Omega$ above it. You can achieve that quite easily by using the \llap and \rlap commands. These produce boxes of zero width whose contents overlap to the left or right respectively.

$\displaystyle \begin{matrix}\Omega\times\Omega & \xrightarrow[\quad\quad\quad]{\alpha} & \Omega\\ \llap{$\scriptstyle\pi\times\pi$}\bigg\downarrow & & \bigg\downarrow\rlap{$\scriptstyle\pi$} \\ \text{Top }\Omega\times\text{Top }\Omega & \xrightarrow[\quad\quad\quad]{\overset{\sim}{\alpha}} & \text{Top }\Omega\end{matrix}$

Originally Posted by Bacterius
Interesting diagram, although the horizontal lines look a bit jagged and blurred on my computer, anyone got the same artifact ?
Yes, that is an artefact caused by the fact that TeX does not have ready-made glyphs for long horizontal arrows. Instead, it constructs them on the fly by joining a sequence of short dashes to an arrowhead. The effect on the screen looks a bit uneven, though the printed version would probably be smoother.

15. Originally Posted by Drexel28
$\displaystyle \varphi(x)=\prod_{z\in\mathbb{C}}(x-z)\overset{?}{=}0$
Overset huh? Been looking for that a while now. Thanks.

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