# Sandbox

(Difference between revisions)

 The sandbox is the page where you can experiment with the wiki syntax. Feel free to write nonsense or clear the page whenever you want.

## 2 Testing equation numbering

(1)$A = B$ == Images == ; \begin{theorem} We have A = B. \end{theorem} {{equation|A = B + C|1.1}} {{eqref|1.1}} By Theorem {{equation|\alpha|1.2}} {{eqref|1.2}} {{beginthm|Theorem}} Frog {{endthm}} Here is some text leading up to an equation {{beginrem| }} A = B {{endrem}} Here is some more text after the equation to see how it looks. Here is some text leading up to an equation A = B Here is some more text after the equation to see how it looks. :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" |- ! 4k !! 8 !! 12 !! 16 !! 20 !! 24 !! 28 !! 32 |- ! order bP4k | 22.7 || 25.31 || 26.127|| 29.511|| 210.2047.691 || 213.8191 || 214.16384.3617 |- |} :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" |- ! k !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 |- ! Bk | 1/6 || 1/30 || 1/42 || 1/30 || 5/66 || 691/2730 || 7/6 || 3617/510 || |- |} :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" |- ! Dim n !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! 17 !! 18 !! 19 !! 20 |- ! order Θ''n'' | 1 || 1 || 1 || 1 || 1 || 1 || 28 || 2 || 8 || 6 || 992 || 1 || 3 || 2 || 16256 || 2 || 16 || 16 || 523264 || 24 |- !''bP''''n''+1 | 1 || 1 || 1 || 1 || 1 || 1 || 28 || 1 || 2 || 1 || 992 || 1 || 1 || 1 || 8128 || 1 || 2 || 1 || 261632 || 1 |- !Θ''n''/''bP''''n''+1 | 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||2×2 || 6 || 1 || 1 || 3 || 2 || 2 || 2 || 2×2×2 || 8×2 || 2 || 24 |- !π''n''''S''/''J'' | 1 || 2 || 1 || 1 || 1 || 2 || 1 || 2 || 2×2 || 6 || 1 || 1 || 3 || 2×2 || 2 || 2 || 2×2×2 || 8×2 || 2 || 24 |- !index | - || 2 || - || - || - || 2 || - || - || - || - || - || - || - || 2 || - || - || - || - || - || - |} [[Media:Spaceform.tiff|link text]] f \colon X \to Y namespace=Main nottitlematch=Main_Page|Sandbox|Links ordermethod=lastedit order=descending minoredits=exclude author=%Diarmuid Crowley% count=10 Just a fest f \colon A \to B. \Q {{beginthm|a theorem}} \label{thma} {{endthm}} \text{Spin} by theorem \ref{thma}
1. Amsterdam
2. Rotterdam
3. The Hague
[[[#{{anchorencode:Mess1990}}|Mess1990]]]{{#RefAdd:Mess1990}} \left( \begin{array}{ll} \alpha & \beta \ \gamma & \delta \end{array} \right) f = T f : X \to Y f : X \to Y \Ker \mathscr{A} \mathscr{B} \bf{ bold} \it{italic} \em{emphasis}
[[Image:Foliation.png|thumb|300px|3-dimensional Reeb foliation]] == Tests == {{citeD|Ranicki1981}} {{cite|Milnor1956}} {{cite|Milnor1956|Theorem 1}} {{citeD|Milnor1956}} {{citeD|Milnor1956|Theorem 1}} {{citeD2|Milnor1956|Frog}} ; {{beginproof}} {{endproof}} == Section == === Subsection === \label{subsection} Refert to subsection \ref{subsection} \begin{theorem} \label{thm} test \end{theorem} Refer to theorem \ref{thm} == Section == ; An [[map-eds:Manifold Atlas:Projects in the Atlas|inter-Wiki link]]. Another Test1 [[map-eds:Manifold Atlas:Projects in the Atlas|inter-Wiki link]]. dfaTest2 ==Footnotes== == Images == ; \begin{theorem} We have A = B. \end{theorem} {{equation|A = B + C|1.1}} {{eqref|1.1}} By Theorem {{equation|\alpha|1.2}} {{eqref|1.2}} {{beginthm|Theorem}} Frog {{endthm}} Here is some text leading up to an equation {{beginrem| }} A = B {{endrem}} Here is some more text after the equation to see how it looks. Here is some text leading up to an equation A = B Here is some more text after the equation to see how it looks. :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" |- ! 4k !! 8 !! 12 !! 16 !! 20 !! 24 !! 28 !! 32 |- ! order bP4k | 22.7 || 25.31 || 26.127|| 29.511|| 210.2047.691 || 213.8191 || 214.16384.3617 |- |} :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" |- ! k !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 |- ! Bk | 1/6 || 1/30 || 1/42 || 1/30 || 5/66 || 691/2730 || 7/6 || 3617/510 || |- |} :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" |- ! Dim n !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! 17 !! 18 !! 19 !! 20 |- ! order Θ''n'' | 1 || 1 || 1 || 1 || 1 || 1 || 28 || 2 || 8 || 6 || 992 || 1 || 3 || 2 || 16256 || 2 || 16 || 16 || 523264 || 24 |- !''bP''''n''+1 | 1 || 1 || 1 || 1 || 1 || 1 || 28 || 1 || 2 || 1 || 992 || 1 || 1 || 1 || 8128 || 1 || 2 || 1 || 261632 || 1 |- !Θ''n''/''bP''''n''+1 | 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||2×2 || 6 || 1 || 1 || 3 || 2 || 2 || 2 || 2×2×2 || 8×2 || 2 || 24 |- !π''n''''S''/''J'' | 1 || 2 || 1 || 1 || 1 || 2 || 1 || 2 || 2×2 || 6 || 1 || 1 || 3 || 2×2 || 2 || 2 || 2×2×2 || 8×2 || 2 || 24 |- !index | - || 2 || - || - || - || 2 || - || - || - || - || - || - || - || 2 || - || - || - || - || - || - |} [[Media:Spaceform.tiff|link text]] f \colon X \to Y namespace=Main nottitlematch=Main_Page|Sandbox|Links ordermethod=lastedit order=descending minoredits=exclude author=%Diarmuid Crowley% count=10 Just a fest f \colon A \to B. \Q {{beginthm|a theorem}} \label{thma} {{endthm}} \text{Spin} by theorem \ref{thma}
1. Amsterdam
2. Rotterdam
3. The Hague
[[[#{{anchorencode:Mess1990}}|Mess1990]]]{{#RefAdd:Mess1990}} \left( \begin{array}{ll} \alpha & \beta \ \gamma & \delta \end{array} \right) f = T f : X \to Y f : X \to Y \Ker \mathscr{A} \mathscr{B} \bf{ bold} \it{italic} \em{emphasis}
[[Image:Foliation.png|thumb|300px|3-dimensional Reeb foliation]] == Tests == {{citeD|Ranicki1981}} {{cite|Milnor1956}} {{cite|Milnor1956|Theorem 1}} {{citeD|Milnor1956}} {{citeD|Milnor1956|Theorem 1}} {{citeD2|Milnor1956|Frog}} ; {{beginproof}} {{endproof}} == Section == === Subsection === \label{subsection} Refert to subsection \ref{subsection} \begin{theorem} \label{thm} test \end{theorem} Refer to theorem \ref{thm} == Section == ; An [[map-eds:Manifold Atlas:Projects in the Atlas|inter-Wiki link]]. Another Test1 [[map-eds:Manifold Atlas:Projects in the Atlas|inter-Wiki link]]. dfaTest2 ==Footnotes== A = B

Here is a reference to equation 1

## 3 Still testing equation numbering

(2)$C = D$$C = D$

## 4 Lists

1. Frog
$\displaystyle A \xrightarrow{f} B$

$--$$--$

Theorem 5.1 [Penrose&Whitehead&Zeeman1961]. For every compact $m$--dimensional PL-manifold $M$ there exists a PL--embedding $M \hookrightarrow \R^{2m}$.

Remark 5.2. For a good exposition of Theorem 5.1 see also [Rourke&Sanderson1972a, p. 63].

Theorem 5.3 [Whitney1944]. For every closed m--dimensional $C^{\infty}$--manifold $M$ there exists a $C^{\infty}$--embedding $M \hookrightarrow \R^{2m}$.

Theorem 5.5. We have $f \colon X \to Y$

Reference 5.5

By Theorem

$\alpha$(1.2)

(3)$\alpha$eqtest

Theorem 5.6. Frog

3 \ref{eqtest}

Here is some text leading up to an equation

5.7. $$A = B$$

Here is some more text after the equation to see how it looks.

Here is some text leading up to an equation $$A = B$$ Here is some more text after the equation to see how it looks.

4k 8 12 16 20 24 28 32
order bP4k 22.7 25.31 26.127 29.511 210.2047.691 213.8191 214.16384.3617
k 1 2 3 4 5 6 7 8
Bk 1/6 1/30 1/42 1/30 5/66 691/2730 7/6 3617/510

Dim n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
order Θn 1 1 1 1 1 1 28 2 8 6 992 1 3 2 16256 2 16 16 523264 24
bPn+1 1 1 1 1 1 1 28 1 2 1 992 1 1 1 8128 1 2 1 261632 1
Θn/bPn+1 1 1 1 1 1 1 1 2 2×2 6 1 1 3 2 2 2 2×2×2 8×2 2 24
πnS/J 1 2 1 1 1 2 1 2 2×2 6 1 1 3 2×2 2 2 2×2×2 8×2 2 24
index - 2 - - - 2 - - - - - - - 2 - - - - - -

$$f \colon X \to Y$$

Extension DPL (warning): current configuration allows execution of DPL code from protected pages only.

Just a fest $f \colon A \to B$.

$\Q$

a theorem 5.8.

$\text{Spin}$

by theorem 5.8

1. Amsterdam
2. Rotterdam
3. The Hague

[Mess1990]

$\left( \begin{array}{ll} \alpha & \beta \\ \gamma & \delta \end{array} \right)$

$f = T$

$f : X \to Y$

$$f : X \to Y$$

$\Ker$

$\mathscr{A}$ $\mathscr{B}$

bold italic emphasis

</wikitex>

File:Foliation.png
3-dimensional Reeb foliation

## 5 Tests

[Ranicki1981] [Milnor1956] [Milnor1956, Theorem 1] [Milnor1956] [Milnor1956, Theorem 1] Frog

Proof.

$\square$$\square$

## 6 Section

### 6.1 Subsection

Refert to subsection 7.1

Theorem 7.1. test

Refer to theorem 7.1

## 7 Section

$\textup{CW}_0$$\textup{CW}_0$

dfa[2]

1. Test1
2. Test2