This page references Wikidot's syntax documentation.
 Headings
 Formatting
 Links
 Equations
 Citations
 Collapsibles
 Footnotes
 Quotes
 Tabs
 Tables
 Theorems & Definitions
 Incomplete Sections
Table of contents can be added using [[toc]]
Headers:
Heading Level 1
+ Heading Level 1
Heading Level 2
++ Heading Level 2
Heading Level 3
+++ Heading Level 3
Heading Level 4
++++ Heading Level 4
Heading Level 5
+++++ Heading Level 5
Basic formatting:
Syntax  Example 

**Bold**  Bold 
//Italics//  Italics 
__Underline__  Underline 
Strikethrough  Strikethrough 
{{Teletype (Monospaced)}}  Teletype (Monospaced) 
Text^^Superscript^^  Text^{Superscript} 
Text,,Subscript,,  Text_{Subscript} 
[[span style="color:red"]]//span// Inline Element[[/span]]  span Inline Element 
##bluePredefined## or ##0000FFHex Color Code##  Predefined or Hex Color Code 
@ @ Escape Parsing {{Example}} @ @  Escape Parsing {{Example}} 
*Note that to escape parsing, there should be no spaces between the two @'s and the text. It is written as above due to @@ failing to escape parsing for itself.
Changing text size and alignment is also possible:
Syntax  Example 

[[size smaller]]Smaller Text[[/size]]  Smaller Text 
[[size larger]]Larger Text[[/size]]  Larger Text 
[[size 80%]]80% Of Current Size[[/size]]  80% Of Current Size 
[[size 100%]]100% Of Current Size[[/size]]  100% Of Current Size 
[[size 150%]]150% Of Current Size[[/size]]  150% Of Current Size 
[[size 0.8em]]80% Of Current Size[[/size]]  80% Of Current Size 
[[size 1em]]100% Of Current Size[[/size]]  100% Of Current Size 
[[size 1.5em]]150% Of Current Size[[/size]]  150% Of Current Size 
Setting the size directly:
Syntax  Example 

[[size xxsmall]]ExtraExtraSmall Text[[/size]]  ExtraExtraSmall Text 
[[size xsmall]]ExtraSmall Text[[/size]]  ExtraSmall Text 
[[size small]]Small Text[[/size]]  Small Text 
[[size large]]Large Text[[/size]]  Large Text 
[[size xlarge]]ExtraLarge Text[[/size]]  ExtraLarge Text 
[[size xxlarge]]ExtraExtra Large Text[[/size]]  ExtraExtra Large Text 
[[size 7px]]Text Size 7 Pixels[[/size]]  Text Size 7 Pixels 
[[size 18.75px]]Text Size 18.75 Pixels[[/size]]  Text Size 18.75 Pixels 
Aligning text left or right:
Syntax:
[[<]]
Align text left.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
[[/<]]
[[>]]
Align text right.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
[[/>]]
[[=]]
Align text center.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
[[/=]]
[[==]]
Align text justified.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
[[/==]]
Example:
Align text left.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
Align text right.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
Align text center.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
Align text justified.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean a libero. Vestibulum adipiscing, felis ac faucibus imperdiet, erat lacus accumsan neque, vitae nonummy lorem pede ac elit.
Maecenas in urna. Curabitur hendrerit risus vitae ligula.
Aligning a single line:
= Line in center
Line in center
URLs will automatically become links:
https://example.com/  https://example.com/
To link specific words or phrases, use the following:
[https://en.wikipedia.org/wiki/Apple_Pie apple pie]  apple pie
Pages within the wiki can be linked to directly with just the title, if the url and title are the same (i.e. the page title that Wikidot generates based on the url you use, noncase sensitive):
[[[Cotangent Bundle]]] is a vector bundle.  Cotangent Bundle is a vector bundle
If they differ, you specify the url and then give your own title:
...simplicial homology is also used in [[[Topological Data Analysisdata analysis]]].  …simplicial homology is also used in data analysis.
Adding an asterisk (*) in front of the url opens the link in a new window:
*https://example.com/  https://example.com/
[*https://example.com/ Example Page]  Example Page
Equations can be rendered in LaTeX using [[$<latex>$]] and [[$$<latex>$$]] escapes.
Inline latex:
Let [[$a,b \in G$]]  Let $a,b \in G$
While,
One observes that for all [[$\alpha, \beta$]], we have: [[$$X_\alpha \cap X_\beta \iff X_\beta \subseteq X_\alpha$$]]
Produces:
One observes that for all $\alpha, \beta$, we have: $$X_\alpha \cap X_\beta \iff X_\beta \subseteq X_\alpha$$
You can simply put the equation between [[math label]] โฆ [[/math]] block tags (the label is optional). The equation is rendered within LaTex \begin{equation} … \end{equation} environment. Please refer to any LaTeX reference manual for details about syntax.
[[math label1]]
\rho _{\rm GJ} = \sigma (r) \left[ (1  \eta _{\ast }^2 {\kappa \over {\eta ^3}}) \cos \chi \right.
+ \left. {3\over 2} \theta (\eta) H(\eta)
\xi \sin \chi \cos \phi \right]
[[/math]]
Produces:
(1)The bibliography block is defined by [[bibliography]]...[[/bibliography]]. Each bibliography item has the form:
label : full reference
To cite a bibliography entry use ((bibcite label)).
The first pulsar was observed by J. Bell and A. Hewish [((bibcite bell))]. Another reference [see ((bibcite guy))].
[[bibliography]]
: bell : Bell, J.; Hewish, A.; Pilkington, J. D. H.; Scott, P. F.; and Collins, R. A. //Observation of a Rapidly Pulsating Radio Source.// Nature 217, 709, 1968.
: guy : Guy, R. K. //Modular Difference Sets and Error Correcting Codes.// ยงC10 in Unsolved Problems in Number Theory, 2nd ed. New York: SpringerVerlag, pp. > 118121, 1994.
[[/bibliography]]
Produces:
The first pulsar was observed by J. Bell and A. Hewish [1]. Another reference [see 2].
Collapsibles are for hiding long blocks of text to prevent the page from getting too long. The hidden text appears once you click on the collapsible link:
[[collapsible show="+ Open" hide=" Close"]]
Collapsed text here
[[/collapsible]]
The collapsible show/hide text is "+ show block" and " hide block" by default, if no show/hide is specified.
For long text blocks, use "hideLocation="both"" to show the hide link at the bottom of the block as well:
[[collapsible hideLocation="both" show="+ Open" hide=" Close"]]
Longer
Collapsed
Text
Here
[[/collapsible]]
Footnotes are good for inserting more information into text without cluttering the text:
Content[[footnote]]Footnote content[[/footnote]]. More content[[footnote]]More footnote content[[/footnote]].
Inserting [[footnoteblock]] determines the position of the footnotes. Otherwise, footnotes will appear at the bottom of the page:
Content^{1}. More content^{2}.
Quoteblocks are handy for inserting text that comes from notes, or just to insert long quotes:
> Quote
>
> More quote
Quote
More quote
Note that there is a "> " to insert the empty line, and a space after the second ">" bracket; without those, the empty line isn't there:
> Quote
>
> More quote
Quote
More quote
> Quote
> More quote
Quote
More quote
In addition to the Wikidot standard blockquotes, there is another way to create the same effect:
[[div class="blockquote"]]
Quote
[[/div]]
Quote
This style of quoteblock saves you the trouble of needing to start every line with a ">" and also lets authors include code that normally doesn't work with the standard quoteblocks.
You are reading this in tabs. Tabs are great for a variety of uses.
[[tabview]]
[[tab Tab 1]]
Contents of tab 1
[[/tab]]
[[tab Tab 2]]
Contents of Tab 2
[[/tab]]
[[tab Tab 3]]
Contents of Tab 3
[[/tab]]
[[/tabview]]
Tabs can be nested within tabs, but the most obvious method (putting a [[tabview]] within another [[tabview]]) will not work. There is a specific method required for nesting tabs, but I don't recommend doing it due to readability issues. Just make another sandbox page at that point.
Tables can be useful for entries with a large number of component entities:
~ TITLEFORMATTED CELL ~ TITLEFORMATTED CELL ~ TITLEFORMATTED CELL 
 Nonformatted cell  Nonformatted cell  Nonformatted cell 
< Leftaligned cell < Leftaligned cell < Leftaligned cell 
> Rightaligned cell > Rightaligned cell > Rightaligned cell 
= Centeraligned cell = Centeraligned cell = Centeraligned cell
TITLEFORMATTED CELL  TITLEFORMATTED CELL  TITLEFORMATTED CELL 

Nonformatted cell  Nonformatted cell  Nonformatted cell 
Leftaligned cell  Leftaligned cell  Leftaligned cell 
Rightaligned cell  Rightaligned cell  Rightaligned cell 
Centeraligned cell  Centeraligned cell  Centeraligned cell 
Adding more cell separators () before the cell's text will make the cell span multiple columns based on how many cell separators you used:
~ Cell title ~ Cell title ~ Cell title 
 Cell spanning one column  Cell spanning two columns 
 Cell spanning three columns
Cell title  Cell title  Cell title 

Cell spanning one column  Cell spanning two columns  
Cell spanning three columns 
On this wiki in particular, it is possible to create vanity boxes for popular theorems and definitions. These are most useful if created as their own pages starting with theorem:<theoremname> and definition:<definitionname>.
For instance, here is a page containing a box for the Van Kampen theorem: theorem:vankampen which is then included on the page about Van Kampen Theorem proper.
Once a unique theorem:<theoremname> or definition:<definitionname> page is created it can be included with a regular [[include theorem<theoremname>]] escape. For example:
[[include theorem:vankampen]]
Produces:
Creating New Theorem Box
New theorem boxes can be created as their own pages. For instance a page for the Equipartition Theorem box would be theorem:equipartition then included into relevant pages as [[include theorem:equipartition]] escape.
[[include inc:theorem
title=Equipartition Theorem
body=For a system with a [[[Hamiltonian]]] [[$H(\mathbf{p}, \mathbf{q})$]] with generalized coordinates [[$\mathbf{q}$]] and momenta [[$\mathbf{p}$]]:[[$$\left\langle q_i \frac{\partial H}{\partial p_i} \right\rangle = k T$$]] for each quadratic degree of freedom, where [[$\langle \cdot \rangle$]] denotes the canonical [[[ensemble average]]].
]]
Produces:
Theorem. For a system with a Hamiltonian $H(\mathbf{p}, \mathbf{q})$ with generalized coordinates $\mathbf{q}$ and momenta $\mathbf{p}$:$$\left\langle q_i \frac{\partial H}{\partial p_i} \right\rangle = k T$$ for each quadratic degree of freedom, where $\langle \cdot \rangle$ denotes the canonical ensemble average. 
Creating new Definition Box
Similarly,
[[include inc:definition
title=[[[Regular Cell Complex]]] 
body=A //regular cell complex// is a topological space [[$X$]] partitioned into subspaces [[$\{X_\alpha\}_{\alpha\in PX}$]] satisfying the following conditions:
# For each [[$x \in X$]], every sufficiently small neighborhood of [[$x$]] intersects finitely many [[$X_\alpha$]].
# For all [[$\alpha, \beta$]], [[$X_\alpha \cap X_\beta \neq \emptyset$]] only if [[$X_\beta \subseteq X_\alpha$]].
# Every [[$X_\alpha$]] is homeomorphic to [[$\mathbb{R}^{n_\alpha}$]] for some [[$n_\alpha$]].
# For every [[$\alpha$]], there is a homeomorphism of a closed ball in [[$\mathbb{R}^{n_\alpha}$]] to [[$X_\alpha$]] that maps the interior of the ball homeomorphically onto [[$X_\alpha$]].]]
Will produce:
Definition. Regular Cell Complex: A regular cell complex is a topological space $X$ partitioned into subspaces $\{X_\alpha\}_{\alpha\in PX}$ satisfying the following conditions:

You can add [[include wiki:box:todo]] to signify unfinished sections.
[[include wiki:box:todo]]
Produces:
TODO
This section has been left to be completed at a later date. You can help by editing it.