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/math/ - Mathematics


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25 Dec 2021Mathchan is launched into public

1 / 2 / 1 / ?

File: 3-adic integers with dual colorings.png ( 660.99 KB , 1200x1200 , 1641009124540.png )

Image
This board is for the discussion of mathematics.



Equations can be embedded in multiple ways:
  • \eqn{...}
    or
    \math{...}
    command substitutions
  • \[ ... \]
    or
    \( ... \)
    block substitutions
  • $$ ... $$
    or
    $ ... $
    special block substitutions
  • \begin{equation} ... \end{equation}
    or
    \begin{math} ... \end{math}
    environments
  • by starting a line with
    ,,
    or
    ,eqn
    like one commonly would with >greentext.


Matrices can be embedded by using
\begin{matrix} ... \end{matrix}
or
\begin{array} ... \end{array}
environments in any of the above ways to embed equations, or by starting a line with
,mat
,
,pmat
,
,smat
,bmat
,
,Bmat
,
,vmat
or
,Vmat
and using
&
and
\\
symbols to delineate between columns and rows respectively.

Arrays can be embedded by using
\begin{array}{c|c:c} ... \end{array}
environment in any of the above ways to embed equations, or by starting a line with
,arr{c|c:c}
and using
&
and
\\
symbols to delineate between columns and rows respectively. NOTE:
c|c:c
is only one example of vertical separation (solid and dotted). Horizontal separation can be accomplished by using
\hline
or
\hdashline
after
\\
.

Alignments can be done by using
\begin{aligned} ... \end{aligned}
in any of the above ways to embed equations, or by starting a line with
,align
and then using
\\
symbols to start new lines and using
&
symbol to specify how to align each line (usually, you want it attached to the equals sign, like
&=
).`
>>

File: tikz-cd-doc.pdf ( 264.95 KB , 1641011017028.pdf )

Image
Mathchan supports embedding commutative diagrams:
AaBbcC=D \qquad\begin{CD} A @>a>> B \\ @VbVV @AAcA \\ C @= D \end{CD}

This can be done by using the
\begin{CD} ... \end{CD}
environment in any of the above ways to to embed equations, or by specifying your code after starting a line with
,cd
.

If KaTeX's support is insufficient, diagrams can rendered using the
\tikzcd{...}
command or by using the
\begin{tikzcd} ... \end{tikzcd}
environment.
For example, pasting the following excerpt from the attached PDF (TikZ-CD manual):

\begin{tikzcd}[row sep=scriptsize, column sep=scriptsize]
   & f^* E_V \arrow[dl] \arrow[rr] \arrow[dd] & & E_V \arrow[dl] \arrow[dd] \\
   f^* E \arrow[rr, crossing over] \arrow[dd] & & E \\
   & U \arrow[dl] \arrow[rr] & & V \arrow[dl] \\
   M \arrow[rr] & & N \arrow[from=uu, crossing over]\\
\end{tikzcd}

Will render as the following figure on Mathchan:



The drawback is that you will have to pause typing and wait until the diagram renders while KaTeX can be displayed instantaneously.
It is recommended that you compile any LaTeX code yourself - or in Overleaf - before attempting to paste it on Mathchan.