chango369 wrote:Pulsar's Latex Tutorial part 2 - reboot

Pulsar wrote:

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[latex]\textbf{A }\mathbf{\LaTeX\ }\textbf{Tutorial, part 2}[/latex]

Greek letters

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[latex]\begin{align}
& \alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta
\vartheta \iota \kappa \varkappa \lambda \mu \nu \xi \omicron \pi \varpi \rho \varrho \sigma \varsigma \tau
\upsilon \phi \varphi \chi \psi \omega\\
& \Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega
\end{align}[/latex]

Miscellaneous symbols

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[latex]\aleph \quad \hbar \quad \infty \quad \partial \quad \nabla \quad \Im \quad \Re \quad \forall \quad
\exists \quad \nexists \quad \emptyset \quad \varnothing \quad \square \quad \triangle \quad \triangledown \quad \prime  \quad \backprime \quad \sphericalangle[/latex]

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[latex]\& \quad \_ \quad \#  \quad \$ \quad  \%[/latex]

Standard function names

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[latex]\begin{align}
&\sin \quad \cos \quad \tan \quad \exp \quad \lim \quad \min \quad \max \quad \sinh \quad \arcsin \quad\\
&\deg \quad \log \quad \ln  \quad \sup  \quad \inf  \quad \arg \quad \cot \quad \det \quad \gcd \quad \mod
\end{align}[/latex]

And various others.

Binary symbols

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[latex]\leq \quad \leqslant \quad \geq \quad \geqslant \quad \neq \quad \sim \quad
\simeq \quad \approx \quad \propto \quad \cong \quad \equiv \quad \ll \quad \gg \quad \perp[/latex]

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[latex]\times  \quad  \div \quad \pm \quad \mp \quad \cdot \quad \ast \quad \star \quad
\odot \quad \oplus \quad \ominus  \quad \otimes \quad \Box \quad \lhd \quad \rhd[/latex]

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[latex]\wedge \quad \vee \quad \subset \quad \supset \quad \in \quad \ni \quad \notin \quad \cup
\quad \cap \quad \setminus \quad \backslash \quad \therefore \quad \because \quad \bullet \quad \diamond[/latex]

Dots

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[latex]1,2,\ldots,10 \qquad
a_1 + a_2 + \cdots + a_n \qquad
\vdots \qquad \ddots[/latex]

chango369 wrote:Pulsar's Latex Tutorial Part 3 - reboot

Pulsar wrote:

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[latex]\textbf{A }\mathbf{\LaTeX\ }\textbf{Tutorial, part 3}[/latex]

Arrows

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[latex]\begin{align}
&\leftarrow \quad \longleftarrow \quad \Leftarrow \quad \Longleftarrow \quad
\rightarrow \quad \longrightarrow \quad \Rightarrow \quad \Longrightarrow  \quad
\overleftarrow{abc} \quad \overrightarrow{abc} \\
&\leftrightarrow \quad \longleftrightarrow \quad \Leftrightarrow \quad \Longleftrightarrow \quad
\leftrightarrows \quad \leftleftarrows \quad \rightrightarrows \quad
\uparrow \quad \Uparrow \quad \downarrow \quad \Downarrow \quad \updownarrow \quad \Updownarrow
\end{align}[/latex]

If you want an arrow with additional text, use \xleftarrow or \xrightarrow. Be aware of the precise format: text below is placed between square brackets [] and can be omitted, while text above is placed between mandatory curly brackets {}.

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[latex]\xrightarrow{\text{above the arrow}} \qquad
\xleftarrow[\text{below}]{}\qquad
\xrightarrow[\text{below}]{\text{above the arrow}}[/latex]

In combination with the \lim operator, you can write something like this:

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[latex]\lim_{x \rightarrow +\infty} f(x) = 0[/latex]

This doesn't look very pretty, but it can be tidied up by enclosing the equation by a \displaystyle{} environment:

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[latex]\displaystyle{
\lim_{x \rightarrow +\infty} f(x) = 0}[/latex]

Various operators

Again, use \displaystyle{} for nice results:

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[latex]\displaystyle{
\sum \quad \sum_{i=1}^{n} \quad \sum_{\substack{i,j \\ i > j}} \quad \prod \quad \prod_{n=0}^{\infty} \quad \coprod
\quad \int \quad \int_0^1 \quad \oint \quad \iint \quad \iiint \quad \sqrt{x} \quad \sqrt[3]{26}
}[/latex]

Note the \substack{} command in the third sum, to stack multiple limits. Fractions and binomials looks as follows, without and with \displaystyle{}:

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[latex]\frac{1}{2} \quad \binom{n}{k}
\qquad
\displaystyle{\frac{1}{2} \quad \binom{n}{k}}[/latex]

Brackets

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[latex]\displaystyle{
() \quad [] \quad \{ \} \quad | \quad \langle \rangle \quad \lfloor \rfloor \quad \lceil \rceil \quad \Vert
}[/latex]

Note the backslash in \{ and \} to produce curly brackets. The size of these delimiters can be increased manually by preceding them with \big, \Big, \bigg or \Bigg. You can also let Latex determine an appropriate size, by using \left and \right. However, every \left delimiter has to be followed by a similar \right delimiter; in case you want only one delimiter, use a dot for the other, i.e. \left. or \right. to generate an empty delimiter. See the examples:

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[latex]\displaystyle{\Bigg( \bigg( \Big( \big( () \big) \Big) \bigg) \Bigg)
\qquad \left(\frac{a}{b}\right) \qquad \left[\frac{A}{B} + \left( C + \sqrt{D}\right) \right]
\qquad \left\langle\left. \psi_1 \right. \right|}[/latex]

The \underbrace{} and \overbrace{} commands produce

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[latex]\underbrace{\underbrace{a + b}_\text{brace 1} +\overbrace{c + d}^\text{brace 2}}_\text{brace 3}= e[/latex]

chango369 wrote:Pulsar's Latex Tutorial Part 4 - reboot

Pulsar wrote:

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[latex]\textbf{A }\mathbf{\LaTeX\ }\textbf{Tutorial, part 4}[/latex]

Equations

I've used the \begin{align} \end{align} environment several times already, without discussing its use: with align, you can type multiple, aligned equations. The ampersand & serves as a tab stop; usually, you want the lines to be aligned on the equation sign:

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[latex]\begin{align}
\binom{5}{3} &= \frac{5!}{2!\; 3!}\\
&= \frac{5\cdot 4 \cdot 3 \cdot 2}{3 \cdot 2 \cdot 2}\\
&= 10
\end{align}[/latex]

You can also align two sets of equation side by side, as follows:

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[latex]\begin{align}
y & =d & z & =1\\
y & =cx+d & z & =x+1
\end{align}[/latex]

If you want even more, use the alignat environment. It has a parameter denoting the amount of aligned columns. Here's an example with three:

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[latex]\begin{alignat}{3}
i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\\
i_{21} & =-i_{11} & i_{22} & =0.5\,i_{12}& i_{23} & =i_{31}\\
i_{31} & =0.33\,i_{22}\qquad & i_{32} & =0.15\,i_{32}\qquad & i_{33} & =i_{11}
\end{alignat}[/latex]

Alternatively, you can centre equations rather than align them. To do this, use the gather environment.

NOTE: I couldn't get the original code to generate an image.

Original code:

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[latex]\begin{gather}\displaystyle{
\Gamma(x) = \int_0^{+\infty} t^{x-1} \, \text{e}^{-t} \, \text{d}t\\
B(x,y) = \int_0^1 t^{x-1}\,(1-t)^{y-1}\,\text{d}t}
\end{gather}[/latex]

So I switched the way the gather and displaystyle were nested with respect to one another.

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\begin{gather}\displaystyle{
\Gamma(x) = \int_0^{+\infty} t^{x-1} \, \text{e}^{-t} \, \text{d}t\\
B(x,y) = \int_0^1 t^{x-1}\,(1-t)^{y-1}\,\text{d}t}
\end{gather}

Long equations can be split with the multline environment. In the example below, you see that the \left( bracket has to be followed by a \right. (an invisible right bracket) at the end of the first line, otherwise Latex will raise an error. Likewise, the second line starts with \left. (an invisible left bracket) and ends with \right).

However, to ensure that the closing \right) is as big as the opening \left( , we need another trick: the command \vphantom{} inserts an invisible vertical space, given by the text inside the brackets - analogous to the horizontal \phantom{}. On the first line, the summation \sum_{i<j} is the largest symbol, so \vphantom{\sum_{i<j}} inserts an equally large, but invisible symbol on the second line, which guarantees that \left( and \right) are of the same size.

I had a similar problem with the original code.

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[latex]\displaystyle{\begin{multline}
\frac{1}{2}\Delta(f_{ij}f^{ij}) = 2\left( \sum_{i<j}\chi_{ij}(\sigma_{i} -
\sigma_{j})^{2} + f^{ij}\nabla_{j}\nabla_{i} (\Delta f) + \right.\\
\left. + \nabla_{k}f_{ij}\nabla^{k}f^{ij} + f^{ij}f^{k}\left[2\nabla_{i}R_{jk} -
\nabla_{k}R_{ij}\right] \vphantom{\sum_{i<j}}\right)
\end{multline}}[/latex]

So I reversed the nesting order of multline and displaystyle

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[latex]
\begin{split}\displaystyle{
\frac{1}{2}\Delta(f_{ij}f^{ij}) = 2\left( \sum_{i<j}\chi_{ij}(\sigma_{i} -
\sigma_{j})^{2} + f^{ij}\nabla_{j}\nabla_{i} (\Delta f) + \right.\\
\left. + \nabla_{k}f_{ij}\nabla^{k}f^{ij} + f^{ij}f^{k}\left[2\nabla_{i}R_{jk} -
\nabla_{k}R_{ij}\right] \vphantom{\sum_{i<j}}\right)
}\end{split}[/latex]

NOTE TO PULSAR: I had to replace multline with split in order to get the effect I think you were looking for.

chango369 wrote:Pulsar's Latex Tutorial Part 5 - reboot

Pulsar wrote:

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[latex]\textbf{A }\mathbf{\LaTeX\ }\textbf{Tutorial, part 5}[/latex]

Math styles

Symbols can be displayed in one the following styles: \displaystyle{} (for standalone equations), \textstyle{} (for equations in a sentence), \scriptstyle{} (for e.g. sub- and superscripts), and \scriptscriptstyle{} (for e.g. subsub- and supersuperscripts). Latex scales sub- and superscripts automatically, but occasionally the explicit commands \scriptstyle{} and \scriptscriptstyle{} are handy in other situations.

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[latex]\displaystyle{\int_0^1 f}\qquad \textstyle{\int_0^1 f} \qquad
\scriptstyle{aA} \qquad \scriptscriptstyle{aA}[/latex]

NOTE TO PULSAR: I had a problem with the \textstyle that was part of your original code, so I took it out

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[latex]\displaystyle{\int_0^1 f}\qquad {\int_0^1 f} \qquad
\scriptstyle{aA} \qquad \scriptscriptstyle{aA}[/latex]

Text and Symbol size

The above styles define relative symbol sizes, which depend on the environment in which they are used. Latex also allows to manually change text font sizes, with the \tiny{}, \scriptsize{}, \small{}, \normalsize{}, \large{}, \Large{}, \LARGE{}, \huge{}, and \Huge{} commands. Surprisingly, MathJax also allows the use of these commands inside formulae.

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[latex]\tiny{a}\scriptsize{a}\small{a}\normalsize{a}\large{a}\Large{a}\LARGE{a}\huge{a}\Huge{a}[/latex]

Text boxes

Normal text can be written inside \text{}. Alternatively, there is the \mbox{} environment, which is almost the same as \text{}. However, unlike the \text{} command, text inside an \mbox{} does not scale when it is part of a sub- or superscript. Math symbols can be used inside a box by putting it between $ signs; unfortunately MathJax doesn't seem to allow any commands inside a textbox.

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[latex]\mbox{this works $\forall n \in \mathbb{N} \backslash \{ 0 \}$, I think}[/latex]

NOTE: I'm not sure the image below is being rendered correctly!



\fbox{} is similar to \mbox, but draws a frame around the text.

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[latex]f_\text{sim} \qquad f_\mbox{sim} \qquad \fbox{text inside a frame}[/latex]

A more general command to draw frames is \boxed{}, which can be used around any formula.

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[latex]\boxed{\displaystyle{ f(x) = \int \frac{\sin x}{x}\,\text{d}x} }[/latex]

Unfortunately, MathJax does not support more advanced text boxes, like \makebox{} and \parbox{}. This makes it difficult to write multi-line text; possible tricks are stacking text, or using arrays (see below)

Stacking symbols and text

There are various ways to stack two lines of symbols or text on top of each other. The \substack{} command was used before, but there's also the slightly different { \atop } command.

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[latex]\text{stacking }\substack{a \\ b}\qquad {a \atop b}[/latex]

The size of the symbols is automatically decreased; to change these sizes to normal, put the symbols inside \displaystyle{}. With the \underset{}{} and \overset{}{} commands, you can put smaller-sized symbols or text below/above a normal line:

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[latex]a = \underset{below}{base}\qquad \overset{above}{base} = b[/latex]

A similar command is \stackrel{}{}, which puts normal-sized symbols/text on top of a normal line.

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[latex]a \stackrel{\text{def}}{=} b[/latex]

\stackrel might help to define new symbols. For instance, MathJax does not support the Angstrom symbol, so we could create one as follows:

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[latex]\text{an ugly }\stackrel{\scriptsize{\circ}}{\text{A}}\text{ symbol}[/latex]

This doesn't look very pretty. Fortunately, there's the \mathring{} command, which I forgot to mention among the accents:

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[latex]\text{this is better: } $\mathring{\text{A}}$[/latex]

NOTE: Adding in \dot example

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[latex]\text{this is better: } \dot{\text{A}}[/latex]

I've mentioned the fraction command \frac{}{} before, but the related \tfrac{}{} and \dfrac{}{} are also worth pointing out: they set the font size to small and normal, respectively:

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[latex]\frac{a}{b} \qquad \tfrac{a}{b}  \qquad \dfrac{a}{b}  \qquad T^\frac{a}{b}  \qquad T^\tfrac{a}{b} \qquad T^\dfrac{a}{b}[/latex]

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[latex]\displaystyle{ \frac{a}{b} \qquad \tfrac{a}{b}  \qquad \dfrac{a}{b}  \qquad T^\frac{a}{b}  \qquad T^\tfrac{a}{b} \qquad T^\dfrac{a}{b} }[/latex]

chango369 wrote:Pulsar's Latex Tutorial Part 6 - reboot

Pulsar wrote:

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[latex]\textbf{A }\mathbf{\LaTeX\ }\textbf{Tutorial, part 6}[/latex]

Colors

MathJax allows different colors, with the command \color{color}{text} (this syntax is different from standard Latex). I don't know which colors are permitted, but all of these work ( NO THEY DON'T ), and probably more:

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[latex]\color{red}{b} \color{darkred}{b} \color{pink}{b} \color{blue}{b} \color{lightblue}{b} \color{green}{b} \color{darkgreen}{b} \color{yellow}{b} \color{orange}{b} \color{cyan}{b} \color{magenta}{b} \color{violet}{b} \color{purple}{b} \color{brown}{b} \color{white}{b} \color{grey}{b} \color{black}{b}[/latex]

NOTE: Some of colors didn't render.



Arrays

The \begin{array}{} \end{array} environment is very useful to create content in several rows and columns. Each column can be left-, right- or center- aligned, which has to be specified with l,r,c respectively inside the brackets following \begin{array}. For example, \begin{array}{l r c} starts an array with three columns; column 1 is left-aligned, column 2 is right-aligned and column 3 is center-aligned. Columns are separated with the ampersand & symbol, and a row is ended by a linebreak \\. Two common examples are

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[latex]f(n) = \left\{
\begin{array}{l l}
n/2 & \quad \mbox{if $n$ is even}\\ 
-(n+1)/2 & \quad \mbox{if $n$ is odd}
\end{array}
\right.[/latex]

and matrices

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[latex]A_{m,n} =
\left(
\begin{array}{cccc} 
a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ 
a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ 
\vdots  & \vdots  & \ddots & \vdots  \\ 
a_{m,1} & a_{m,2} & \cdots & a_{m,n}
\end{array}
\right)[/latex]

In fact, these examples are so common that Latex contains special commands for them: the first example can be written with the \begin{cases} \end{cases} environment, which also takes care of the initial left bracket (and notice that the lines are slightly closer to each other). No column format specification is needed: cases always defines two left-aligned columns.

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[latex]f(n) =
\begin{cases}
n/2 & \quad \mbox{if $n$ is even}\\ 
-(n+1)/2 & \quad \mbox{if $n$ is odd}
\end{cases}[/latex]

Matrices can be defined with the \begin{pmatrix} \end{pmatrix} environment, which includes the parentheses, and defines every column as center-aligned:

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[latex]A_{m,n} = \begin{pmatrix}  a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\  a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\  \vdots  & \vdots  & \ddots & \vdots  \\  a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix}[/latex]

[img]http://latex.numberempire.com/render?A_%7Bm%2Cn%7D%20%3D%20%5Cbegin%7Bpmatrix%7D%20%20a_%7B1%2C1%7D%20%26%20a_%7B1%2C2%7D%20%26%20%5Ccdots%20%26%20a_%7B1%2Cn%7D%20%5C%5C%20%20a_%7B2%2C1%7D%20%26%20a_%7B2%2C2%7D%20%26%20%5Ccdots%20%26%20a_%7B2%2Cn%7D%20%5C%5C%20%20%5Cvdots%20%20%26%20%5Cvdots%20%20%26%20%5Cddots%20%26%20%5Cvdots%20%20%5C%5C%20%20a_%7Bm%2C1%7D%20%26%20a_%7Bm%2C2%7D%20%26%20%5Ccdots%20%26%20a_%7Bm%2Cn%7D%20%5Cend%7Bpmatrix%7D&sig=a25bb9b35dfe77e3a6cb1f2113be1fc0/img]

Apart from pmatrix, there are also matrix, bmatrix, vmatrix, Bmatrix, Vmatrix, and smallmatrix.

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[latex]\begin{matrix} a & b \\ c & d \end{matrix}\qquad
\begin{bmatrix} a & b \\ c & d \end{bmatrix}\qquad
\begin{vmatrix} a & b \\ c & d \end{vmatrix}\qquad
\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}\qquad
\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}\qquad
\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}[/latex]

With the array environment, one can simulate multi-line text:

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[latex]\begin{array}{r}
\text{Right-aligned}\\
\text{text, nothing}\\
\text{really important}
\end{array}
\quad \textit{and} \quad
\begin{array}{c}
\text{Center-aligned}\\
\text{text, nothing}\\
\text{really important}
\end{array}
\quad \textbf{and} \quad
\begin{array}{l}
\text{Left-aligned}\\
\text{text, nothing}\\
\text{really important}
\end{array}[/latex]

This example also contains the \textit{} and \textbf{} commands, to write italics and bold text.

Finally, the array environment can serve to create a simple table. One can add vertical lines by adding | symbols in the column format header, and horizontal lines with the \hline command inside the array.

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[latex]\begin{array}{|c|r|}
\text{symbol} & \quad\text{value} \\
\hline
\pi & 3.1415 \\
e & 2.7182
\end{array}[/latex]

-------------------------------------------------------------------------

I think I have now covered most of the Latex formatting that is currently possible with MathJax.

A full overview of Latex commands supported by MathJax can be found here:

http://www.mathjax.org/docs/1.1/tex.html#supported-latex-commands

If you have any comments, questions or additions, feel free to post!

Evolving wrote:That's very cool: thank you for the recommendation!

Only thing: it doesn't seem to want to let me move to the next line. This was supposed to be two formulae on separate lines:

CodeCogsEqn.gif

But obviously I can save a separate GIF for each line.

It's a great improvement on not being able to use Latex at all!