My.SUPA

• Ordinary whitespace to be used after a dot not denoting the end of a sentence
• After commands without parameters use \~ (tilde) instead in order to avoid browser specific problems

• \, inserts the smallest predefined space in a formula
• Equivalent: \hspace{2}
• Ex.: $$a\,b$$ gives $a\,b$
• Ex.: $$a~\hspace{2}~b$$ gives also $a~\hspace{2}~b$

• \; (backslash semicolon) inserts the third smallest predefined space in a formula
• Equivalent: \hspace{6}
• Ex.: $$a\;b$$ gives $a\;b$
• Ex.: $$a~\hspace{6}~b$$ gives also $a~\hspace{6}~b$

• \: inserts the second smallest predefined space in a formula
• Equivalent: \hspace{4}
• Ex.: $$a\:b$$ gives $a\:b$
• Ex.: $$a~\hspace{4}~b$$ gives also $a~\hspace{4}~b$

• \/ (backslash slash) avoids ligatures
• Ex.: $$V\/A$$ gives $V\/A$ in contrast to $$VA$$ which gives $VA$

• In order to prevent some browser specific problems with whitespaces, it is advisable to use ~ (tilde) as the whitespace instead of the normal blank key (in places where whitespaces are mandatory, e.g. after commands).
• Ex.: $$\frac~xy$$ to produce $\frac~xy$
• Ex.: $$\sqrt~n$$ to produce $\sqrt~n$

• inserts a space of n pixels
• Ex.: $$f(x)\hspace{6}=\hspace{6}0$$ gives $f(x)\hspace{6}=\hspace{6}0$
• can be combined with the preceding command \unitlength{m}(default: m=1px) , which defines the applied unit
• Ex.: $$\unitlength{20}a\hspace{2}b$$ gives $\unitlength{20}a\hspace{2}b$ , i.e. a space of 20x2=40px

• Everthing following the \LARGE command will be output in the largest predefined font size until the system encounters another font size command.
• Note: This command is case sensitive, since large, Large and LARGE are different sizes! 
• Ex.: $$\LARGE~3x$$ gives $\LARGE~3x$

• Everthing following the \Large command will be output in the second largest font size until the system encounters another font size command.
• Note: This command is case sensitive, since large, Large and LARGE are different sizes! 
• Ex.: $$\Large~3x$$ gives $\Large~3x$

• Everthing following the \large command will be output in the large font size until the system encounters another font size command.
• Note: This command is case sensitive, since large, Large and LARGE are different sizes! 
• Ex.: $$\large~3x$$ gives $\large~3x$

• Everthing following the \normalsize command will be output in the smallest predefined font size until the system encounters another font size command.
• \normalsize is the default font size, i.e. the size automatically chosen if there is no font size command
• Ex.: $$\normalsize~3x$$ gives $\normalsize~3x$

• inserts a double space of current character set size
• Ex.: $$a\qquad~b$$ gives $a\qquad~b$

• inserts a space of current character set size
• Ex.: $$a\quad~b$$ gives $a\quad~b$

• \small
• Ex.: $$\small~3x$$ gives $\small~3x$

• Everthing following the \tiny command will be output in the smallest predefined font size until the system encounters another font size command.
• Ex.: $$\tiny~3x$$ gives $\tiny~3x$

• Syntax: \left<...\right>
• Ex.: $$\left<f,g\right>$$ gives

$\left$

• Type arithmetic operations and "=" as usual.
• Exp.: $$f(x)=x-2b+(3a/c)$$ gives

$f(x)=x-2b+(3a/c)$

• See also keyword "fraction" for extended capabilities.

• Syntax for an n-dimensional array:
  \begin{array}a₁&...&a_n\end{array}
• Ex.: $$$\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array}$$$ gives

$(\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array})$

• Syntax: \left{...\right}
• Ex.: $$M=\left{a, b, c\right}$$ gives

$M=\left{a, b, c\right}$

• Numbers in formulas are interpreted as constants and they are rendered in non-italic roman font face, which is a widely used convention.
• Following this convention, variables are shown in italic.
• Exp.: $$f(x)=3a+x$$ gives

$f(x)=3a+x$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{lowerexpression}^{upperexpression}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for the contour integral symbol:

$$\bigoint_{0}^{\infty}$$   gives  

$\bigoint_{0}^{\infty}$

and

$$\oint_{0}^{\infty}$$   gives 

$\oint_{0}^{\infty}$

• Use font size commands for a nicer picture:

$$\LARGE\bigoint_{\small0}^{\small\infty}$$   gives  

$\LARGE\bigoint_{\small0}^{\small\infty}$

and

$$\large\oint_{\small0}^{\small\infty}$$   gives 

$\large\oint_{\small0}^{\small\infty}$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{lowerexpression}^{upperexpression}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Note: mimeTeX seems currently only to support the \bigcoprod command.
• Syntax for coproduct symbol:

$$\bigcoprod_{i=k}^{n}$$   gives  

$\bigcoprod_{i=k}^{n}$

• Use font size commands for a nicer picture:

$$\LARGE\bigcoprod_{\small{i=k}}^{\small~n}$$   gives  

$\LARGE\bigcoprod_{\small{i=k}}^{\small~n}$

Note: The delimiters are automatically sizes.

• Syntax: \left\|...\right\|
• Exp.: $$\left\|af\right\| = \left|a\right|\left\|f\right\|$$ gives

$\left\|af\right\| = \left|a\right|\left\|f\right\|$

• With two triple $'s embracing an expression you can make the filter to escape and the code itself is shown (with two embracing double $'s).
• Ex.: $$$a^2$$$ produces $$a^2$$, i.e. prevents the filter to render it as a formula gif.

$$\fbox{x=\frac{1}{2}}$$  gives

$\fbox{x=\frac{1}{2}}$

• Syntax: \frac{numerator}{denominator}
• Use font sizing commands for specific sizing if you don't want the predefined one to be taken.
• Ex. (with predefined sizing): $$f(x,y)=\frac{2a}{x+y}$$ gives

$f(x,y)=\frac{2a}{x+y}$

• Ex. (with specific sizing): $$f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$$ gives

$f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$

• You may nest fractions as much as you want.
• Ex. (nested fractions): $$\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$$ gives

$\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$

\arccos \cos \csc \exp \ker \limsup
\arcsin \cosh \deg \gcd \lg \ln
\arctan \cot \det \hom \lim \log
\arg \coth \dim \inf \liminf \max
\sinh \sup \tan \tanh \min \Pr
\sec \sin

$$x>y$$  gives

$x>y$

$$x\ge~y$$ or $$x\geq~y$$ gives

$x\ge~y$

Simply write \greekletter for lower case and \Greekletter for upper case.

Here's a list of all known greek letters (Note: not all upper case greek letters are known):

Lower Case Greek Letters:

Upper Case Greek Letters:

Introduction to LaTeX

LaTeX (pronounced Lay-teck or Laytech) is a text processing language, designed to make it easy to typeset high quality technical documents. In the context of My.SUPA, it makes it easy to include mathematical expressions in forum postings. In this short introduction we'll cover some basic expressions to give you a flavour of the possibilities. There is a huge range of resources available for LaTeX and we'll give a short list of these at the end.

Getting Started - symbols

LaTeX expressions are indicated in My.SUPA by enclosing them in double dollar signs. So, typing $$1+2$$ gives the following LaTeX output: $1+2$. Note that My.SUPA renders the LaTeX commands and creates an image as output.

The first useful thing that LaTeX can do is to translate commands mathematical symbols and characters. For example, $$\omega$$ gives $\omega$. These commands are case sensitive - $$\Omega$$ gives $\Omega$. Search for "greek letters (overview)" in this glossary to find a full list.

Formulae

Useful as using LaTeX to type symbols is, you can also use it to create complex mathematical expressions. In the following example, we'll create a finite integral from 0 to 5 of the function f(x). The command for an integral in LaTeX is \int. We can indicate limits to the integral by using the superscript command, ^, and the subscript command, _ . The complete command is then: $$ \int_0^5 f(x) dx$$:

LaTeX recognises that we want to make 0 a subscript and 5 a superscript. What if we would like to use more than one character for our limits, for example integrating sine(x) in the following example?

In this case we use the following set of commands: $$ \int_0^{2\pi}\sin(x) dx $$. Note that the 2\pi is enclosed in curly brackets to tell LaTeX that we want everything contained within to be made a superscript. We've also used in this example the standard function \sin.

Fractions

To use fractions in LaTeX, we use the command \frac, with 2 sets of curly brackets for the numerator and denominator. For example, $\frac{1}{2}$ is written $$\frac{1}{2}$$. We can combine multiple commands together - for example, the quadratic formula can be written as $$x=\frac{-b\pm\sqrt{ b^2 - 4ac}}{2a}$$:

where \pm gives $\pm$ and \sqrt gives the square root symbol. Notice again how we enclose everything we want under the square root sign in curly brackets.

Matrices

Another useful feature of LaTeX is the ability to format matrices. To demonstrate the different parts of writing a matrix, we'll use the following example:

The code for this is: $$\left(\begin{array}{cccc}a&b&c&d\\e&f&g&h\\i&j&k&l\\m&n&o&p\end{array}\right)$$. You can split this over several lines if you would like, but make sure that you don't put any spaces between the double dollar signs. Working from the outside in:

• \left(... \right): tell LaTeX to put brackets round the enclosed code and to match the size of the brackets to match the contents.
• \begin{array}{cccc} ... \end{array}: tell LaTeX that you're creating a matrix. This is called an environment. {cccc} indicates that you're making a 4 column matrix each of which is centre justified.
• a&b&c&d\\...\m&n&o&p: these are the contents of the matrix. '&' is used as the column separator and '\\' indicates the end of each line. Note that you don't need this at the end of the last line.

Going further

• Latex: A Document Preparation System : User's Guide and Reference Manual, Leslie Lamport, Addison-Wesley, 1994
• The TeXBook, Donald Knuth, Addison-Wesley, 1984
• The Not So Short Introduction to LaTeX: An excellent short primer for LaTeX

If you are interested in using LaTeX away from My.SUPA for creating documents, try some of the following resources:

• The TeX Users Group: A central respository of TeX information, installations and packages
• MiKTeX: A good LaTeX installation for Windows
• MacTeX: A comprehensive LaTeX installation for Mac OS X
• LyX: A LaTeX editor for Windows, Mac OS X and Linux which resembles document processors such as Microsoft Word.

$$\infty$$  gives $\infty$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{lowerexpression}^{upperexpression}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for integral symbol:

$$\bigint_{0}^{\infty}$$   gives  

$\bigint_{0}^{\infty}$

and

$$\int_{0}^{\infty}$$   gives 

$\int_{0}^{\infty}$

• Use font size commands for a nicer picture:

$$\LARGE\bigint_{\small0}^{\small\infty}$$   gives  

$\LARGE\bigint_{\small0}^{\small\infty}$

and

$$\large\int_{\small0}^{\small\infty}$$   gives 

$\large\int_{\small0}^{\small\infty}$

• Syntax: \left{...\right.  (note the dot at the end!)
• Ex.: $$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$ gives

$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$

(\rm~something switches to roman style)

$$<$$   gives

$$x\le~y$$ or $$x\leq~y$$ gives

$x\le~y$

List of predefined spaces:

Note: Simple blank spaces and tildes (~) are ignored by the TeX filter and don't produce any space. You must use one of the defined math spaces to get a visible (extra) space.

• A valid expression inside the $'s is rendered as mathematics in an inserted gif image.
• Ex.: $$x=y^2$$ creates 

$x=y^2$

• An (m,n)-matrix is considered as an array of m*n elements, where the elements of a column are separated by "&" and the rows by "\\".

• Syntax for an (m,n)-matrix:
  \begin{array}{colformat}a₁₁&...&a_1n\\a₂₁&...&a_2n\\... \\a_m1&...&a_mn \end{array}

  where
  colformat defines the format of each of the n columns: l for left, r for right and c for center (hence {ccccc} defines for a (m,5)-matrix in which all columns are centered)

• Ex.: $$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$$ gives

$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$

Note in the example above that "lcr" has the effect that column 1 is left aligned, column 2 centered and colums 3 right aligned.

$$x\neq~y$$ gives

$x\neq~y$

note: \neg produces the logical negation, i.e. $$\neg~A$$ gives

$\neg~A$

$$o$$ gives $o$

(note this exceptional syntax!)

• Syntax: \left(...\right) or $...$
• Ex.: $$2a\left(b+c\right)$$ gives

$2a\left(b+c\right)$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{lowerexpression}^{upperexpression}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for product symbol:

$$\bigprod_{i=k}^{n}$$   gives  

$\bigprod_{i=k}^{n}$

and

$$\prod_{i=k}^{n}$$   gives 

$\prod_{i=k}^{n}$

• Use font size commands for a nicer picture:

$$\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}$$   gives  

$\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}$ 

and

$$\large\prod_{\small{i=k}}^{\small{n}}$$   gives 

$\large\prod_{\small{i=k}}^{\small{n}}$

\begin{fmffile}{schannel}
\begin{fmfgraph*}(100,160)
\fmfpen{thick}
\fmfleftn{i}{2}\fmfrightn{o}{4}
\fmflabel{$e_-$}{i1}\fmflabel{$e_+$}{i2}
\fmflabel{$\noexpand\bar c$}{o1}
\fmflabel{$\nu_{\mu}$}{o2}
\fmflabel{$\mu_+$}{o3}
\fmflabel{$s$}{o4}
\fmf{boson,label=$\gamma,,Z$}{v1,v2}
\fmf{fermion}{i1,v1,i2}
\fmf{fermion}{o1,v2,v3,o4}
\fmffreeze \fmf{boson}{v3,v4}\fmf{fermion}{o3,v4,o2}
\fmfdotn{v}{4}
\end{fmfgraph*}
\end{fmffile}

• Syntax: \left.{...\right}  (note the dot!)
• Ex.: $$\left.{{\rm~term1\atop\rm~term2}\right}=y$$ gives

$\left.{{\rm~term1\atop\rm~term2}\right}=y$

(\rm~something switches to roman style)

• Syntax: \sqrt[n]{arg} or simply  \sqrt{arg} for \sqrt[2]{arg}
• Ex.: $$\sqrt[3]{8}$$ gives

$\sqrt[3]{8}$

• Ex.: $$\sqrt{-1}$$ gives

$\sqrt{-1}$

• Nesting of roots (and combining with fractions, ...etc.) are possible.
• Ex.: $$\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$$ gives

$\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$

• Ex.: $$\sqrt[3]{-q+\sqrt{q^2+p^3}}$$ gives

$\sqrt[3]{-q+\sqrt{q^2+p^3}}$

• Synatx: \left[...\right]
• Ex.: $$\left[a,b\right]$$ gives $\left[a,b\right]$

• $$\sqrt{a}$$ or $$\sqrt~a$$ gives $\sqrt~a$
• Use braces for terms with more than one character: $$\sqrt{x+y}$$ gives

$\sqrt{x+y}$

• The command character "_" triggers subscription of the following expression(s).
• For more than one subscripted character put them in braces {...}.
• Use font sizing commands for appropriate sizing.
• Ex.:$$x_1$$ gives

$x_1$

• Ex.:$$a_{m+2n}$$ gives

$a_{m+2n}$

• Ex. (with specific sizing):  $$x_{\small1}=a_{\small{m+2n}}$$ gives

$x_{\small1}=a_{\small{m+2n}}$

• Combine subscripting with superscripting (command character "^").
  Syntax: Expr_{subExpr}^{supExpr}.
• Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$$ gives

$A_{\small{i,j,k}}^{\small{-n+2}}$

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{lowerexpression}^{upperexpression}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for summation symbol:

$$\bigsum_{i=k}^{n}$$   gives  

$\bigsum_{i=k}^{n}$

and

$$\sum_{i=k}^{n}$$   gives 

$\sum_{i=k}^{n}$

• Use font size commands for a nicer picture:

$$\LARGE\bigsum_{\small{i=1}}^{\small{n}}$$   gives  

$\LARGE\bigsum_{\small{i=1}}^{\small{n}}$

and

$$\large\sum_{\small{i=1}}^{\small{n}}$$   gives 

$\large\sum_{\small{i=1}}^{\small{n}}$

• The command character "^" triggers superscription of the following expression(s).
• For more than one superscripted character put them in braces {...}.
• Use font sizing commands for appropriate sizing.
• Ex.: $$x^2$$ gives

$x^2$

• Ex.: $$a^{m+2n}$$ gives

$a^{m+2n}$

• Ex. (with specific sizing): $$x^{\small2}=a^{\small{m+2n}}$$ gives

$x^{\small2}=a^{\small{m+2n}}$

• Combine superscripting with subscripting (command character "_").
  Syntax: Expr_{subExpr}^{supExpr}.
• Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$$ gives

$A_{\small{i,j,k}}^{\small{-n+2}}$

$ $
\unitlength = 1mm
\begin{fmffile}{tree}
\begin{fmfgraph*}(100,60)
 \fmfleftn{i}{2} \fmfrightn{o}{4}
 \fmflabel{$e_-$}{i1}\fmflabel{$e_+$}{i2}
 \fmflabel{$\mu_+$}{o1}
 \fmflabel{$\nu_{\mu}$}{o2}
 \fmflabel{$s$}{o3}
 \fmflabel{$\noexpand\bar c$}{o4}
 \fmf{fermion}{i1,v1,i2}
 \fmf{boson,label=$\gamma,,Z$}{v1,v2}
 \fmf{boson}{v3,v2,v4}
 \fmf{fermion}{o1,v3,o2}
 \fmf{fermion}{o4,v4,o3}
 \fmfdot{v1,v3,v4}\fmfblob{.12w}{v2}
\end{fmfgraph*}
\end{fmffile}
$ $

• Two double $'s embracing a valid math expression trigger the filter to generate and insert the formula gif.
• Ex.:  $$a^2$$ produces $a^2$
  

• Variables in formulas are rendered in italic roman font face, which is a widely used convention.
• Following this convention, constants are shown as non-italic.
• Exp.: $$f(x)=3a+x$$ gives

$f(x)=3a+x$

• Syntax: \left|...\right|
• Ex.: $$\left|b-a\right|$$ gives $\left|b-a\right|$
• Ex.: $${\rm~det}\left|\begin{array}{cc}a&b\\c&d \end{array}\right|$$ gives  

${\rm~det}\left|\begin{array}{cc}a&b\\c&d \end{array}\right|$ 

 
("\rm~something" renders "something" in roman style)