Math
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Contents
Introduction
TeX was designed for ease of typesetting books that contained mathematics. As ConTeXt is built on top of TeX, it inherits all those features. In addition to these, ConTeXt adds lot of macros to make the typesetting of mathematics easier.
For typesetting of mathematics follows different rules than that of normal text, TeX uses something called "math mode" where some characters get a different meaning to enable a simple syntax for complicated formulas.
Simple Math
Typesetting mathematics can be divided into two parts, inline math (mathematical formulas set within ordinary paragraphs as part of the text) and display math mathematics set on lines by themselves, often with equation numbers). Inline math consists of maths that is typed in a sentence. For example
There are two ways of typing inline math. The TeX way is to surround what you want to type within $
...$
. Thus, the above will be typed as
Pythagoras formula, stating $a^2 + b^2 = c^2$ was one of the first trigonometric results
ConTeXt also provides an alternative way of typing the same result. Instead of dollars, you can write the material for maths inside \mathematics or \math (which is shorter). Thus, an alternate way to type the above is,
Pythagoras formula, stating \mathematics{a^2 + b^2 = c^2} was one of the first trigonometric results
Choose the method that suits your style.
Display math is enclosed in a \startformula / \stopformula pair. Thus
The famous result (once more) is given by \startformula c^2 = a^2 + b^2. \stopformula 
This, when typeset, produces the following:

Numbering Formulae
ConTeXt provides an easy way to number the display maths equations. Simply, put \placeformula before \startformula / \stopformula pair and you will get numbered equations. Thus,
The famous result (once more) is given by \placeformula \startformula c^2 = a^2 + b^2. \stopformula 
This, when typeset, produces the following:

The \placeformula command is optional, and produces the equation number; leaving it off produces an unnumbered equation.
Changing format of numbers
You can use \setupformulas to change the format of numbers. For example to get bold numbers inside square brackets use
\setupformulas[left={[},right={]},numberstyle=bold] 
which gives

To get alphabets instead of numbers, use
\setupformulas[conversion=Character] 
which gives

Referencing formulae
Equations can be referred to by simply adding a label to \placeformula and using \ref to create the reference:
The famous result (and again) is given by \placeformula[formulalabel] \startformula c^2 = a^2 + b^2. \stopformula And now we can refer to formula \ref[formulalabel]. 
This, when typeset, produces the following:

By default, only the formula number appears as a reference. This can be changed by using \definereferenceformat. For example, to create a command \eqref
which shows the formula number in brackets, use
\definereferenceformat[eqref][left=(,right=)]
See References for more examples of \definereferenceformat.
Not so Simple Maths
ConTeXt's base mathematics support is built on the mathematics support in plain TeX, thus allowing quite complicated formulas. (There are also some additional macros, such as the \text command for textmode notes within math.) For instance:
A more complicated equation: \placeformula \startformula {{\theta_{\text{\CONTEXT}}}^2 \over x+2} = \pmatrix{a_{11}&a_{12}&\ldots&a_{1n}\cr a_{21}&a_{22}&\ldots&a_{2n}\cr \vdots&\vdots&\ddots&\vdots\cr a_{n1}&a_{n2}&\ldots&a_{nn}\cr} \pmatrix{b_1 \cr b_2 \cr \vdots \cr b_n} + \sum_{j=1}^\infty z^j \left( \sum_{\scriptstyle n=1 \atop \scriptstyle n \ne j}^\infty Z_j^n \right) \stopformula
which produces
Context provides a wrapper around tex \pmatrix. The above can be typeset in a contextish way as
A more complicated equation: \definemathmatrix[pmatrix][left={\left(\,},right={\,\right)}] \placeformula \startformula {{\theta_{\text{\CONTEXT}}}^2 \over x+2} = \startpmatrix \NC a_{11} \NC a_{12} \NC \ldots \NC a_{1n} \NR \NC a_{21} \NC a_{22} \NC \ldots \NC a_{2n} \NR \NC \vdots \NC \vdots \NC \ddots \NC \vdots \NR \NC a_{n1} \NC a_{n2} \NC \ldots \NC a_{nn} \NR \stoppmatrix \startpmatrix b_1 \NR b_2 \NR \vdots \NR b_n \NR \stoppmatrix + \sum_{j=1}^\infty z^j \left( \sum_{\scriptstyle n = 1 \atop \scriptstyle n \ne j}^\infty Z_j^n \right) \stopformula
Here you can try it "live" (you must go to login first).
Equation alignment is covered on a separate page.
SubFormula Numbering
As mentioned above, formulas can be numbered using the \placeformula command. This (and the related \placesubformula command have an optional argument which can be used to produce subformula numbering. For example:
Examples: \placeformula{a} \startformula c^2 = a^2 + b^2 \stopformula \placesubformula{b} \startformula c^2 = a^2 + b^2 \stopformula 

What's going on here is simpler than it might appear at first glance. Both \placeformula and \placesubformula produce equation numbers with the optional tag added at the end; the sole difference is that the former increments the equation number first, while the latter does not (and thus can be used for the second and subsequent formulas that use the same formula number but presumably have different tags).
This is sufficient for cases where the standard ConTeXt equation numbers suffice, and where only one equation number is needed per formula. However, there are many cases where this is insufficient, and \placeformula defines \formulanumber and \subformulanumber commands, which provide hooks to allow the use of ConTeXtmanaged formula numbers with plain TeX equation numbering. These, when used within a formula, simply return the formula number in properly formatted form, as can be seen in this simple example with plain TeX's \eqno. Note that the optional tag is inherited from \placeformula.
More examples: \placeformula{c} \startformula \let\doplaceformulanumber\empty c^2 = a^2 + b^2 \eqno{\formulanumber} \stopformula 

In order for this to work properly, we need to turn off ConTeXt's automatic formula number placement; thus the \let command to empty \doplaceformulanumber, which must be placed after the start of the formula. In many practical examples, however, this is not necessary; ConTeXt redefines \displaylines and \eqalignno to do this automatically.
For more control over subformula numbering, \formulanumber and \subformulanumber have an optional argument parallel to that of \placeformula, as demonstrated in this use of plain TeX's \eqalignno, which places multiple equation numbers within one formula.
Yet more examples: \placeformula \startformula \eqalignno{c^2 &= a^2 + b^2 &\formulanumber{a} \cr c &= \left(a^2 + b^2\right)^{\vfrac{1}{2}} &\subformulanumber{b}\cr a^2 + b^2 &= c^2 &\subformulanumber{c} \cr d^2 &= e^2 &\formulanumber\cr} \stopformula 

Note that both \formulanumber and \subformulanumber can be used within the same formula, and the formula number is incremented as expected. Also, if an optional argument is specified in both \placefigure and \formulanumber, the latter takes precedence.
More examples for leftlocated equation number: \setupformulas[location=left] \placeformula{d} \startformula \let\doplaceformulanumber\empty c^2 = a^2 + b^2 \leqno{\formulanumber} \stopformula and \placeformula \startformula \leqalignno{c^2 &= a^2 + b^2 &\formulanumber{a} \cr a^2 + b^2 &= c^2 &\subformulanumber{b} \cr d^2 &= e^2 &\formulanumber\cr} \stopformula 

 23:46, 15 Aug 2005 (CEST) Prinse Wang
If you want named subformula with a reference see the solution proposed by Aditya Mahajan on the mailinglist [1] (20061029). This feature should be added to the core eventually.
List of Formulas
You can have a list of the formulas contained in a document by using \placenamedformula instead of \placeformula. Only the formulas written with \placenamedformula are not put in the list, so that you can control precisely the content of the list.
\placenamedformula takes as first parameter the name of the formula put in the list. The other \placeformula features are still available. The list can be formatted like any other list.
Example:
\subsubject{List of Formulas} \placelist[formula][criterium=text,alternative=c] \subsubject{Formulas} \placenamedformula[one]{First listed Formula} \startformula a = 1 \stopformula \endgraf \placeformula \startformula a = 2 \stopformula \endgraf \placenamedformula{Second listed Formula}{b} \startformula a = 3 \stopformula \endgraf
Gives:
Other Methods
 There are two different math modules on CTAN, nath and amsl. And there's a new math module in the distribution.
 Context now has inbuilt support for Multiline equations
 It is also possible to use most LaTeX equations in ConTeXt with a relatively small set of supporting definitions.
 The "native" ConTeXt way of math is MathML, an application of XML  rather verbose but mighty.
Number Formatting
There's a special command, \digits, and a own manual about formatting numbers, see Pasting digits together
Math Fonts
 Bold Math
 Euler in ConTeXt (using Euler math font) by Adam Lindsay
 rsfs Using Ralph Smith's Formal Script
 doublestroke Using Double Stroke Font
 Product integral symbol