Multiline equations

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Be sure to also read 2010 - Using \startalign and friends written by Aditya Mahajan (My Way article).

Basic Alignment with \startalign

\startformula\startalign
 \NC v \NC = u + at \NR
 \NC h \NC = ut + \frac12 gt^2 \NR
\stopalign\stopformula

\NC stands for new column, \NR stands for new row.

Changing the number of columns

The above equations were aligned at =. Suppose you also want the + to align. Well, this is simple in context, simply specify the number of columns with \startalign

\startformula \startalign[n=3]
 \NC v \NC = u  \NC + at \NR
 \NC h \NC = ut \NC + \frac12 gt^2 \NR
\stopalign \stopformula

Equation numbering with \startplaceformula

Aligned equations can be numbered by using \startplaceformula (as usual), and by placing a tag after \NR

\setuplayout[scale=0.8,width=13cm]
\startplaceformula
\startformula \startalign
 \NC v \NC = u + at \NR[eq:v]
 \NC h \NC = ut + \frac12 gt^2 \NR[eq:h]
\stopalign \stopformula 
\stopplaceformula
Equation~(\in[eq:v]) tells the final velocity after time~$t$ and equation~(\in[eq:h]) tells the distance travelled in time~$t$.

Sub-numbering with \startsubformulas

The numbering can be changed to a subformula style by encapsulating \startplaceformula with \startsubformulas :

\setuplayout[scale=0.8,width=13cm]
\startsubformulas[eq:total]
\startplaceformula
\startformula \startalign
 \NC v \NC = u + at \NR[eq:v]
 \NC h \NC = ut + \frac12 gt^2 \NR[eq:h]
\stopalign \stopformula 
\stopplaceformula
\stopsubformulas 

In~(\in[eq:total]), equation~(\in[eq:v]) tells the final velocity after time~$t$ and equation (\in[eq:h]) tells the distance travelled in time~$t$.

Specifying and defining alignment with \definemathalignment

If you want more control over the formatting, and want the middle column to be center aligned, you can do that by

\startformula \startalign[n=3,align={1:right,2:middle,3:left}]
 \NC v \NC = u \NC+ at \NR
 \NC h \NC= ut \NC+ \frac12 gt^2 \NR
\stopalign \stopformula

This mechanism allows fancier alignments like

\startformula \startalign[n=4,align={1:right,2:right,3:middle,4:left}]
 \NC \text{We have} \quad \NC v \NC = u \NC+ at \NR
 \NC \text{and}     \quad \NC h \NC= ut \NC+ \frac12 gt^2 \NR
\stopalign \stopformula

These kind of new alignment can be defined using \definemathalignment.

\definemathalignment
    [demom]
    [n=4,align={1:right,2:right,3:middle,4:left}]

\startformula \startdemom
 \NC \text{We have} \quad \NC v \NC = u \NC+ at \NR
 \NC \text{and}     \quad \NC h \NC= ut \NC+ \frac12 gt^2 \NR
\stopdemom \stopformula

A second example, to emulate gather environment of amsmath, we can use

\definemathalignment
    [gather]
    [n=1,align={1:middle}]

\startformula \startgather
 \NC  ax^2 + bx + c = 0 \NR
 \NC \text{roots} = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \NR
\stopgather \stopformula

Cases

Context provides a \startmathcases \stopmathcases pair to make it easy to get cases.

\startformula
\delta_{ij} =
 \startmathcases
 \NC 1 \NC \text{if } i = j \NR
 \NC 0 \NC \text{otherwise} \NR
 \stopmathcases
\stopformula

gives

The cases environment consists of two columns, separated by \NC. The second column is by default in math mode. To typeset the second column in text mode, use \TC

\startformula
\delta_{ij} =
 \startmathcases
 \NC 1 \TC if \m{i = j} \NR
 \NC 0 \TC otherwise \NR
 \stopmathcases
\stopformula

Each line must end with a \NR.

TO BE MERGED

There are several built-in commands for displaying mathematical formulas. For instance

\startcases, \stopcases
\startmathmatrix, \stopmathmatrix
\startalign,\stopalign

Each has its own advantage and can be customized: for a thorough understanding of these commands please refer to Aditya Mohajan's excellent user's guide Using \startalign and friends. These commands can be found in core-mat.tex file, which contains most of the core ConTeXt math macros.

This is an example of aligned equations:
\startformula
 \startcases[align={right,left},distance=3pt]
   \NC 2x + 3y \NC{} = 10 \NR
   \NC 3x + 2y \NC{} = 5,   \NR
 \stopcases
\stopformula
and this is another one:
\startformula
 \startmatrix[align={right,left},distance=3pt,left={\left\{}, right={\right.}]
   \NC 2x + 3y \NC{} = 10 \NR
   \NC 3x + 2y \NC{} = 5   \NR
 \stopmatrix
\stopformula

In these structures it is important (well, in the above example it is not important and the result is the same, but I have been told that it is necessary in some other situations...) to notice that the sign "=" is preceded by "\NC{}, since otherwise that sign would be considered as a binary operator and the alignment would be disturbed (at least this is what I guess…Otared K.).

One of the powerful structures in displaying mathematical formulas is the possibility of defining custom maths alignment. For instance the following definition

\definemathmatrix[alignedcases]
		[align={right,left,left},
		distance=3pt,
		left={\left\{},
		right={\right.},
		style=\displaystyle]

creates two new commands,

\startalignedcases, \stopalignedcases:

after which one may use them in a displayed formula as follows:

The following formula is displayed in two lines with an appropriate alignment of the equations:

\startformula
\startalignedcases
 \NC -\Delta u + g(u) \NC{} = f \NC \quad\mbox{in } \Omega\NR
 \NC {\partial u \over \partial {\bf n} } \NC{} = h(u) \NC \quad\mbox{on } \partial\Omega   \NR
\stopalignedcases
\stopformula