Difference between revisions of "Math"

From ConTeXt wiki
m (Changing format of numbers: conversion)
m (Reverted edits by Papseo (talk) to last revision by Adityam)
 
(42 intermediate revisions by 19 users not shown)
Line 5: Line 5:
 
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.
 
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.
+
There are '''two''' kinds of '''math modes''' --- '''inline math and display math'''. Mathematical expressions that are written with the running text are called inline math; while mathematical expressions that break the flow of the text (such as formulas or equations) are called display math. TeX takes care of proper spacing around expressions and provides macros to typeset most mathematical constructs.
 +
Complicated expressions can be built by working in steps---break down the expression into sub-expressions, build the sub-expressions and then combine them to get the complicated expression.
  
==Simple Math==
+
The basics of typesetting math in ConTeXt is explained here.
  
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
+
=== Display math mode ===
 +
Type
  
<context>
 
\setuplayout[scale=0.8,width=13cm]
 
Pythagoras formula, stating \mathematics{a^2 + b^2 = c^2} was one of the first trignometric results
 
</context>
 
 
There are two ways of typing inline math. The TeX way is to surround what you want to type within <code>$</code>...<code>$</code>. Thus, the above will be typed as
 
<texcode>
 
Pythagoras formula, stating $a^2 + b^2 = c^2$ was one of the first trignometric results
 
</texcode>
 
 
ConTeXt also provides an alternative way of typing the same result. Instead of dollars, you can write the material for maths inside <cmd>mathematics</cmd>. Thus, an alternate way to type the above is,
 
<texcode>
 
Pythagoras formula, stating \mathematics{a^2 + b^2 = c^2} was one of the first trignometric results
 
</texcode>
 
 
Choose the method that suits your style.
 
((I do not know if there are pros and cons of $..$ vs \mathematics{}. If someone knows, then please elaborate -- aditya ))
 
 
Display math is enclosed in a <cmd>startformula</cmd> / <cmd>stopformula</cmd> pair. Thus
 
 
<table width="100%" cols="2"><tr valign="top"><td width="50%">
 
<texcode>
 
The famous result (once more) is given by
 
\startformula
 
c^2 = a^2 + b^2.
 
\stopformula
 
</texcode>
 
</td><td>
 
This, when typeset, produces the following:
 
 
<context>
 
\setuplayout[scale=0.8,width=8cm]
 
The famous result (once more) is given by
 
\startformula
 
c^2 = a^2 + b^2.
 
\stopformula
 
</context>
 
</td></tr></table>
 
 
== Numbering Formulae ==
 
 
ConTeXt provides an easy way to number the display maths equations. Simply, put <cmd>placeformula</cmd> before  <cmd>startformula</cmd> / <cmd>stopformula</cmd> pair and you will get numbered equations. Thus,
 
<table width="100%" cols="2"><tr valign="top"><td width="50%">
 
<texcode>
 
The famous result (once more) is given by
 
\placeformula
 
\startformula
 
c^2 = a^2 + b^2.
 
\stopformula
 
</texcode>
 
</td><td>
 
This, when typeset, produces the following:
 
 
<context>
 
\setuplayout[scale=0.8,width=8cm]
 
The famous result (once more) is given by
 
\placeformula
 
\startformula
 
c^2 = a^2 + b^2.
 
\stopformula
 
</context>
 
</td></tr></table>
 
 
The <cmd>placeformula</cmd> command is optional, and produces the equation number; leaving it off produces an unnumbered equation.
 
 
=== Changing format of numbers ===
 
You can use <cmd>setupformulas</cmd> to change the format of numbers. For example to get bold numbers inside square brackets use
 
 
<table>
 
<tr><td>
 
 
<texcode>
 
<texcode>
\setupformulas[left={[},right={]},numberstyle=bold]
+
\startformula ... \stopformula
 
</texcode>
 
</texcode>
</td>
 
  
<td>which gives
+
to get display math mode.
  
<context>
+
=== Inline math mode ===
\setuplayout[scale=0.8,width=8cm]
+
There are four equivalent commands to get inline math mode:
\setupformulas[left={[},right={]},numberstyle=bold]
 
The famous result (once more) is given by
 
\placeformula
 
\startformula
 
c^2 = a^2 + b^2.
 
\stopformula
 
</context>
 
</td></tr></table>
 
  
To get alphabets instead of numbers, use
 
<table>
 
<tr><td>
 
 
<texcode>
 
<texcode>
\setupformulas[conversion=Character]
+
$ ... $              % TeX style.
 +
\m{ ... }           
 +
\math{ ... }       
 +
\mathematics{ ... }
 
</texcode>
 
</texcode>
</td>
 
<td>which gives
 
<context>
 
\setuplayout[scale=0.8,width=8cm]
 
\setupformulas[conversion=Character]
 
\placeformula
 
\startformula
 
c^2 = a^2 + b^2
 
\stopformula
 
</context>
 
</td></tr></table>
 
  
== Not so Simple Maths ==
+
=== Note to Plain TeX Users ===
 +
ConTeXt is plain TeX compatible. So, if you have any old document written in plain TeX, it will work with ConTeXt. This does not mean that you will get pixel by pixel identical output with ConTeXt. For inline math, everything that you learnt for plain TeX is also true for ConTeXt. However, display math is significantly different. '''Do not use <code>$$ .... $$</code>''' to write display math formulas in ConTeXt, since you will not get the correct spacing around the formulas. Instead use
  
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 <cmd>text</cmd> command for text-mode notes within math.)  For instance:
 
 
<texcode>
 
<texcode>
A more complicated equation:
+
\startformula ... \stopformula
\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
 
 
</texcode>
 
</texcode>
  
which produces
+
See [[Math/Display]] for more details on how to use display math in ConTeXt.
  
<context>
+
=== Note to AMSTeX/LaTeX Users ===
\setuplayout[scale=0.8,width=13cm]
+
ConTeXt offers almost all the features that are present in AMSTeX and LaTeX. However, ConTeXt syntax is different. See this [http://dl.contextgarden.net/myway/context-latex-math.pdf My Way] for how to 'translate' from amsmath syntax to ConTeXt syntax. [[LaTeX_Math_in_ConTeXt]] gives some brief ideas on how to get the LaTeX syntax to run in ConTeXt.
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
 
</context>
 
  
Context provides a wrapper around tex <cmd>pmatrix</cmd>. The above can be typeset in a contextish way as
+
== The details ==
<texcode>
 
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
 
</texcode>
 
<context>
 
\setuplayout[scale=0.8,width=13cm]
 
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
 
</context>
 
  
[http://www.pragma-ade.com/texmath.html Here] you can try it "live" (you must go to [http://www.pragma-ade.com/exalogin login] first).
+
=== Math symbols ===
 +
* [[Math/basic | How to input math]] (binary relations, greek letters, subscripts and superscripts)
 +
* Accents
 +
* underbrace, overbrace
 +
* [[Math/fractions | Fractions, Binomials, genfrac, continued fractions.]]
 +
* Delimiters (big, bigg, left, middle, right)
 +
* Integrals and Sums
 +
* ([[Math/functions|Log like]]) functions
 +
* dots
 +
* [[Multiline_equations#Cases|Cases]], matrices, bordermatrix
 +
* Arrows (see [http://dl.contextgarden.net/myway/matharrows.pdf Math Arrows])
 +
* [[Vectors]]
 +
* [[Product integral]]
  
[[MathAlignment]] is covered on a separate page.
+
=== Display Math ===
 +
* [[Math/Display | Formula, formula number]]
 +
* [[Multiline equations]] (see [http://dl.contextgarden.net/myway/mathalign.pdf Using \mathalign and friends])
 +
* Math sub-alignment
 +
* [[Math spacing]]
 +
* Discussion: [[User_talk:Zenlima | summary of formula numbering problems]] (comment: unverified)
  
==Sub-Formula Numbering==
+
==Math Fonts==
  
As mentioned above, formulas can be numbered using the <cmd>placeformula</cmd> command.  This (and the related <cmd>placesubformula</cmd> command have an optional argument which can be used to produce sub-formula numbering.  For example:
+
''See [[Math fonts]]'' for the main article about this subject.
 
 
<table width="100%" cols="2"><tr valign="top"><td width="50%">
 
<texcode>
 
Examples:
 
\placeformula{a}
 
\startformula
 
c^2 = a^2 + b^2
 
\stopformula
 
 
 
\placesubformula{b}
 
\startformula
 
c^2 = a^2 + b^2
 
\stopformula
 
</texcode>
 
</td><td>
 
<context>
 
\setuplayout[scale=0.8,width=8cm]
 
Examples:
 
\placeformula{a}
 
\startformula
 
c^2 = a^2 + b^2
 
\stopformula
 
 
 
\placesubformula{b}
 
\startformula
 
c^2 = a^2 + b^2
 
\stopformula
 
</context>
 
</td></tr></table>
 
 
 
What's going on here is simpler than it might appear at first glance.  Both <cmd>placeformula</cmd> and <cmd>placesubformula</cmd> 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 <cmd>placeformula</cmd> defines <cmd>formulanumber</cmd> and <cmd>subformulanumber</cmd> commands, which provide hooks to allow the use of ConTeXt-managed 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 <cmd>eqno</cmd>.  Note that the optional tag is inherited from <cmd>placeformula</cmd>.
 
 
 
<table width="100%" cols="2"><tr valign="top"><td width="50%">
 
<texcode>
 
More examples:
 
\placeformula{c}
 
\startformula
 
\let\doplaceformulanumber\empty
 
c^2 = a^2 + b^2  \eqno{\formulanumber}
 
\stopformula
 
</texcode>
 
</td><td>
 
<context>
 
\setuplayout[scale=0.8,width=8cm]
 
More examples:
 
\placeformula{c}
 
\startformula
 
\let\doplaceformulanumber\empty
 
c^2 = a^2 + b^2  \eqno{\formulanumber}
 
\stopformula
 
</context>
 
</td></tr></table>
 
 
 
In order for this to work properly, we need to turn off ConTeXt's automatic formula number placement; thus the <cmd>let</cmd> command to empty <cmd>doplaceformulanumber</cmd>, which must be placed <em>after</em> the start of the formula.  In many practical examples, however, this is not necessary; ConTeXt redefines <cmd>displaylines</cmd> and <cmd>eqalignno</cmd> to do this automatically.
 
 
 
For more control over sub-formula numbering, <cmd>formulanumber</cmd> and <cmd>subformulanumber</cmd> have an optional argument parallel to that of <cmd>placeformula</cmd>, as demonstrated in this use of plain TeX's <cmd>eqalignno</cmd>, which places multiple equation numbers within one formula.
 
 
 
<table width="100%" cols="2"><tr valign="top"><td width="50%">
 
<texcode>
 
Yet more examples:
 
\placeformula
 
\startformula
 
\eqalignno{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
 
</texcode>
 
</td><td>
 
<context>
 
\setuplayout[scale=0.8,width=8cm]
 
Yet more examples:
 
\placeformula
 
\startformula
 
\eqalignno{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
 
</context>
 
</td></tr></table>
 
 
 
Note that both <cmd>formulanumber</cmd> and <cmd>subformulanumber</cmd> can be used within the same formula, and the formula number is incremented as expected.  Also, if an optional argument is specified in both <cmd>placefigure</cmd> and <cmd>formulanumber</cmd>, the latter takes precedence.
 
 
 
<table width="100%" cols="2"><tr valign="top"><td width="50%">
 
<texcode>
 
More examples for left-located 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
 
</texcode>
 
</td><td>
 
<context>
 
\setuplayout[scale=0.8,width=8cm]
 
More examples for left-located equation no.:
 
\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
 
</context>
 
</td></tr></table>
 
 
 
-- 23:46, 15 Aug 2005 (CEST) Prinse Wang
 
==List of Formulas==
 
 
 
You can have a list of the formulas contained in a document by using <cmd>placenamedformula</cmd> instead of <cmd>placeformula</cmd>. Only the formulas written with <cmd>placenamedformula</cmd> are not put in the list, so that you can control precisely the content of the list.
 
 
 
<cmd>placenamedformula</cmd> takes as first parameter the name of the formula put in the list. The other <cmd>placeformula</cmd> features are still available. The list can be formatted like any other list.
 
 
 
Example:
 
<texcode>
 
\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
 
</texcode>
 
 
 
Gives:
 
 
 
<context>
 
\setuplayout[scale=0.8,width=13cm]
 
\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
 
</context>
 
  
 
== Other Methods ==
 
== Other Methods ==
 
* There are two different math modules on [http://dante.ctan.org/tex-archive/macros/context/contrib/maths/ CTAN], [[Math with nath|nath]] and [[Math with amsl|amsl]]. And there's a [[Math with newmat|new math]] module in the distribution.
 
* There are two different math modules on [http://dante.ctan.org/tex-archive/macros/context/contrib/maths/ CTAN], [[Math with nath|nath]] and [[Math with amsl|amsl]]. And there's a [[Math with newmat|new math]] module in the distribution.
* Context now has inbuilt support for [[Math_structures]]
+
* Context now has inbuilt support for [[Multiline equations]]
 
* It is also possible to use most [[LaTeX Math in ConTeXt|LaTeX equations in ConTeXt]] with a relatively small set of supporting definitions.
 
* It is also possible to use most [[LaTeX Math in ConTeXt|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.
 
* The "native" ConTeXt way of math is [[MathML]], an application of [[XML]] - rather verbose but mighty.
 
==Number Formatting==
 
There's a special command, <cmd>digits</cmd>, and a own manual about formatting numbers, see [http://www.pragma-ade.com/general/magazines/mag-0003.pdf Pasting digits together]
 
 
==Math [[Fonts]]==
 
* [[Bold Math]]
 
* [http://homepage.mac.com/atl/tex/EulerContext.pdf Euler in ConTeXt (using Euler math font)] by Adam Lindsay
 
* [[rsfs]] Using Ralph Smith's Formal Script
 
  
 
==Science==
 
==Science==
* Esp. for physics there’s the [[units]] module.
+
* Esp. for physics there’s the [[Units]] module.
 
* Additions to [[MathML]] are PhysML and ChemML.
 
* Additions to [[MathML]] are PhysML and ChemML.
 
* [[Chemistry]]
 
* [[Chemistry]]
 
* There's a module for chemical structure formulae: [[Chemistry|PPCHTeX]] (works also with LaTeX).
 
* There's a module for chemical structure formulae: [[Chemistry|PPCHTeX]] (works also with LaTeX).
 +
 +
==Number Formatting==
 +
There's a special command, <cmd>digits</cmd>, with its own manual about formatting numbers, see [http://www.pragma-ade.com/general/magazines/mag-0003.pdf Pasting digits together]
 +
 +
==Evaluating expressions in ConTeXt==
 +
(i.e. ''doing'' math)
 +
* See also [[Expressions]].
  
 
[[Category:Math]]
 
[[Category:Math]]

Latest revision as of 18:22, 25 January 2017

< Main Page | Math with newmat | MathML | Math_structures>

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.

There are two kinds of math modes --- inline math and display math. Mathematical expressions that are written with the running text are called inline math; while mathematical expressions that break the flow of the text (such as formulas or equations) are called display math. TeX takes care of proper spacing around expressions and provides macros to typeset most mathematical constructs. Complicated expressions can be built by working in steps---break down the expression into sub-expressions, build the sub-expressions and then combine them to get the complicated expression.

The basics of typesetting math in ConTeXt is explained here.

Display math mode

Type

\startformula ... \stopformula

to get display math mode.

Inline math mode

There are four equivalent commands to get inline math mode:

$ ... $              % TeX style.
\m{ ... }            
\math{ ... }         
\mathematics{ ... }

Note to Plain TeX Users

ConTeXt is plain TeX compatible. So, if you have any old document written in plain TeX, it will work with ConTeXt. This does not mean that you will get pixel by pixel identical output with ConTeXt. For inline math, everything that you learnt for plain TeX is also true for ConTeXt. However, display math is significantly different. Do not use $$ .... $$ to write display math formulas in ConTeXt, since you will not get the correct spacing around the formulas. Instead use

\startformula ... \stopformula

See Math/Display for more details on how to use display math in ConTeXt.

Note to AMSTeX/LaTeX Users

ConTeXt offers almost all the features that are present in AMSTeX and LaTeX. However, ConTeXt syntax is different. See this My Way for how to 'translate' from amsmath syntax to ConTeXt syntax. LaTeX_Math_in_ConTeXt gives some brief ideas on how to get the LaTeX syntax to run in ConTeXt.

The details

Math symbols

Display Math

Math Fonts

See Math fonts for the main article about this subject.

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.

Science

  • Esp. for physics there’s the Units module.
  • Additions to MathML are PhysML and ChemML.
  • Chemistry
  • There's a module for chemical structure formulae: PPCHTeX (works also with LaTeX).

Number Formatting

There's a special command, \digits, with its own manual about formatting numbers, see Pasting digits together

Evaluating expressions in ConTeXt

(i.e. doing math)