Difference between revisions of "Math"

From Wiki
Jump to navigation Jump to search
m (Fixed explanation of turning off automatic numbering.)
 
(209 intermediate revisions by 32 users not shown)
Line 1: Line 1:
−
< [[Main Page]] | [[Math with newmat]] | [[MathML]] >
+
= Introduction =
  
−
Many people start with TeX because they want to set formulae.
+
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.
−
Simple math typesetting exists since PlainTeX and these commands work in ConTeXt as in LaTeX.
 
−
Advanced math was introduced to TeX by AMS (American Mathematical Society); nowadays AMSTeX and LaTeX are united. But how can one use advanced math with ConTeXt?
 
  
−
* 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]].
+
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.
−
* It is also possible to use most [[LaTeX Math in ConTeXt|LaTeX equations in ConTeXt]] with a relatively small set of supporting definitions.
+
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 "native" ConTeXt way of math is [[MathML]], an application of [[XML]] - rather verbose but mighty.
+
 
−
* And there's a [[Math with newmat|new math]] module in the distribution.
+
The basics of typesetting math in ConTeXt is explained here.
  
−
==Simple Math==
+
== Display math mode ==
  
−
ConTeXt supports 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 is enclosed in "$" signs, while display math is enclosed in a <cmd>startformula</cmd> / <cmd>stopformula</cmd> pair.
+
Type {{cmd|startformula}} to get display math mode, or {{cmd|dm}} to get a inline typesetting but keeping display sizing and rules.
  
−
<texcode>
+
<context source="yes">
−
Inline math is set as $c^2 = a^2 + b^2$, and display math as
+
The famous result (once more) is given by
−
\placeformula
 
 
\startformula
 
\startformula
 
c^2 = a^2 + b^2.
 
c^2 = a^2 + b^2.
 
\stopformula
 
\stopformula
−
</texcode>
 
  
−
This, when typeset, produces the following:
+
\dm{c^2 = a^2 + b^2}
−
 
 
−
<context>
 
−
Inline math is set as $c^2 = a^2 + b^2$, and display math as
 
−
\placeformula
 
−
\startformula
 
−
c^2 = a^2 + b^2.
 
−
\stopformula
 
 
</context>
 
</context>
  
−
The <cmd>placeformula</cmd> command is optional, and produces the equation number; leaving it off produces an unnumbered equation.
+
== Inline math mode ==
  
−
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:
+
There are four equivalent commands to get inline math mode: {{cmd|$}}, {{cmd|m}}, {{cmd|math}}, {{cmd|mathematics}} to get display inline math mode.
−
<texcode>
 
−
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
 
−
</texcode>
 
  
−
which produces
+
<context source="yes">
−
<context>
+
\framed[align=normal,frame=off]{%
−
A more complicated equation:
+
The famous result (once more) is given by $ c^2 = a^2 + b^2 $.\par        % TeX style.
−
\placeformula
+
The famous result (once more) is given by \m{c^2 = a^2 + b^2}.\par           
−
\startformula
+
The famous result (once more) is given by \math{c^2 = a^2 + b^2}.\par       
−
{{\theta_{\text{ConTeXt}}}^2 \over x+2}
+
The famous result (once more) is given by \mathematics{c^2 = a^2 + b^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>
  
−
[http://www.ntg.nl:8061/texmath.pdf Here] you can try it "live" (PDF interface!).
 
−
 
−
[[MathAlignment]] is covered on a separate page.
 
−
 
−
==Formula Numbering==
 
  
−
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:
+
For examples
 +
<code>$x$</code> gives <context>\setuplayout[scale=0.8]$x$</context>, while
 +
<code>$2$</code> gives <context>\setuplayout[scale=0.8]$2$</context>.
 +
Notice that the ''x'' is in italic while the ''2'' is upright. This is the usual mathematic convention.
  
−
<texcode>
+
= Formula, formulae, equations =
−
Examples:
 
−
\placeformula{a}
 
−
\startformula
 
−
c^2 = a^2 + b^2
 
−
\stopformula
 
  
−
\placesubformula{b}
+
* '''[[Math/Display | Math display]]'''
−
\startformula
+
** numbering
−
c^2 = a^2 + b^2
+
** referencing
−
\stopformula
+
** sub-formulae
−
</texcode>
+
** list of Formulae
 +
** formating
 +
* '''[[Math/Multiline_equations | Multiline equations]]'''
 +
** alignment
 +
** number of columns
 +
** equation numbering and sub-numbering (very similar to above)
 +
** formating, specifying and defining alignment
 +
** cases
 +
* '''[[Math/Matrices| Matrices]]'''
 +
** definition
 +
** delimiters
 +
** block matrices and vertical/ horizontal lines
 +
** border matrices
  
−
<context>
+
= Typesetting Math =
−
Examples:
 
−
\placeformula{a}
 
−
\startformula
 
−
c^2 = a^2 + b^2
 
−
\stopformula
 
  
−
\placesubformula{b}
+
* '''[[Math/basic | Math glyphs]]'''
−
\startformula
+
** Binary Operators Relations
−
c^2 = a^2 + b^2
+
** Sums, products and integrals. A specific page is for [[Product integral]]
−
\stopformula
+
** Greek Letters
−
</context>
+
** Subscript and superscript
 +
** List of all math macros
 +
* '''[[Math/functions]]''' (typesetting of usual functions, and defining new ones)
 +
* '''[[Math/Vectors]]'''
 +
* '''[[Math/stackers]]'''
 +
** how to stack some characters over another one (and accent)
 +
** underbrace and overbrace
 +
* '''[[Math/Fonts]]'''
 +
** [[math calligraphic]] seems to be old content
 +
* '''[[Math/fractions | Math/Fractions and binomials]]'''
 +
* '''[[Math/Delimiters]]'''
 +
* '''Formatting numbers with {{cmd|digits}}''', and its manual <i>[http://www.pragma-ade.nl/general/magazines/mag-0003.pdf Pasting digits together (2003)]</i>. Don't forget the [http://www.pragma-ade.nl/general/manuals/units-mkiv.pdf Units manual (2020)]
  
−
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).
+
= Plotting =
  
−
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>.
+
* [http://www.pragma-ade.nl/general/manuals/luametafun.pdf LuaMetafun manual] (2021)
 +
** [http://www.pragma-ade.nl/general/manuals/luametafun.pdf#page=30 Contours]
 +
** [http://www.pragma-ade.nl/general/manuals/luametafun.pdf#page=41 Surfaces]
 +
** [http://www.pragma-ade.nl/general/manuals/luametafun.pdf#page=44 Meshes]
 +
** [http://www.pragma-ade.nl/general/manuals/luametafun.pdf#page=48 Functions]
 +
** [http://www.pragma-ade.nl/general/manuals/luametafun.pdf#page=54 Charts]
 +
* [https://akela.mendelu.cz/~thala/statcharts/ The New (2020) graph module]
 +
** with its dedicated [https://akela.mendelu.cz/~thala/statcharts/statistical-charts.pdf manual "Drawing Statistical Charts"]
 +
** and a [https://meeting.contextgarden.net/2020/talks/2020-09-11-tamara-and-adriana-statistical-charts/AK-TK_charts.pdf short presentation]
 +
* Data plotting with [[MPgraph|module graph]].
 +
* Some alternatives:
 +
** [[TikZ]] (2016)
 +
** [[Gnuplot]] (2012)
 +
** [[Pgfplot]] (2009).
  
−
<texcode>
+
= Key links =
−
More examples:
 
−
\placeformula{c}
 
−
\startformula
 
−
\let\doplaceformulanumber\empty
 
−
c^2 = a^2 + b^2  \eqno{\formulanumber}
 
−
\stopformula
 
−
</texcode>
 
  
−
<context>
 
−
More examples:
 
−
\placeformula{c}
 
−
\startformula
 
−
\let\doplaceformulanumber\empty
 
−
c^2 = a^2 + b^2  \eqno{\formulanumber}
 
−
\stopformula
 
−
</context>
 
  
−
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.
+
* '''[http://www.pragma-ade.nl/general/manuals/math-mkiv.pdf <i>Math rendering</i>] manual (2018)'''
 +
* '''from Mikael P. Sundqvist'''
 +
** 2022 — TUG — <i>Pushing math forward with luametatex and ConTeXt</i>
 +
*** [https://www.youtube.com/watch?v=WuRa4cnXK-I video]
 +
*** [https://tug.org/tug2022/assets/served/Mikael_P._Sundqvist-TUG2022-sundqvist-lmtx-math-slides.pdf slides]
 +
*** [https://tug.org/TUGboat/tb43-2/tb134hagen-math.pdf article] (TUGboat, Volume 43 (2022), No. 2)
 +
** [https://tug.org/TUGboat/tb43-3/tb135hagen-mathchange.pdf 2022 — TUG — <i>New directions in math fonts</i> (TUGboat, Volume 43 (2022), No. 2)] .
 +
* '''from Aditya Mahajan'''
 +
** [https://wiki.contextgarden.net/images/archive/b/b4/20100530075041!Mathalign.pdf 2010 - <i>Using \startalign and friends</i>] (My Way article)
 +
** [https://meeting.contextgarden.net/2008/talks/2008-08-24-aditya-display-math/presentation.pdf 2008 - <i>Display Math in Formula - Where is it and where can it go</i>] (presentation)
 +
** [https://www.ntg.nl/maps/34/06.pdf 2006 - <i>Display Math in ConTeXt</i>, MAPS <b>34</b>, 22–34.], ConTEXt rehab for amsmath addicts (article)
  
−
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.
+
= Notes =
  
−
<texcode>
+
==Evaluating expressions in ConTeXt==
−
Yet more examples:
+
See also [[Expressions]] (i.e. ''doing'' math).
−
\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>
 
  
−
<context>
+
== Note to Plain TeX Users ==
−
Yet more examples:
+
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 {{cmd|startformula}} and <tt>\stopformula</tt>.
−
\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>
 
  
−
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.
+
== 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 [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.
  
−
==Number Formatting==
+
== Other Methods ==
−
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]
+
* The "native" ConTeXt way of math is [[MathML]], an application of [[XML]] - rather verbose but mighty.
 +
* 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.
 +
* It is also possible to use most [[LaTeX Math in ConTeXt|LaTeX equations in ConTeXt]] with a relatively small set of supporting definitions.
  
−
==Math [[Fonts]]==
+
== To do ==
−
* [[Bold Math]]
+
* dots
−
* [http://homepage.mac.com/atl/tex/EulerContext.pdf Euler in ConTeXt (using Euler math font)] by Adam Lindsay
+
* Arrows (see [http://dl.contextgarden.net/myway/matharrows.pdf Math Arrows]) broken link
 +
{{todo|}}
  
−
==Science==
+
[[Category:Math]]
−
* Esp. for physics there’s the [[units]] module.
 
−
* Additions to [[MathML]] are PhysML and ChemML.
 
−
* [[Chemistry]]
 
−
* There's a module for chemical structure formulae: [[Chemistry|PPCHTeX]] (works also with LaTeX). It's based on [[Metapost]] and [[MetaFun]].
 

Latest revision as of 19:10, 13 May 2024

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 to get display math mode, or \dm to get a inline typesetting but keeping display sizing and rules. 

The famous result (once more) is given by
\startformula
c^2 = a^2 + b^2.
\stopformula

\dm{c^2 = a^2 + b^2}

Inline math mode

There are four equivalent commands to get inline math mode: \$, \m, \math, \mathematics to get display inline math mode. 

\framed[align=normal,frame=off]{%
The famous result (once more) is given by $ c^2 = a^2 + b^2 $.\par         % TeX style.
The famous result (once more) is given by \m{c^2 = a^2 + b^2}.\par            
The famous result (once more) is given by \math{c^2 = a^2 + b^2}.\par         
The famous result (once more) is given by \mathematics{c^2 = a^2 + b^2}.}


For examples $x$ gives , while $2$ gives . Notice that the x is in italic while the 2 is upright. This is the usual mathematic convention.

Formula, formulae, equations

  • Math display
    • numbering
    • referencing
    • sub-formulae
    • list of Formulae
    • formating
  • Multiline equations
    • alignment
    • number of columns
    • equation numbering and sub-numbering (very similar to above)
    • formating, specifying and defining alignment
    • cases
  • Matrices
    • definition
    • delimiters
    • block matrices and vertical/ horizontal lines
    • border matrices

Typesetting Math

Plotting

Key links

Notes

Evaluating expressions in ConTeXt

See also Expressions (i.e. doing math).

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 and \stopformula.

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.

Other Methods

  • The "native" ConTeXt way of math is MathML, an application of XML - rather verbose but mighty.
  • There are two different math modules on CTAN, nath and amsl. And there's a new math module in the distribution.
  • It is also possible to use most LaTeX equations in ConTeXt with a relatively small set of supporting definitions.

To do


 TODO: (See: To-Do List)
Retrieved from "https://wiki.contextgarden.net/index.php?title=Math&oldid=35300"