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### Text::ASCIIMathMLPerl extension for parsing ASCIIMathML text into MathML

Text::ASCIIMathML - Perl extension for parsing ASCIIMathML text into MathML

Text::ASCIIMathML - Perl extension for parsing ASCIIMathML text into MathML

# SYNOPSIS


use Text::ASCIIMathML;

$parser=new Text::ASCIIMathML(); $parser->SetAttributes(ForMoz => 1);

$ASCIIMathML = "int_0^1 e^x dx";$mathML = $parser->TextToMathML($ASCIIMathML);

$mathML =$parser->TextToMathML($ASCIIMathML, [title=>$ASCIIMathML]);

$mathML =$parser->TextToMathML($ASCIIMathML, undef, [displaystyle=>1]); $mathMLTree = $parser->TextToMathMLTree($ASCIIMathML);

$mathMLTree =$parser->TextToMathMLTree($ASCIIMathML, [title=>$ASCIIMathML]);

$mathMLTree =$parser->TextToMathMLTree($ASCIIMathML,undef,[displaystyle=>1]); $mathML = $mathMLTree->text();$latex  = \$mathMLTree->latex();

# DESCRIPTION

Text::ASCIIMathML is a parser for ASCIIMathML text which produces MathML XML markup strings that are suitable for rendering by any MathML-compliant browser.

The parser uses the following attributes which are settable through the SetAttributes method:

ForMoz
Specifies that the fonts should be optimized for Netscape/Mozilla/Firefox.

The output of the TextToMathML method always follows the schema $<mstyle>...</mstyle>$ The first argument of TextToMathML is the ASCIIMathML text to be parsed into MathML. The second argument is a reference to an array of attribute/value pairs to be attached to the [itex] node and the third argument is a reference to an array of attribute/value pairs for the <mstyle> node. Common attributes for the [itex] node are title'' and xmlns''=>&mathml;''. Common attributes for the <mstyle> node are mathcolor'' (for text color), displaystyle''=>true'' for using display style instead of inline style, and fontfamily''.

## ASCIIMathML markup

The syntax is very permissive and does not generate syntax errors. This allows mathematically incorrect expressions to be displayed, which is important for teaching purposes. It also causes less frustration when previewing formulas.

If you encode 'x^2' or 'a_(mn)' or 'a_{mn}' or '(x+1)/y' or 'sqrtx', you pretty much get what you expect. The choice of grouping parenthesis is up to you (they don't have to match either). If the displayed expression can be parsed uniquely without them, they are omitted. Most LaTeX commands are also supported, so the last two formulas above can also be written as '\frac{x+1}{y}' and '\sqrt{x}'.

The parser uses no operator precedence and only respects the grouping brackets, subscripts, superscript, fractions and (square) roots. This is done for reasons of efficiency and generality. The resulting MathML code can quite easily be processed further to ensure additional syntactic requirements of any particular application.

### The grammar

Here is a definition of the grammar used to parse ASCIIMathML expressions. In the Backus-Naur form given below, the letter on the left of the ::= represents a category of symbols that could be one of the possible sequences of symbols listed on the right. The vertical bar | separates the alternatives.


c ::= [A-z] | numbers | greek letters | other constant symbols

(see below)

u ::= 'sqrt' | 'text' | 'bb' | other unary symbols for font commands

b ::= 'frac' | 'root' | 'stackrel' | 'newcommand' | 'newsymbol'

binary symbols

l ::= ( | [ | { | (: | {:          left brackets

r ::= ) | ] | } | :) | :}          right brackets

S ::= c | lEr | uS | bSS | "any"   simple expression

E ::= SE | S/S |S_S | S^S | S_S^S  expression (fraction, sub-,

super-, subsuperscript)

### The translation rules

Each terminal symbol is translated into a corresponding MathML node. The constants are mostly converted to their respective Unicode symbols. The other expressions are converted as follows:


lSr      ->    <mrow>lSr</mrow>

(note that any pair of brackets can be used to

delimit subexpressions, they don't have to match)

sqrt S   ->    <msqrt>S'</msqrt>

text S   ->    <mtext>S'</mtext>

"any"    ->    <mtext>any</mtext>

frac S1 S2     ->      <mfrac>S1' S2'</mfrac>

root S1 S2     ->      <mroot>S2' S1'</mroot>

stackrel S1 S2 ->      <mover>S2' S1'</mover>

S1/S2    ->    <mfrac>S1' S2'</mfrac>

S1_S2    ->    <msub>S1 S2'</msub>

S1^S2    ->    <msup>S1 S2'</msup>

S1_S2^S3 ->    <msubsup>S1 S2' S3'</msubsup> or

<munderover>S1 S2' S3'</munderover> (in some cases)

In the rules above, the expression S' is the same as S, except that if S has an outer level of brackets, then S' is the expression inside these brackets.

### Matrices

A simple syntax for matrices is also recognized:


l(S11,...,S1n),(...),(Sm1,...,Smn)r

or

l[S11,...,S1n],[...],[Sm1,...,Smn]r.

Here l and r stand for any of the left and right brackets (just like in the grammar they do not have to match). Both of these expressions are translated to


<mrow>l<mtable><mtr><mtd>S11</mtd>...

<mtd>S1n</mtd></mtr>...

<mtr><mtd>Sm1</mtd>...

<mtd>Smn</mtd></mtr></mtable>r</mrow>.

Note that each row must have the same number of expressions, and there should be at least two rows.

LaTeX matrix commands are not recognized.

### Tokenization

The input formula is broken into tokens using a longest matching initial substring search''. Suppose the input formula has been processed from left to right up to a fixed position. The longest string from the list of constants (given below) that matches the initial part of the remainder of the formula is the next token. If there is no matching string, then the first character of the remainder is the next token. The symbol table at the top of the ASCIIMathML.js script specifies whether a symbol is a math operator (surrounded by a <mo> tag) or a math identifier (surrounded by a <mi> tag). For single character tokens, letters are treated as math identifiers, and non-alphanumeric characters are treated as math operators. For digits, see Numbers'' below.

Spaces are significant when they separate characters and thus prevent a certain string of characters from matching one of the constants. Multiple spaces and end-of-line characters are equivalent to a single space.

### Numbers

A string of digits, optionally followed by a decimal point (a period) and another string of digits, is parsed as a single token and converted to a MathML number, i.e., enclosed with the <mn> tag.

### Greek letters

Lowercase letters
alpha beta chi delta epsilon eta gamma iota kappa lambda mu nu omega phi pi psi rho sigma tau theta upsilon xi zeta

Uppercase letters
Delta Gamma Lambda Omega Phi Pi Psi Sigma Theta Xi

Variants
varepsilon varphi vartheta

### Standard functions

sin cos tan csc sec cot sinh cosh tanh log ln det dim lim mod gcd lcm min max

### Operation symbols


Type     Description                                   Entity

+        +                                             +

-        -                                             -

*        Mid dot                                       &sdot;

**       Star                                          &Star;

//       /                                             /

\\       \                                             \

xx       Cross product                                 &times;

-:       Divided by                                    &divide;

@        Compose functions                             &SmallCircle;

o+       Circle with plus                              &oplus;

ox       Circle with x                                 &otimes;

o.       Circle with dot                               &CircleDot;

sum      Sum for sub- and superscript                  &sum;

prod     Product for sub- and superscript              &prod;

^^       Logic "and"                                   &and;

^^^      Logic "and" for sub- and superscript          &Wedge;

vv       Logic "or"                                    &or;

vvv      Logic "or" for sub- and superscript           &Vee;

nn       Logic "intersect"                             &cap;

nnn      Logic "intersect" for sub- and superscript    &Intersection;

uu       Logic "union"                                 &cup;

uuu      Logic "union" for sub- and superscript        &Union;

### Relation symbols


Type     Description                                   Entity

=        =                                             =

!=       Not equals                                    &ne;

<        <                                             &lt;

>        >                                             &gt;

<=       Less than or equal                            &le;

>=       Greater than or equal                         &ge;

-lt      Precedes                                      &Precedes;

>-       Succeeds                                      &Succeeds;

in       Element of                                    &isin;

!in      Not an element of                             &notin;

sub      Subset                                        &sub;

sup      Superset                                      &sup;

sube     Subset or equal                               &sube;

supe     Superset or equal                             &supe;

-=       Equivalent                                    &equiv;

~=       Congruent to                                  &cong;

~~       Asymptotically equal to                       &asymp;

prop     Proportional to                               &prop;

### Logical symbols


Type     Description                                   Entity

and      And                                           " and "

or       Or                                            " or "

not      Not                                           &not;

=>       Implies                                       &rArr;

if       If                                            " if "

iff      If and only if                                &hArr;

AA       For all                                       &forall;

EE       There exists                                  &exist;

_|_      Perpendicular, bottom                         &perp;

TT       Top                                           &DownTee;

|--      Right tee                                     &RightTee;

|==      Double right tee                              &DoubleRightTee;

### Grouping brackets


Type     Description                                   Entity

(        (                                             (

)        )                                             )

[        [                                             [

]        ]                                             ]

{        {                                             {

}        }                                             }

(:       Left angle bracket                            &lang;

:)       Right angle bracket                           &rang;

{:       Invisible left grouping element

:}       Invisible right grouping element

### Miscellaneous symbols


Type     Description                                   Entity

int      Integral                                      &int;

oint     Countour integral                             &ContourIntegral;

del      Partial derivative                            &del;

+-       Plus or minus                                 &plusmn;

O/       Null set                                      &empty;

oo       Infinity                                      &infin;

aleph    Hebrew letter aleph                           &alefsym;

/_       Angle                                         &ang;

:.       Therefore                                     &there4;

...      Ellipsis                                      ...

cdots    Three centered dots                           &ctdot;

\<sp>    Non-breaking space (<sp> means space)         &nbsp;

diamond  Diamond                                       &Diamond;

square   Square                                        &Square;

|__      Left floor                                    &lfloor;

__|      Right floor                                   &rfloor;

|~       Left ceiling                                  &lceil;

~|       Right ceiling                                 &rceil;

CC       Complex numbers                               &Copf;

NN       Natural numbers                               &Nopf;

QQ       Rational numbers                              &Qopf;

RR       Real numbers                                  &Ropf;

ZZ       Integers                                      &Zopf;

### Arrows


Type     Description                                   Entity

uarr     Up arrow                                      &uarr;

darr     Down arrow                                    &darr;

rarr     Right arrow                                   &rarr;

->       Right arrow                                   &rarr;

larr     Left arrow                                    &larr;

harr     Horizontal (two-way) arrow                    &harr;

rArr     Right double arrow                            &rArr;

lArr     Left double arrow                             &lArr;

hArr     Horizontal double arrow                       &hArr;

### Accents


Type    Description         Output

hat x   Hat over x          <mover><mi>x</mi><mo>^</mo></mover>

bar x   Bar over x          <mover><mi>x</mi><mo>&macr;</mo></mover>

ul x    Underbar under x    <munder><mi>x</mi><mo>&UnderBar;</mo></munder>

vec x   Right arrow over x  <mover><mi>x</mi><mo>&rarr;</mo><mover>

dot x   Dot over x          <mover><mi>x</mi><mo>.</mo><mover>

ddot x  Double dot over x   <mover><mi>x</mi><mo>..</mo><mover>

### Font commands


Type     Description

bb A     Bold A

bbb A    Double-struck A

cc A     Calligraphic (script) A

tt A     Teletype (monospace) A

fr A     Fraktur A

sf A     Sans-serif A

### Defining new commands and symbols

It is possible to define new commands and symbols using the 'newcommand' and 'newsymbol' binary operators. The former defines a macro that gets expanded and reparsed as ASCIIMathML and the latter defines a constant that gets used as a math operator (<mo>) element. Both of the arguments must be text, optionally enclosed in grouping operators. The 'newsymbol' operator also allows the second argument to be a group of two text strings where the first is the mathml operator and the second is the latex code to be output.

For example, 'newcommand DDX'' {:d/dx:}''' would define a new command 'DDX'. It could then be invoked like 'DDXf(x)', which would expand to '{:d/dx:}f(x)'. The text 'newsymbol{!le''}{&#x2270;''}' could be used to create a symbol you could invoke with '!le', as in 'a !le b'.



=head2 Attributes for [itex]
title
The title attribute for the element, if specified. In many browsers, this string will appear if you hover over the MathML markup.

id
The id attribute for the element, if specified.

class
The class attribute for the element, if specified.

## Attributes for <mstyle>

displaystyle
The displaystyle attribute for the element, if specified. One of the values true'' or false''. If the displaystyle is false, then fractions are represented with a smaller font size and the placement of subscripts and superscripts of sums and integrals changes.

mathvariant
The mathvariant attribute for the element, if specified. One of the values normal'', bold'', italic'', bold-italic'', double-struck'', bold-fraktur'', script'', bold-script'', fraktur'', sans-serif'', bold-sans-serif'', sans-serif-italic'', sans-serif-bold-italic'', or monospace''.

mathsize
The mathsize attribute for the element, if specified. Either small'', normal'' or big'', or of the form number v-unit''.

mathfamily
A string representing the font family.

mathcolor
The mathcolor attribute for the element, if specified. It be in one of the forms #rgb'' or #rrggbb'', or should be an html-color-name.

mathbackground
The mathbackground attribute for the element, if specified. It should be in one of the forms #rgb'' or #rrggbb'', or an html-color-name, or the keyword transparent''.

# BUGS AND SUGGESTIONS

If you find bugs, think of anything that could improve Text::ASCIIMathML or have any questions related to it, feel free to contact the author.

# AUTHOR

Mark Nodine <mnodine@alum.mit.edu>


MathML::Entities,

<http://www1.chapman.edu/~jipsen/mathml/asciimathsyntax.xml>;

# ACKNOWLEDGEMENTS

This Perl module has been created by modifying Peter Jipsen's ASCIIMathML.js script. He deserves full credit for the original implementation; any bugs have probably been introduced by me.