package Text::ASCIIMathML; =pod =head1 NAME Text::ASCIIMathML - Perl extension for parsing ASCIIMathML text into MathML =head1 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(); =head1 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: =over 4 =item C Specifies that the fonts should be optimized for Netscape/Mozilla/Firefox. =back The output of the TextToMathML method always follows the schema ... 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 node and the third argument is a reference to an array of attribute/value pairs for the node. Common attributes for the node are "title" and "xmlns"=>"&mathml;". Common attributes for the node are "mathcolor" (for text color), "displaystyle"=>"true" for using display style instead of inline style, and "fontfamily". =head2 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. =head3 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 C<::=> represents a category of symbols that could be one of the possible sequences of symbols listed on the right. The vertical bar C<|> separates the alternatives. =over 4 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) =back =head3 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: =over 4 lSr -> lSr (note that any pair of brackets can be used to delimit subexpressions, they don't have to match) sqrt S -> S' text S -> S' "any" -> any frac S1 S2 -> S1' S2' root S1 S2 -> S2' S1' stackrel S1 S2 -> S2' S1' S1/S2 -> S1' S2' S1_S2 -> S1 S2' S1^S2 -> S1 S2' S1_S2^S3 -> S1 S2' S3' or S1 S2' S3' (in some cases) S1^S2_S3 -> S1 S3' S2' or S1 S3' S2' (in some cases) =back In the rules above, the expression C is the same as C, except that if C has an outer level of brackets, then C is the expression inside these brackets. =head3 Matrices A simple syntax for matrices is also recognized: l(S11,...,S1n),(...),(Sm1,...,Smn)r or l[S11,...,S1n],[...],[Sm1,...,Smn]r. Here C and C 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 lS11... S1n... Sm1... Smnr. 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. =head3 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 C<< >> tag) or a math identifier (surrounded by a C<< >> 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. =head3 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 C<< >> tag. =head3 Greek letters =over 4 =item Lowercase letters C C C C C C C C C C C C C C C C C C C C C C C =item Uppercase letters C C C C C C C C C C =item Variants C C C =back =head3 Standard functions sin cos tan csc sec cot sinh cosh tanh log ln det dim lim mod gcd lcm min max =head3 Operation symbols Type Description Entity + + + - - - * Mid dot ⋅ ** Star ⋆ // / / \\ \ \ xx Cross product × -: Divided by ÷ @ Compose functions ∘ o+ Circle with plus ⊕ ox Circle with x ⊗ o. Circle with dot ⊙ sum Sum for sub- and superscript ∑ prod Product for sub- and superscript ∏ ^^ Logic "and" ∧ ^^^ Logic "and" for sub- and superscript ⋀ vv Logic "or" ∨ vvv Logic "or" for sub- and superscript ⋁ nn Logic "intersect" ∩ nnn Logic "intersect" for sub- and superscript ⋂ uu Logic "union" ∪ uuu Logic "union" for sub- and superscript ⋃ =head3 Relation symbols Type Description Entity = = = != Not equals ≠ < < < > > > <= Less than or equal ≤ >= Greater than or equal ≥ -lt Precedes ≺ >- Succeeds ≻ in Element of ∈ !in Not an element of ∉ sub Subset ⊂ sup Superset ⊃ sube Subset or equal ⊆ supe Superset or equal ⊇ -= Equivalent ≡ ~= Congruent to ≅ ~~ Asymptotically equal to ≈ prop Proportional to ∝ =head3 Logical symbols Type Description Entity and And " and " or Or " or " not Not ¬ => Implies ⇒ if If " if " iff If and only if ⇔ AA For all ∀ EE There exists ∃ _|_ Perpendicular, bottom ⊥ TT Top ⊤ |-- Right tee ⊢ |== Double right tee ⊨ =head3 Grouping brackets Type Description Entity ( ( ( ) ) ) [ [ [ ] ] ] { { { } } } (: Left angle bracket ⟨ :) Right angle bracket ⟩ {: Invisible left grouping element :} Invisible right grouping element =head3 Miscellaneous symbols Type Description Entity int Integral ∫ oint Countour integral ∮ del Partial derivative &del; grad Gradient ∇ +- Plus or minus ± O/ Null set ∅ oo Infinity ∞ aleph Hebrew letter aleph ℵ & Ampersand & /_ Angle ∠ :. Therefore ∴ ... Ellipsis ... cdots Three centered dots ⋯ \ Non-breaking space ( means space)   quad Quad space    diamond Diamond ⋄ square Square □ |__ Left floor ⌊ __| Right floor ⌋ |~ Left ceiling ⌈ ~| Right ceiling ⌉ CC Complex numbers ℂ NN Natural numbers ℕ QQ Rational numbers ℚ RR Real numbers ℝ ZZ Integers ℤ =head3 Arrows Type Description Entity uarr Up arrow ↑ darr Down arrow ↓ rarr Right arrow → -> Right arrow → larr Left arrow ← harr Horizontal (two-way) arrow ↔ rArr Right double arrow ⇒ lArr Left double arrow ⇐ hArr Horizontal double arrow ⇔ =head3 Accents Type Description Output hat x Hat over x x^ bar x Bar over x x¯ ul x Underbar under x x_ vec x Right arrow over x x→ dot x Dot over x x. ddot x Double dot over x x.. =head3 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 =head3 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 (C<< >>) 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"}{"≰"}' could be used to create a symbol you could invoke with '!le', as in 'a !le b'. =head2 Attributes for =over 4 =item C The title attribute for the element, if specified. In many browsers, this string will appear if you hover over the MathML markup. =item C The id attribute for the element, if specified. =item C The class attribute for the element, if specified. =back =head2 Attributes for =over 4 =item C 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. =item C 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". =item C The mathsize attribute for the element, if specified. Either "small", "normal" or "big", or of the form "number v-unit". =item C A string representing the font family. =item C 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. =item C 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". =head1 METHODS =head2 C =head3 C Converts C<$text> to a MathML string. If the optional C<$math_attr> argument is provided, it should be a reference to a hash of attribute/value pairs for the C< > node. If the optional C<$mstyle_attr> argument is provided, it should be a reference to a hash of attribute/value pairs for the C< > node. =head3 C Like C except that instead of returning a string, it returns a C representing the parsed MathML structure. =head2 C =head3 C Returns a MathML string representing the parsed MathML structure encoded by the C. =head3 C Returns a LaTeX string representing the parsed MathML structure encoded by the C. =head1 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. =head1 AUTHOR Mark Nodine =head1 SEE ALSO MathML::Entities, =head1 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. =head1 COPYRIGHT The Text::ASCIIMathML module is copyright (c) 2006 Mark Nodine, USA. All rights reserved. You may use and distribute them under the terms of either the GNU General Public License or the Artistic License, as specified in the Perl README file. =cut use strict; use warnings; our $VERSION = '0.81'; # Creates a new Text::ASCIIMathML parser object sub new { my ($class) = @_; return bless {}, $class; } # Sets an attribute to a given value # Arguments: Attribute name, attribute value # Returns: None # Supported attributes: # ForMoz Boolean to optimize for Netscape/Mozilla/Firefox sub SetAttribute : method { my ($self, $attr, $val) = @_; $self->{attr}{$attr} = $val; } # Converts an AsciiMathML string to a MathML one # Arguments: AsciiMathML string, # optional ref to array of attribute/value pairs for math node, # optional ref to array of attribute/value pairs for mstyle node # Returns: MathML string sub TextToMathML : method { my $tree = TextToMathMLTree(@_); return $tree ? $tree->text : ''; } # Converts an AsciiMathML string to a tree of MathML nodes # Arguments: AsciiMathML string, # optional ref to array of attribute/value pairs for math node, # optional ref to array of attribute/value pairs for mstyle node # Returns: top Text::ASCIIMathML::Node object or undefined sub TextToMathMLTree : method { my ($self, $expr, $mathAttr, $mstyleAttr) = @_; $expr = '' unless defined $expr; my $mstyle = $self->_createElementMathML('mstyle'); $mstyle->setAttribute (ref $mstyleAttr eq 'ARRAY' ? @$mstyleAttr : %$mstyleAttr) if $mstyleAttr; $self->{nestingDepth} = 0; $expr =~ s/^\s+//; $mstyle->appendChild(($self->_parseExpr($expr, 0))[0]); return unless $mstyle->childNodes > 0; my $math = $self->_createMmlNode('math', $mstyle); $expr =~ s/\n\s*//g; $math->setAttribute(ref $mathAttr eq 'ARRAY' ? @$mathAttr : %$mathAttr) if $mathAttr; return $math; } # Creates an Text::ASCIIMathML::Node object with no tag # Arguments: None # Returns: node object sub _createDocumentFragment : method { my ($self) = @_; return Text::ASCIIMathML::Node->new($self); } # Creates an Text::ASCIIMathML::Node object # Arguments: tag # Returns: node object sub _createElementMathML : method { my ($self, $t) = @_; return Text::ASCIIMathML::Node->new($self, $t); } # Creates an Text::ASCIIMathML::Node object and appends a node as a child # Arguments: tag, node # Returns: node object sub _createMmlNode : method { my ($self, $t, $obj) = @_; my $node = Text::ASCIIMathML::Node->new($self, $t); $node->appendChild($obj); return $node; } # Creates an Text::ASCIIMathML::Node text object with the given text # Arguments: text # Returns: node object sub _createTextNode : method { my ($self, $text) = @_; return Text::ASCIIMathML::Node->newText ($self, $text); } # Finds maximal initial substring of str that appears in names # return null if there is none # Arguments: string # Returns: matched input, entry from AMSymbol (if any) sub _getSymbol : method { my $self = shift; my ($input, $symbol) = $self->_getSymbol_(@_); $self->{previousSymbol} = $symbol->{ttype} if $symbol; return $input, $symbol; } BEGIN { # character lists for Mozilla/Netscape fonts my $AMcal = [0xEF35,0x212C,0xEF36,0xEF37,0x2130,0x2131,0xEF38,0x210B,0x2110,0xEF39,0xEF3A,0x2112,0x2133,0xEF3B,0xEF3C,0xEF3D,0xEF3E,0x211B,0xEF3F,0xEF40,0xEF41,0xEF42,0xEF43,0xEF44,0xEF45,0xEF46]; my $AMfrk = [0xEF5D,0xEF5E,0x212D,0xEF5F,0xEF60,0xEF61,0xEF62,0x210C,0x2111,0xEF63,0xEF64,0xEF65,0xEF66,0xEF67,0xEF68,0xEF69,0xEF6A,0x211C,0xEF6B,0xEF6C,0xEF6D,0xEF6E,0xEF6F,0xEF70,0xEF71,0x2128]; my $AMbbb = [0xEF8C,0xEF8D,0x2102,0xEF8E,0xEF8F,0xEF90,0xEF91,0x210D,0xEF92,0xEF93,0xEF94,0xEF95,0xEF96,0x2115,0xEF97,0x2119,0x211A,0x211D,0xEF98,0xEF99,0xEF9A,0xEF9B,0xEF9C,0xEF9D,0xEF9E,0x2124]; # Create closure for static variables my %AMSymbol = ( "sqrt" => { tag=>"msqrt", output=>"sqrt", tex=>'', ttype=>"UNARY" }, "root" => { tag=>"mroot", output=>"root", tex=>'', ttype=>"BINARY" }, "frac" => { tag=>"mfrac", output=>"/", tex=>'', ttype=>"BINARY" }, "/" => { tag=>"mfrac", output=>"/", tex=>'', ttype=>"INFIX" }, "stackrel" => { tag=>"mover", output=>"stackrel", tex=>'', ttype=>"BINARY" }, "_" => { tag=>"msub", output=>"_", tex=>'', ttype=>"INFIX" }, "^" => { tag=>"msup", output=>"^", tex=>'', ttype=>"INFIX" }, "text" => { tag=>"mtext", output=>"text", tex=>'', ttype=>"TEXT" }, "mbox" => { tag=>"mtext", output=>"mbox", tex=>'', ttype=>"TEXT" }, "\"" => { tag=>"mtext", output=>"mbox", tex=>'', ttype=>"TEXT" }, # new for perl "newcommand" => { ttype=>"BINARY"}, "newsymbol" => { ttype=>"BINARY" }, # some greek symbols "alpha" => { tag=>"mi", output=>"α", tex=>'', ttype=>"CONST" }, "beta" => { tag=>"mi", output=>"β", tex=>'', ttype=>"CONST" }, "chi" => { tag=>"mi", output=>"χ", tex=>'', ttype=>"CONST" }, "delta" => { tag=>"mi", output=>"δ", tex=>'', ttype=>"CONST" }, "Delta" => { tag=>"mo", output=>"Δ", tex=>'', ttype=>"CONST" }, "epsi" => { tag=>"mi", output=>"ε", tex=>"epsilon", ttype=>"CONST" }, "varepsilon" => { tag=>"mi", output=>"ɛ", tex=>'', ttype=>"CONST" }, "eta" => { tag=>"mi", output=>"η", tex=>'', ttype=>"CONST" }, "gamma" => { tag=>"mi", output=>"γ", tex=>'', ttype=>"CONST" }, "Gamma" => { tag=>"mo", output=>"Γ", tex=>'', ttype=>"CONST" }, "iota" => { tag=>"mi", output=>"ι", tex=>'', ttype=>"CONST" }, "kappa" => { tag=>"mi", output=>"κ", tex=>'', ttype=>"CONST" }, "lambda" => { tag=>"mi", output=>"λ", tex=>'', ttype=>"CONST" }, "Lambda" => { tag=>"mo", output=>"Λ", tex=>'', ttype=>"CONST" }, "mu" => { tag=>"mi", output=>"μ", tex=>'', ttype=>"CONST" }, "nu" => { tag=>"mi", output=>"ν", tex=>'', ttype=>"CONST" }, "omega" => { tag=>"mi", output=>"ω", tex=>'', ttype=>"CONST" }, "Omega" => { tag=>"mo", output=>"Ω", tex=>'', ttype=>"CONST" }, "phi" => { tag=>"mi", output=>"ϕ", tex=>'', ttype=>"CONST" }, "varphi" => { tag=>"mi", output=>"φ", tex=>'', ttype=>"CONST" }, "Phi" => { tag=>"mo", output=>"Φ", tex=>'', ttype=>"CONST" }, "pi" => { tag=>"mi", output=>"π", tex=>'', ttype=>"CONST" }, "Pi" => { tag=>"mo", output=>"Π", tex=>'', ttype=>"CONST" }, "psi" => { tag=>"mi", output=>"ψ", tex=>'', ttype=>"CONST" }, "Psi" => { tag=>"mi", output=>"Ψ", tex=>'', ttype=>"CONST" }, "rho" => { tag=>"mi", output=>"ρ", tex=>'', ttype=>"CONST" }, "sigma" => { tag=>"mi", output=>"σ", tex=>'', ttype=>"CONST" }, "Sigma" => { tag=>"mo", output=>"Σ", tex=>'', ttype=>"CONST" }, "tau" => { tag=>"mi", output=>"τ", tex=>'', ttype=>"CONST" }, "theta" => { tag=>"mi", output=>"θ", tex=>'', ttype=>"CONST" }, "vartheta" => { tag=>"mi", output=>"ϑ", tex=>'', ttype=>"CONST" }, "Theta" => { tag=>"mo", output=>"Θ", tex=>'', ttype=>"CONST" }, "upsilon" => { tag=>"mi", output=>"υ", tex=>'', ttype=>"CONST" }, "xi" => { tag=>"mi", output=>"ξ", tex=>'', ttype=>"CONST" }, "Xi" => { tag=>"mo", output=>"Ξ", tex=>'', ttype=>"CONST" }, "zeta" => { tag=>"mi", output=>"ζ", tex=>'', ttype=>"CONST" }, # binary operation symbols "*" => { tag=>"mo", output=>"⋅", tex=>"cdot", ttype=>"CONST" }, "**" => { tag=>"mo", output=>"⋆", tex=>"star", ttype=>"CONST" }, "//" => { tag=>"mo", output=>"/", tex=>'', ttype=>"CONST" }, "\\\\" => { tag=>"mo", output=>"\\", tex=>"backslash", ttype=>"CONST" }, "setminus" => { tag=>"mo", output=>"\\", tex=>'', ttype=>"CONST" }, "xx" => { tag=>"mo", output=>"×", tex=>"times", ttype=>"CONST" }, "-:" => { tag=>"mo", output=>"÷", tex=>"div", ttype=>"CONST" }, "@" => { tag=>"mo", output=>"∘", tex=>"circ", ttype=>"CONST" }, "o+" => { tag=>"mo", output=>"⊕", tex=>"oplus", ttype=>"CONST" }, "ox" => { tag=>"mo", output=>"⊗", tex=>"otimes", ttype=>"CONST" }, "o." => { tag=>"mo", output=>"⊙", tex=>"odot", ttype=>"CONST" }, "sum" => { tag=>"mo", output=>"∑", tex=>'', ttype=>"UNDEROVER" }, "prod" => { tag=>"mo", output=>"∏", tex=>'', ttype=>"UNDEROVER" }, "^^" => { tag=>"mo", output=>"∧", tex=>"wedge", ttype=>"CONST" }, "^^^" => { tag=>"mo", output=>"⋀", tex=>"bigwedge", ttype=>"UNDEROVER" }, "vv" => { tag=>"mo", output=>"∨", tex=>"vee", ttype=>"CONST" }, "vvv" => { tag=>"mo", output=>"⋁", tex=>"bigvee", ttype=>"UNDEROVER" }, "nn" => { tag=>"mo", output=>"∩", tex=>"cap", ttype=>"CONST" }, "nnn" => { tag=>"mo", output=>"⋂", tex=>"bigcap", ttype=>"UNDEROVER" }, "uu" => { tag=>"mo", output=>"∪", tex=>"cup", ttype=>"CONST" }, "uuu" => { tag=>"mo", output=>"⋃", tex=>"bigcup", ttype=>"UNDEROVER" }, # binary relation symbols "!=" => { tag=>"mo", output=>"≠", tex=>"ne", ttype=>"CONST" }, ":=" => { tag=>"mo", output=>":=", tex=>'', ttype=>"CONST" }, #"lt" => { tag=>"mo", output=>"<", tex=>'', ttype=>"CONST" }, "lt" => { tag=>"mo", output=>"<", tex=>'', ttype=>"CONST" }, "<=" => { tag=>"mo", output=>"≤", tex=>"le", ttype=>"CONST" }, "lt=" => { tag=>"mo", output=>"≤", tex=>"leq", ttype=>"CONST", latex=>1 }, ">=" => { tag=>"mo", output=>"≥", tex=>"ge", ttype=>"CONST" }, "geq" => { tag=>"mo", output=>"≥", tex=>'', ttype=>"CONST", latex=>1 }, "-<" => { tag=>"mo", output=>"≺", tex=>"prec", ttype=>"CONST", latex=>1 }, "-lt" => { tag=>"mo", output=>"≺", tex=>'', ttype=>"CONST" }, ">-" => { tag=>"mo", output=>"≻", tex=>"succ", ttype=>"CONST" }, "in" => { tag=>"mo", output=>"∈", tex=>'', ttype=>"CONST" }, "!in" => { tag=>"mo", output=>"∉", tex=>"notin", ttype=>"CONST" }, "sub" => { tag=>"mo", output=>"⊂", tex=>"subset", ttype=>"CONST" }, "sup" => { tag=>"mo", output=>"⊃", tex=>"supset", ttype=>"CONST" }, "sube" => { tag=>"mo", output=>"⊆", tex=>"subseteq", ttype=>"CONST" }, "supe" => { tag=>"mo", output=>"⊇", tex=>"supseteq", ttype=>"CONST" }, "-=" => { tag=>"mo", output=>"≡", tex=>"equiv", ttype=>"CONST" }, "~=" => { tag=>"mo", output=>"≅", tex=>"cong", ttype=>"CONST" }, "~~" => { tag=>"mo", output=>"≈", tex=>"approx", ttype=>"CONST" }, "prop" => { tag=>"mo", output=>"∝", tex=>"propto", ttype=>"CONST" }, # new for perl "<" => { tag=>"mo", output=>"<", tex=>'', ttype=>"CONST" }, "gt" => { tag=>"mo", output=>">", tex=>'', ttype=>"CONST" }, ">" => { tag=>"mo", output=>">", tex=>'', ttype=>"CONST" }, "\\!" => { tag=>"", output=>'', tex=>'', ttype=>"NOP" }, # logical symbols "and" => { tag=>"mtext", output=>"and", tex=>'', ttype=>"SPACE" }, "or" => { tag=>"mtext", output=>"or", tex=>'', ttype=>"SPACE" }, "not" => { tag=>"mo", output=>"¬", tex=>"neg", ttype=>"CONST" }, "=>" => { tag=>"mo", output=>"⇒", tex=>"implies", ttype=>"CONST" }, "if" => { tag=>"mo", output=>"if", tex=>'if', ttype=>"SPACE" }, "<=>" => { tag=>"mo", output=>"⇔", tex=>"iff", ttype=>"CONST" }, "AA" => { tag=>"mo", output=>"∀", tex=>"forall", ttype=>"CONST" }, "EE" => { tag=>"mo", output=>"∃", tex=>"exists", ttype=>"CONST" }, "_|_" => { tag=>"mo", output=>"⊥", tex=>"bot", ttype=>"CONST" }, "TT" => { tag=>"mo", output=>"⊤", tex=>"top", ttype=>"CONST" }, "|--" => { tag=>"mo", output=>"⊢", tex=>"vdash", ttype=>"CONST" }, "|==" => { tag=>"mo", output=>"⊨", tex=>"models", ttype=>"CONST" }, # grouping brackets "(" => { tag=>"mo", output=>"(", tex=>'', ttype=>"LEFTBRACKET" }, ")" => { tag=>"mo", output=>")", tex=>'', ttype=>"RIGHTBRACKET" }, "[" => { tag=>"mo", output=>"[", tex=>'', ttype=>"LEFTBRACKET" }, "]" => { tag=>"mo", output=>"]", tex=>'', ttype=>"RIGHTBRACKET" }, "{" => { tag=>"mo", output=>"{", tex=>'', ttype=>"LEFTBRACKET" }, "}" => { tag=>"mo", output=>"}", tex=>'', ttype=>"RIGHTBRACKET" }, "|" => { tag=>"mo", output=>"|", tex=>'', ttype=>"LEFTRIGHT" }, # {input:"||", tag:"mo", output:"||", tex:null, ttype:LEFTRIGHT}, "(:" => { tag=>"mo", output=>"〈", tex=>"langle", ttype=>"LEFTBRACKET" }, ":)" => { tag=>"mo", output=>"〉", tex=>"rangle", ttype=>"RIGHTBRACKET" }, "<<" => { tag=>"mo", output=>"〈", tex=>'langle', ttype=>"LEFTBRACKET" }, ">>" => { tag=>"mo", output=>"〉", tex=>'rangle', ttype=>"RIGHTBRACKET" }, "{:" => { tag=>"mo", output=>"{:", tex=>'', ttype=>"LEFTBRACKET", invisible=>"true" }, ":}" => { tag=>"mo", output=>":}", tex=>'', ttype=>"RIGHTBRACKET", invisible=>"true" }, # miscellaneous symbols "int" => { tag=>"mo", output=>"∫", tex=>'', ttype=>"CONST" }, "dx" => { tag=>"mi", output=>"{:d x:}", tex=>'', ttype=>"DEFINITION" }, "dy" => { tag=>"mi", output=>"{:d y:}", tex=>'', ttype=>"DEFINITION" }, "dz" => { tag=>"mi", output=>"{:d z:}", tex=>'', ttype=>"DEFINITION" }, "dt" => { tag=>"mi", output=>"{:d t:}", tex=>'', ttype=>"DEFINITION" }, "oint" => { tag=>"mo", output=>"∮", tex=>'', ttype=>"CONST" }, "del" => { tag=>"mo", output=>"∂", tex=>"partial", ttype=>"CONST" }, "grad" => { tag=>"mo", output=>"∇", tex=>"nabla", ttype=>"CONST" }, "+-" => { tag=>"mo", output=>"±", tex=>"pm", ttype=>"CONST" }, "O/" => { tag=>"mo", output=>"∅", tex=>"emptyset", ttype=>"CONST" }, "oo" => { tag=>"mo", output=>"∞", tex=>"infty", ttype=>"CONST" }, "aleph" => { tag=>"mo", output=>"ℵ", tex=>'', ttype=>"CONST" }, "..." => { tag=>"mo", output=>"...", tex=>"ldots", ttype=>"CONST" }, ":." => { tag=>"mo", output=>"∴", tex=>"therefore", ttype=>"CONST" }, "/_" => { tag=>"mo", output=>"∠", tex=>"angle", ttype=>"CONST" }, "&" => { tag=>"mo", output=>"&", tex=>'\&', ttype=>"CONST" }, "\\ " => { tag=>"mo", output=>" ", tex=>'\,', ttype=>"CONST" }, "quad" => { tag=>"mo", output=>"  ", tex=>'', ttype=>"CONST" }, "qquad" => { tag=>"mo", output=>"    ", tex=>'', ttype=>"CONST" }, "cdots" => { tag=>"mo", output=>"⋯", tex=>'', ttype=>"CONST" }, "vdots" => { tag=>"mo", output=>"⋮", tex=>'', ttype=>"CONST" }, "ddots" => { tag=>"mo", output=>"⋱", tex=>'', ttype=>"CONST" }, "diamond" => { tag=>"mo", output=>"⋄", tex=>'', ttype=>"CONST" }, "square" => { tag=>"mo", output=>"□", tex=>'', ttype=>"CONST" }, "|__" => { tag=>"mo", output=>"⌊", tex=>"lfloor", ttype=>"CONST" }, "__|" => { tag=>"mo", output=>"⌋", tex=>"rfloor", ttype=>"CONST" }, "|~" => { tag=>"mo", output=>"⌈", tex=>"lceil", ttype=>"CONST" }, "~|" => { tag=>"mo", output=>"⌉", tex=>"rceil", ttype=>"CONST" }, "CC" => { tag=>"mo", output=>"ℂ", tex=>'', ttype=>"CONST" }, "NN" => { tag=>"mo", output=>"ℕ", tex=>'', ttype=>"CONST" }, "QQ" => { tag=>"mo", output=>"ℚ", tex=>'', ttype=>"CONST" }, "RR" => { tag=>"mo", output=>"ℝ", tex=>'', ttype=>"CONST" }, "ZZ" => { tag=>"mo", output=>"ℤ", tex=>'', ttype=>"CONST" }, "f" => { tag=>"mi", output=>"f", tex=>'', ttype=>"UNARY", func=>"true" }, "g" => { tag=>"mi", output=>"g", tex=>'', ttype=>"UNARY", func=>"true" }, # standard functions "lim" => { tag=>"mo", output=>"lim", tex=>'', ttype=>"UNDEROVER" }, "Lim" => { tag=>"mo", output=>"Lim", tex=>'', ttype=>"UNDEROVER" }, "sin" => { tag=>"mo", output=>"sin", tex=>'', ttype=>"UNARY", func=>"true" }, "cos" => { tag=>"mo", output=>"cos", tex=>'', ttype=>"UNARY", func=>"true" }, "tan" => { tag=>"mo", output=>"tan", tex=>'', ttype=>"UNARY", func=>"true" }, "sinh" => { tag=>"mo", output=>"sinh", tex=>'', ttype=>"UNARY", func=>"true" }, "cosh" => { tag=>"mo", output=>"cosh", tex=>'', ttype=>"UNARY", func=>"true" }, "tanh" => { tag=>"mo", output=>"tanh", tex=>'', ttype=>"UNARY", func=>"true" }, "cot" => { tag=>"mo", output=>"cot", tex=>'', ttype=>"UNARY", func=>"true" }, "sec" => { tag=>"mo", output=>"sec", tex=>'', ttype=>"UNARY", func=>"true" }, "csc" => { tag=>"mo", output=>"csc", tex=>'', ttype=>"UNARY", func=>"true" }, "log" => { tag=>"mo", output=>"log", tex=>'', ttype=>"UNARY", func=>"true" }, "ln" => { tag=>"mo", output=>"ln", tex=>'', ttype=>"UNARY", func=>"true" }, "det" => { tag=>"mo", output=>"det", tex=>'', ttype=>"UNARY", func=>"true" }, "dim" => { tag=>"mo", output=>"dim", tex=>'', ttype=>"CONST" }, "mod" => { tag=>"mo", output=>"mod", tex=>'', ttype=>"CONST" }, "gcd" => { tag=>"mo", output=>"gcd", tex=>'', ttype=>"UNARY", func=>"true" }, "lcm" => { tag=>"mo", output=>"lcm", tex=>'', ttype=>"UNARY", func=>"true" }, "lub" => { tag=>"mo", output=>"lub", tex=>'', ttype=>"CONST" }, "glb" => { tag=>"mo", output=>"glb", tex=>'', ttype=>"CONST" }, "min" => { tag=>"mo", output=>"min", tex=>'', ttype=>"UNDEROVER" }, "max" => { tag=>"mo", output=>"max", tex=>'', ttype=>"UNDEROVER" }, # arrows "uarr" => { tag=>"mo", output=>"↑", tex=>"uparrow", ttype=>"CONST" }, "darr" => { tag=>"mo", output=>"↓", tex=>"downarrow", ttype=>"CONST" }, "rarr" => { tag=>"mo", output=>"→", tex=>"rightarrow", ttype=>"CONST" }, "->" => { tag=>"mo", output=>"→", tex=>"to", ttype=>"CONST", latex=>1 }, "|->" => { tag=>"mo", output=>"↦", tex=>"mapsto", ttype=>"CONST" }, "larr" => { tag=>"mo", output=>"←", tex=>"leftarrow", ttype=>"CONST" }, "harr" => { tag=>"mo", output=>"↔", tex=>"leftrightarrow", ttype=>"CONST" }, "rArr" => { tag=>"mo", output=>"⇒", tex=>"Rightarrow", ttype=>"CONST", latex=>1 }, "lArr" => { tag=>"mo", output=>"⇐", tex=>"Leftarrow", ttype=>"CONST" }, "hArr" => { tag=>"mo", output=>"⇔", tex=>"Leftrightarrow", ttype=>"CONST", latex=>1 }, # commands with argument "hat" => { tag=>"mover", output=>"^", tex=>'', ttype=>"UNARY", acc=>"true" }, "bar" => { tag=>"mover", output=>"¯", tex=>"overline", ttype=>"UNARY", acc=>"true" }, "vec" => { tag=>"mover", output=>"→", tex=>'', ttype=>"UNARY", acc=>"true" }, "dot" => { tag=>"mover", output=>".", tex=>'', ttype=>"UNARY", acc=>"true" }, "ddot" => { tag=>"mover", output=>"..", tex=>'', ttype=>"UNARY", acc=>"true" }, "ul" => { tag=>"munder", output=>"̲", tex=>"underline", ttype=>"UNARY", acc=>"true" }, "bb" => { tag=>"mstyle", atname=>"fontweight", atval=>"bold", output=>"bb", tex=>'', ttype=>"UNARY" }, "mathbf" => { tag=>"mstyle", atname=>"fontweight", atval=>"bold", output=>"mathbf", tex=>'', ttype=>"UNARY" }, "sf" => { tag=>"mstyle", atname=>"fontfamily", atval=>"sans-serif", output=>"sf", tex=>'', ttype=>"UNARY" }, "mathsf" => { tag=>"mstyle", atname=>"fontfamily", atval=>"sans-serif", output=>"mathsf", tex=>'', ttype=>"UNARY" }, "bbb" => { tag=>"mstyle", atname=>"mathvariant", atval=>"double-struck", output=>"bbb", tex=>'', ttype=>"UNARY", codes=>$AMbbb }, "mathbb" => { tag=>"mstyle", atname=>"mathvariant", atval=>"double-struck", output=>"mathbb", tex=>'', ttype=>"UNARY", codes=>$AMbbb }, "cc" => { tag=>"mstyle", atname=>"mathvariant", atval=>"script", output=>"cc", tex=>'', ttype=>"UNARY", codes=>$AMcal }, "mathcal" => { tag=>"mstyle", atname=>"mathvariant", atval=>"script", output=>"mathcal", tex=>'', ttype=>"UNARY", codes=>$AMcal }, "tt" => { tag=>"mstyle", atname=>"fontfamily", atval=>"monospace", output=>"tt", tex=>'', ttype=>"UNARY" }, "mathtt" => { tag=>"mstyle", atname=>"fontfamily", atval=>"monospace", output=>"mathtt", tex=>'', ttype=>"UNARY" }, "fr" => { tag=>"mstyle", atname=>"mathvariant", atval=>"fraktur", output=>"fr", tex=>'', ttype=>"UNARY", codes=>$AMfrk }, "mathfrak" => { tag=>"mstyle", atname=>"mathvariant", atval=>"fraktur", output=>"mathfrak", tex=>'', ttype=>"UNARY", codes=>$AMfrk }, ); # Preprocess AMSymbol for lexer regular expression # Preprocess AMSymbol for tex input my %AMTexSym = map(($AMSymbol{$_}{tex} || $_, $_), grep($AMSymbol{$_}{tex}, keys %AMSymbol)); my $Ident_RE = join '|', map("\Q$_\E", sort {length($b) - length($a)} (keys %AMSymbol, keys %AMTexSym)); sub _getSymbol_ : method { my ($self, $str) = @_; for ($str) { /^(\d+(\.\d+)?)/ || /^(\.\d+)/ and return $1, {tag=>'mn', output=>$1, ttype=>'CONST'}; $self->{Definition_RE} && /^($self->{Definition_RE})/ and return $1, $self->{Definitions}{$1}; /^($Ident_RE)/o and return $1,$AMTexSym{$1} ? $AMSymbol{$AMTexSym{$1}} : $AMSymbol{$1}; /^([A-Za-z])/ and return $1, {tag=>'mi', output=>$1, ttype=>'CONST'}; /^(.)/ and return $1 eq '-' && defined $self->{previousSymbol} && $self->{previousSymbol} eq 'INFIX' ? ($1, {tag=>'mo', output=>$1, ttype=>'UNARY', func=>"true"} ) : ($1, {tag=>'mo', output=>$1, ttype=>'CONST'}); } } # Used so that Text::ASCIIMathML::Node can get access to the symbol table sub _get_amsymbol_ { return \%AMSymbol; } } # Parses an E expression # Arguments: string to parse, whether to look for a right bracket # Returns: parsed node (if successful), remaining unparsed string sub _parseExpr : method { my ($self, $str, $rightbracket) = @_; my $newFrag = $self->_createDocumentFragment(); my ($node, $input, $symbol); do { $str = _removeCharsAndBlanks($str, 0); ($node, $str) = $self->_parseIexpr($str); ($input, $symbol) = $self->_getSymbol($str); if (defined $symbol && $symbol->{ttype} eq 'INFIX' && $input eq '/') { $str = _removeCharsAndBlanks($str, length $input); my @result = $self->_parseIexpr($str); if ($result[0]) { _removeBrackets($result[0]); } else { # show box in place of missing argument $result[0] = $self->_createMmlNode ('mo', $self->_createTextNode('A1;')); } $str = $result[1]; _removeBrackets($node); $node = $self->_createMmlNode($symbol->{tag}, $node); $node->appendChild($result[0]); $newFrag->appendChild($node); ($input, $symbol) = $self->_getSymbol($str); } elsif (defined $node) { $newFrag->appendChild($node); } } while (defined $symbol && ($symbol->{ttype} ne 'RIGHTBRACKET' && ($symbol->{ttype} ne 'LEFTRIGHT' || $rightbracket) || $self->{nestingDepth} == 0) && $symbol->{output} ne ''); if (defined $symbol && $symbol->{ttype} =~ /RIGHTBRACKET|LEFTRIGHT/) { my @childNodes = $newFrag->childNodes; if (@childNodes > 1 && $childNodes[-1]->nodeName eq 'mrow' && $childNodes[-2]->nodeName eq 'mo' && $childNodes[-2]->firstChild->nodeValue eq ',') { # matrix my $right = $childNodes[-1]->lastChild->firstChild->nodeValue; if ($right =~ /[\)\]]/) { my $left = $childNodes[-1]->firstChild->firstChild->nodeValue; if ("$left$right" =~ /^\(\)$/ && $symbol->{output} ne '}' || "$left$right" =~ /^\[\]$/) { my @pos; # positions of commas my $matrix = 1; my $m = @childNodes; for (my $i=0; $matrix && $i < $m; $i += 2) { $pos[$i] = []; $node = $childNodes[$i]; $matrix = $node->nodeName eq 'mrow' && ($i == $m-1 || $node->nextSibling->nodeName eq 'mo' && $node->nextSibling->firstChild->nodeValue eq ',')&& $node->firstChild->firstChild->nodeValue eq $left&& $node->lastChild->firstChild->nodeValue eq $right if $matrix; if ($matrix) { for (my $j=0; $j<($node->childNodes); $j++) { if (($node->childNodes)[$j]->firstChild-> nodeValue eq ',') { push @{$pos[$i]}, $j; } } } if ($matrix && $i > 1) { $matrix = @{$pos[$i]} == @{$pos[$i-2]}; } } if ($matrix) { my $table = $self->_createDocumentFragment(); for (my $i=0; $i<$m; $i += 2) { my $row = $self->_createDocumentFragment(); my $frag = $self->_createDocumentFragment(); # (-,-,...,-,-) $node = $newFrag->firstChild; my $n = $node->childNodes; my $k = 0; $node->removeChild($node->firstChild); # remove ( for (my $j=1; $j<$n-1; $j++) { if ($k < @{$pos[$i]} && $j == $pos[$i][$k]) { # remove , $row->appendChild ($self->_createMmlNode('mtd', $frag)); $frag = $self->_createDocumentFragment(); $k++; } else { $frag->appendChild($node->firstChild); } $node->removeChild($node->firstChild); } $row->appendChild ($self->_createMmlNode('mtd', $frag)); if ($newFrag->childNodes > 2) { # remove ) $newFrag->removeChild($newFrag->firstChild); # remove , $newFrag->removeChild($newFrag->firstChild); } $table->appendChild ($self->_createMmlNode('mtr', $row)); } $node = $self->_createMmlNode('mtable', $table); $node->setAttribute('columnalign', 'left') if $symbol->{invisible}; $newFrag->replaceChild($node, $newFrag->firstChild); } } } } $str = _removeCharsAndBlanks($str, length $input); if (! $symbol->{invisible}) { $node = $self->_createMmlNode ('mo', $self->_createTextNode($symbol->{output})); $newFrag->appendChild($node); } } return $newFrag, $str; } # Parses an I expression # Arguments: string to parse # Returns: parsed node (if successful), remaining unparsed string sub _parseIexpr : method { my ($self, $str) = @_; $str = _removeCharsAndBlanks($str, 0); my ($in1, $sym1) = $self->_getSymbol($str); my $node; ($node, $str) = $self->_parseSexpr($str); my ($input, $symbol) = $self->_getSymbol($str); if (defined $symbol && $symbol->{ttype} eq 'INFIX' && $input ne '/') { # if (symbol.input == "/") result = AMparseIexpr(str); else ... $str = _removeCharsAndBlanks($str, length $input); my @result = $self->_parseSexpr($str); if ($result[0]) { _removeBrackets($result[0]); } else { # show box in place of missing argument $result[0] = $self->_createMmlNode ('mo', $self->_createTextNode("A1;")); } $str = $result[1]; if ($input eq '_') { my ($in2, $sym2) = $self->_getSymbol($str); my $underover = $sym1->{ttype} eq 'UNDEROVER'; if ($in2 eq '^') { $str = _removeCharsAndBlanks($str, length $in2); my @res2 = $self->_parseSexpr($str); _removeBrackets($res2[0]); $str = $res2[1]; $node = $self->_createMmlNode ($underover ? 'munderover' : 'msubsup', $node); $node->appendChild($result[0]); $node->appendChild($res2[0]); $node = $self->_createMmlNode('mrow',$node); # so sum does not stretch } else { $node = $self->_createMmlNode ($underover ? 'munder' : 'msub', $node); $node->appendChild($result[0]); } } elsif ($input eq '^') { my ($in2, $sym2) = $self->_getSymbol($str); my $underover = $sym1->{ttype} eq 'UNDEROVER'; if ($in2 eq '_') { $str = _removeCharsAndBlanks($str, length $in2); my @res2 = $self->_parseSexpr($str); _removeBrackets($res2[0]); $str = $res2[1]; $node = $self->_createMmlNode ($underover ? 'munderover' : 'msubsup', $node); $node->appendChild($res2[0]); $node->appendChild($result[0]); $node = $self->_createMmlNode('mrow',$node); # so sum does not stretch } else { $node = $self->_createMmlNode ($underover ? 'mover' : 'msup', $node); $node->appendChild($result[0]); } } else { $node = $self->_createMmlNode($symbol->{tag}, $node); $node->appendChild($result[0]); } } return $node, $str; } # Parses an S expression # Arguments: string to parse # Returns: parsed node (if successful), remaining unparsed string sub _parseSexpr : method { my ($self, $str) = @_; my $newFrag = $self->_createDocumentFragment(); $str = _removeCharsAndBlanks($str, 0); my ($input, $symbol) = $self->_getSymbol($str); return (undef, $str) if ! defined $symbol || $symbol->{ttype} eq 'RIGHTBRACKET' && $self->{nestingDepth} > 0; if ($symbol->{ttype} eq 'DEFINITION') { $str = $symbol->{output} . _removeCharsAndBlanks($str, length $input); ($input, $symbol) = $self->_getSymbol($str); } my $ttype = $symbol->{ttype}; if ($ttype =~ /UNDEROVER|CONST/) { $str = _removeCharsAndBlanks($str, length $input); return $self->_createMmlNode($symbol->{tag}, $self->_createTextNode($symbol->{output})), $str; } if ($ttype eq 'LEFTBRACKET') { $self->{nestingDepth}++; $str = _removeCharsAndBlanks($str, length $input); my @result = $self->_parseExpr($str, 1); $self->{nestingDepth}--; my $node; if ($symbol->{invisible}) { $node = $self->_createMmlNode('mrow', $result[0]); } else { $node = $self->_createMmlNode ('mo', $self->_createTextNode($symbol->{output})); $node = $self->_createMmlNode('mrow', $node); $node->appendChild($result[0]); } return $node, $result[1]; } if ($ttype eq 'TEXT') { $str = _removeCharsAndBlanks($str, length $input) unless $input eq '"'; my $st; ($input, $st) = ($1, $2) if $str =~ /^(\"()\")/ || $str =~ /^(\"((?:\\\\|\\\"|.)+?)\")/; ($input, $st) = ($1, $2) if ($str =~ /^(\((.*?)\))/ || $str =~ /^(\[(.*?)\])/ || $str =~ /^(\{(.*?)\})/); ($input, $st) = ($str) x 2 unless defined $st; if (substr($st, 0, 1) eq ' ') { my $node = $self->_createElementMathML('mspace'); $node->setAttribute(width=>'1ex'); $newFrag->appendChild($node); } $newFrag->appendChild ($self->_createMmlNode($symbol->{tag}, $self->_createTextNode($st))); if (substr($st, -1) eq ' ') { my $node = $self->_createElementMathML('mspace'); $node->setAttribute(width=>'1ex'); $newFrag->appendChild($node); } $str = _removeCharsAndBlanks($str, length $input); return $self->_createMmlNode('mrow', $newFrag), $str; } if ($ttype eq 'UNARY') { $str = _removeCharsAndBlanks($str, length $input); my @result = $self->_parseSexpr($str); return ($self->_createMmlNode ($symbol->{tag}, $self->_createTextNode($symbol->{output})), $str) if ! defined $result[0]; if ($symbol->{func}) { return ($self->_createMmlNode ($symbol->{tag}, $self->_createTextNode($symbol->{output})), $str) if $str =~ m!^[\^_/|]!; my $node = $self->_createMmlNode ('mrow', $self->_createMmlNode ($symbol->{tag}, $self->_createTextNode($symbol->{output}))); $node->appendChild($result[0]); return $node, $result[1]; } _removeBrackets($result[0]); if ($symbol->{acc}) { # accent my $node = $self->_createMmlNode($symbol->{tag}, $result[0]); $node->appendChild ($self->_createMmlNode ('mo', $self->_createTextNode($symbol->{output}))); return $node, $result[1]; } if ($symbol->{atname}) { # font change command if ($self->{attr}{ForMoz} && $symbol->{codes}) { my @childNodes = $result[0]->childNodes; my $nodeName = $result[0]->nodeName; for (my $i=0; $i<@childNodes; $i++) { if ($childNodes[$i]->nodeName eq 'mi'||$nodeName eq 'mi') { my $st = $nodeName eq 'mi' ? $result[0] ->firstChild->nodeValue : $childNodes[$i]->firstChild->nodeValue; $st =~ s/([A-Z])/sprintf "&#x%X;",$symbol->{codes}[ord($1)-65]/ge; if ($nodeName eq 'mi') { $result[0] = $self->_createTextNode($st); } else { $result[0]->replaceChild ($self->_createTextNode($st), $childNodes[$i]); } } } } my $node = $self->_createMmlNode($symbol->{tag}, $result[0]); $node->setAttribute($symbol->{atname}=>$symbol->{atval}); return $node, $result[1]; } return $self->_createMmlNode($symbol->{tag}, $result[0]), $result[1]; } if ($ttype eq 'BINARY') { $str = _removeCharsAndBlanks($str, length $input); my @result = $self->_parseSexpr($str); return ($self->_createMmlNode ('mo', $self->_createTextNode($input)), $str) if ! defined $result[0]; _removeBrackets($result[0]); my @result2 = $self->_parseSexpr($result[1]); return ($self->_createMmlNode ('mo', $self->_createTextNode($input)), $str) if ! defined $result2[0]; _removeBrackets($result2[0]); if ($input =~ /new(command|symbol)/) { my $what = $1; # Look for text in both arguments my $text1 = $result[0]; my $haveTextArgs = 0; $text1 = $text1->firstChild while $text1->nodeName eq 'mrow'; if ($text1->nodeName eq 'mtext') { my $text2 = $result2[0]; $text2 = $text2->firstChild while $text2->nodeName eq 'mrow'; my $latex; if ($result2[0]->childNodes > 1 && $input eq 'newsymbol') { # Process the latex string for a newsymbol my $latexdef = $result2[0]->child(1); $latexdef = $latexdef->firstChild while $latexdef->nodeName eq 'mrow'; $latex = $latexdef->firstChild->nodeValue; } if ($text2->nodeName eq 'mtext') { $self->{Definitions}{$text1->firstChild->nodeValue} = { tag =>'mo', output=>$text2->firstChild->nodeValue, ttype =>$what eq 'symbol' ? 'CONST' : 'DEFINITION', }; $self->{Definition_RE} = join '|', map("\Q$_\E", sort {length($b) - length($a)} keys %{$self->{Definitions}}); $self->{Latex}{$text2->firstChild->nodeValue} = $latex if defined $latex; $haveTextArgs = 1; } } if (! $haveTextArgs) { $newFrag->appendChild($self->_createMmlNode ('mo', $self->_createTextNode($input)), $result[0], $result2[0]); return $self->_createMmlNode('mrow', $newFrag), $result2[1]; } return undef, $result2[1]; } if ($input =~ /root|stackrel/) { $newFrag->appendChild($result2[0]); } $newFrag->appendChild($result[0]); if ($input eq 'frac') { $newFrag->appendChild($result2[0]); } return $self->_createMmlNode($symbol->{tag}, $newFrag), $result2[1]; } if ($ttype eq 'INFIX') { $str = _removeCharsAndBlanks($str, length $input); return $self->_createMmlNode ('mo', $self->_createTextNode($symbol->{output})), $str; } if ($ttype eq 'SPACE') { $str = _removeCharsAndBlanks($str, length $input); my $node = $self->_createElementMathML('mspace'); $node->setAttribute('width', '1ex'); $newFrag->appendChild($node); $newFrag->appendChild ($self->_createMmlNode($symbol->{tag}, $self->_createTextNode($symbol->{output}))); $node = $self->_createElementMathML('mspace'); $node->setAttribute('width', '1ex'); $newFrag->appendChild($node); return $self->_createMmlNode('mrow', $newFrag), $str; } if ($ttype eq 'LEFTRIGHT') { $self->{nestingDepth}++; $str = _removeCharsAndBlanks($str, length $input); my @result = $self->_parseExpr($str, 0); $self->{nestingDepth}--; my $st = $result[0]->lastChild ? $result[0]->lastChild->firstChild->nodeValue : ''; my $node = $self->_createMmlNode ('mo',$self->_createTextNode($symbol->{output})); $node = $self->_createMmlNode('mrow', $node); if ($st eq '|') { # it's an absolute value subterm $node->appendChild($result[0]); return $node, $result[1]; } # the "|" is a \mid return $node, $str; } if ($ttype eq 'NOP') { $str = _removeCharsAndBlanks($str, length $input); return $self->_parseSexpr($str); } $str = _removeCharsAndBlanks($str, length $input); return $self->_createMmlNode ($symbol->{tag}, # it's a constant $self->_createTextNode($symbol->{output})), $str; } # Removes brackets at the beginning or end of an mrow node # Arguments: node object # Returns: None # Side-effects: may change children of node object sub _removeBrackets { my ($node) = @_; if ($node->nodeName eq 'mrow') { my $st = $node->firstChild->firstChild->nodeValue; $node->removeChild($node->firstChild) if $st =~ /^[\(\[\{]$/; $st = $node->lastChild->firstChild->nodeValue; $node->removeChild($node->lastChild) if $st =~ /^[\)\]\}]$/; } } # Removes the first n characters and any following blanks # Arguments: string, n # Returns: resultant string sub _removeCharsAndBlanks { my ($str, $n) = @_; my $st = substr($str, substr($str, $n) =~ /^\\[^\\ ,!]/ ? $n+1 : $n); $st =~ s/^[\x00-\x20]+//; return $st; } # Removes outermost parenthesis # Arguments: string # Returns: string with parentheses removed sub _unparen { my ($s) = @_; $s =~ s!^()[\(\[\{]!$1!; $s =~ s![\)\]\}]()$!$1!; $s; } BEGIN { my %Conversion = ('<'=>'lt', '>'=>'gt', '"'=>'quot', '&'=>'amp'); # Encodes special xml characters # Arguments: string # Returns: encoded string sub _xml_encode { my ($s) = @_; $s =~ s/([<>\"&])/&$Conversion{$1};/g; $s; } } package Text::ASCIIMathML::Node; { # Create a closure for the following attributes my %parser_of; # Creates a new Text::ASCIIMathML::Node object # Arguments: Text::ASCIIMathML object, optional tag # Returns: new object sub new { my ($class, $parser, $tag) = @_; my $obj = bless { children=>[] }, $class; if (defined $tag) { $obj->{tag} = $tag } else { $obj->{frag} = 1 } $parser_of{$obj} = $parser; return $obj; } # Creates a new Text::ASCIIMathML::Node text object # Arguments: Text::ASCIIMathML object, text # Returns: new object sub newText { my ($class, $parser, $text) = @_; $text =~ s/^\s*(.*?)\s*$/$1/; # Delete leading/trailing spaces my $obj = bless { text=>$text }, $class; $parser_of{$obj} = $parser; return $obj; } my %Parent; my $Null; BEGIN { $Null = new Text::ASCIIMathML::Node; } # Appends one or more node objects to the children of an object # Arguments: list of objects to append # Returns: self sub appendChild : method { my $self = shift; my @new = map $_->{frag} ? @{$_->{children}} : $_, @_; push @{$self->{children}}, @new; map do {$Parent{$_} = $self}, @new; return $self; } # Returns a the value for an attribute of a node object # Arguments: Attribute name # Returns: Value for the attribute sub attribute { my ($self, $attr) = @_; return $self->{attr}{$attr}; } # Returns a list of the attributes of a node object # Arguments: None # Returns: Array of attribute names sub attributeList { my ($self) = @_; return $self->{attrlist} ? @{$self->{attrlist}} : (); } # Returns a child with a given index in the array of children of a node # Arguments: index # Returns: Array of node objects sub child { my ($self, $index) = @_; return $self->{children} && @{$self->{children}} > $index ? $self->{children}[$index] : $Null; } # Returns an array of children of a node # Arguments: None # Returns: Array of node objects sub childNodes { my ($self) = @_; return $self->{children} ? @{$self->{children}} : (); } # Returns the first child of a node; ignores any fragments # Arguments: None # Returns: node object or self sub firstChild { my ($self) = @_; return $self->{children} && @{$self->{children}} ? $self->{children}[0] : $Null; } # Returns true if the object is a fragment # Arguments: None # Returns: Boolean sub isFragment { return $_[0]->{frag}; } # Returns true if the object is a named node # Arguments: None # Returns: Boolean sub isNamed { return $_[0]->{tag}; } # Returns true if the object is a text node # Arguments: None # Returns: Boolean sub isText { return defined $_[0]->{text}; } # Returns the last child of a node # Arguments: None # Returns: node object or self sub lastChild { my ($self) = @_; return $self->{children} && @{$self->{children}} ? $self->{children}[-1] : $Null; } BEGIN { # Creates closure for following "static" variables my (%LatexSym, %LatexMover, %LatexFont, %LatexOp); # Returns a latex representation of a node object # Arguments: None # Returns: Text string sub latex : method { my ($self) = @_; my $parser = $parser_of{$self}; if (! %LatexSym) { # Build the entity to latex symbol translator my $amsymbol = Text::ASCIIMathML::_get_amsymbol_(); foreach my $sym (keys %$amsymbol) { next unless (defined $amsymbol->{$sym}{output} && $amsymbol->{$sym}{output} =~ /&\#x.*;/); my ($output, $tex) = map $amsymbol->{$sym}{$_}, qw(output tex); next if defined $LatexSym{$output} && ! $amsymbol->{$sym}{latex}; $tex = $sym if $tex eq ''; $LatexSym{$output} = "\\$tex"; } my %math_font = (bbb => 'mathds', mathbb => 'mathds', cc => 'cal', mathcal => 'cal', fr => 'mathfrak', mathfrak => 'mathfrak', ); # Add character codes foreach my $coded (grep $amsymbol->{$_}{codes}, keys %$amsymbol) { @LatexSym{map(sprintf("&#x%X;", $_), @{$amsymbol->{$coded}{codes}})} = map("\\$math_font{$coded}\{$_}", ('A' .. 'Z')); } # Post-process protected symbols $LatexSym{$_} =~ s/^\\\\/\\/ foreach keys %LatexSym; %LatexMover = ('^' => '\hat', '\overline' => '\overline', '\to' => '\vec', '\vec' => '\vec', '\rightarrow' => '\vec', '.' => '\dot', '..' => '\ddot', ); %LatexFont = (bold => '\bf', 'double-struck' => '\mathds', fraktur => '\mathfrak', monospace => '\tt', 'sans-serif' => '\sf', script => '\cal', ); %LatexOp = (if => '\mbox{if }', lcm => '\mbox{lcm}', newcommand => '\mbox{newcommand}', "\\" => '\backslash', '<' => '<', '>' => '>', '&' => '\&', '...' => '\ldots', ); } if (defined $self->{text}) { my $text = $self->{text}; $text =~ s/([{}])/\\$1/; $text =~ s/(&\#x.*?;)/ defined $parser->{Latex}{$1} ? $parser->{Latex}{$1} : defined $LatexSym{$1} ? $LatexSym{$1} : $1/eg; $text =~ s/([\#])/\\$1/; return $text; } my $tag = $self->{tag}; my @child_str; my $child_str = ''; if (@{$self->{children}}) { foreach (@{$self->{children}}) { push @child_str, $_->latex($parser); } } # mo if ($tag eq 'mo') { # Need to distinguish bmod from pmod my $parent = $self->parent; return $self eq $parent->child(1) && $parent->firstChild->firstChild->{text} eq '(' ? '\pmod' : '\bmod' if $child_str[0] eq 'mod'; return $LatexOp{$child_str[0]} if $LatexOp{$child_str[0]}; return $child_str[0] =~ /^\w+$/ ? "\\$child_str[0]" : $child_str[0]; } # mrow if ($tag eq 'mrow') { @child_str = grep $_ ne '', @child_str; # Check for pmod function if (@child_str > 1 && $child_str[1] eq '\pmod') { pop @child_str if $child_str[-1] eq ')'; splice @child_str, 0, 2; return "\\pmod{@child_str}"; } # Check if we need \left ... \right my $is_tall = grep(/[_^]|\\(begin\{array\}|frac|sqrt|stackrel)/, @child_str); if ($is_tall && @child_str > 1 && ($child_str[0] =~ /^([\(\[|]|\\\{)$/ || $child_str[-1] =~ /^([\)\]|]|\\\})$/)) { if ($child_str[0] =~ /^([\(\[|]|\\\{)$/) { $child_str[0] = "\\left$child_str[0]"; } else { unshift @child_str, "\\left."; } if ($child_str[-1] =~ /^([\)\]|]|\\\})$/) { $child_str[-1] = "\\right$child_str[-1]"; } else { push @child_str, "\\right."; } } return "@child_str"; } # mi # mn # math # mtd if ($tag =~ /^m([in]|ath|row|td)$/) { @child_str = grep $_ ne '', @child_str; return "@child_str"; } # msub # msup # msubsup # munderover if ($tag =~ /^(msu[bp](sup)?|munderover)$/) { my $base = shift @child_str; $base = '\mbox{}' if $base eq ''; # Put {} around arguments with more than one character @child_str = map length($_) > 1 ? "{$_}" : $_, @child_str; return ($tag eq 'msub' ? "${base}_$child_str[0]" : $tag eq 'msup' ? "${base}^$child_str[0]" : "${base}_$child_str[0]^$child_str[1]"); } # mover if ($tag eq 'mover') { # Need to special-case math mode accents return ($child_str[1] eq '\overline' && length($child_str[0]) == 1 ? "\\bar{$child_str[0]}" : $LatexMover{$child_str[1]} ? "$LatexMover{$child_str[1]}\{$child_str[0]\}" : "\\stackrel{$child_str[1]}{$child_str[0]}"); } # munder if ($tag eq 'munder') { return $child_str[1] eq '\underline' ? "$child_str[1]\{$child_str[0]}" : "$child_str[0]_\{$child_str[1]\}"; } # mfrac if ($tag eq 'mfrac') { return "\\frac{$child_str[0]}{$child_str[1]}"; } # msqrt if ($tag eq 'msqrt') { return "\\sqrt{$child_str[0]}"; } # mroot if ($tag eq 'mroot') { return "\\sqrt[$child_str[1]]{$child_str[0]}"; } # mtext if ($tag eq 'mtext') { my $text = $child_str[0]; my $next = $self->nextSibling; my $prev = $self->previousSibling; if (defined $next->{tag} && $next->{tag} eq 'mspace') { $text = "$text "; } if (defined $prev->{tag} && $prev->{tag} eq 'mspace') { $text = " $text"; } $text = ' ' if $text eq ' '; return "\\mbox{$text}"; } # mspace if ($tag eq 'mspace') { return ''; } # mtable if ($tag eq 'mtable') { my $cols = ($child_str[0] =~ tr/&//) + 1; my $colspec = ($self->{attr}{columnalign} || '') eq 'left' ? 'l' : 'c'; my $colspecs = $colspec x $cols; return ("\\begin{array}{$colspecs}\n" . join('', map(" $_ \\\\\n", @child_str)) . "\\end{array}\n"); } # mtr if ($tag eq 'mtr') { return join ' & ', @child_str; } # mstyle if ($tag eq 'mstyle') { @child_str = grep $_ ne '', @child_str; if ($self->parent->{tag} eq 'math') { push @child_str, ' ' unless @child_str; # The top-level mstyle return (defined $self->{attr}{displaystyle} && $self->{attr}{displaystyle} eq 'true') ? "\$\$@child_str\$\$" : "\$@child_str\$"; } else { # It better be a font changing command return $child_str[0] if $self->{attr}{mathvariant}; my ($attr) = map($self->{attr}{$_}, grep $self->{attr}{$_}, qw(fontweight fontfamily)); return $attr && $LatexFont{$attr} ? "$LatexFont{$attr}\{$child_str[0]}" : $child_str[0]; } } } } # Returns the next sibling of a node # Arguments: None # Returns: node object or undef sub nextSibling { my ($self) = @_; my $parent = $self->parent; for (my $i=0; $i<@{$parent->{children}}; $i++) { return $parent->{children}[$i+1] if $self eq $parent->{children}[$i]; } return $Null; } # Returns the tag of a node # Arguments: None # Returns: string sub nodeName : method { return $_[0]{tag} || ''; } # Returns the text of a text node # Arguments: None # Returns: string sub nodeValue : method { return $_[0]{text} || ''; } # Returns the parent of a node # Arguments: none # Returns: parent node object or undef sub parent : method { return $Parent{$_[0]} || $Null; } # Returns the previous sibling of a node # Arguments: None # Returns: node object or undef sub previousSibling { my ($self) = @_; my $parent = $self->parent; for (my $i=1; $i<@{$parent->{children}}; $i++) { return $parent->{children}[$i-1] if $self eq $parent->{children}[$i]; } return $Null; } # Removes a given child node from a node # Arguments: child node # Returns: None # Side-effects: May affect children of the node sub removeChild : method { my ($self, $child) = @_; @{$self->{children}} = grep $_ ne $child, @{$self->{children}} if $self->{children}; delete $Parent{$child}; } # Replaces one child node object with another # Arguments: old child node object, new child node object # Returns: None sub replaceChild : method { my ($self, $new, $old) = @_; @{$self->{children}} = map $_ eq $old ? $new : $_, @{$self->{children}}; delete $Parent{$old}; $Parent{$new} = $self; } # Sets one or more attributes on a node object # Arguments: set of attribute/value pairs # Returns: None sub setAttribute : method { my $self = shift; if (@_) { $self->{attr} = {} unless $self->{attr}; $self->{attrlist} = [] unless $self->{attrlist}; } while (my($aname, $aval) = splice(@_, 0, 2)) { $aval =~ s/\n//g; push @{$self->{attrlist}}, $aname unless defined $self->{attr}{$aname}; $self->{attr}{$aname} = $aval; } } # Returns the ASCII representation of a node object # Arguments: None # Returns: Text string sub text : method { my ($self) = @_; return $self->{text} if defined $self->{text}; my $tag = $self->{tag}; my $attr = join '', map(" $_=\"" . ($_ eq 'xmlns' ? $self->{attr}{$_} : Text::ASCIIMathML::_xml_encode($self->{attr}{$_})) . "\"", @{$self->{attrlist}}) if $tag; if (@{$self->{children}}) { my $child_str; foreach (@{$self->{children}}) { $child_str .= $_->text; } return $tag ? "<$tag$attr>$child_str" : $child_str; } return $tag ? "<$tag$attr/>" : ''; } } 1;