itutor-mathlive
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Beautifully typeset math made easy
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<h3 class="group-title home"><a href="index.html">MathLive Docs</a></h3><input class="search" placeholder="Search" type="text"><div class="list"><h3 class="group-title">Tutorials</h3><ul><li><a href="tutorial-CONTRIBUTOR_GUIDE.html">Contributor Guide</a></li><li><a href="tutorial-MASTON.html">MASTON</a></li><li><a href="tutorial-USAGE_GUIDE.html">Usage Guide</a></li></ul><h3 class="group-title">Classes</h3><ul><li class="private"><a href="Context.html" class="className">Context</a><ul class='methods private'><li data-type='method' class='private'><a href="Context.html#clone" class="methodName">clone</a></li><li data-type='method' class='private'><a href="Context.html#cloneWith" class="methodName">cloneWith</a></li><li data-type='method' class='private'><a href="Context.html#getBackgroundColor" class="methodName">getBackgroundColor</a></li><li data-type='method' class='private'><a href="Context.html#getColor" class="methodName">getColor</a></li><li data-type='method' class='private'><a 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<h1 class="page-title">addons/maston.js</h1>
<section>
<article>
<pre class="prettyprint source linenums">
<code>define([
'mathlive/core/lexer',
'mathlive/core/mathAtom',
'mathlive/core/parser',
'mathlive/core/definitions',
],
function(Lexer, MathAtom, ParserModule, Definitions) {
const CANONICAL_NAMES = {
// CONSTANTS
'\\imaginaryI': '\u2148',
'\\imaginaryJ': '\u2149',
'\\pi': 'π',
'\\exponentialE': '\u212f',
// ARITHMETIC
'﹢': '+', // SMALL PLUS SIGN
'＋': '+', // FULL WIDTH PLUS SIGN
'−': '-', // MINUS SIGN
'-': '-', // HYPHEN-MINUS
'﹣': '-', // SMALL HYPHEN-MINUS
'－': '-', // FULLWIDTH HYPHEN-MINUS
'\\times': '*',
'⨉': '*', // N-ARY TIMES OPERATOR U+
'️✖': '*', // MULTIPLICATION SYMBOL
'️×': '*', // MULTIPLICATION SIGN
'.': '*',
'÷': '/', // DIVISION SIGN
// '/': '/', // SOLIDUS
'⁄': '/', // FRACTION SLASH
'／': '/', // FULLWIDTH SOLIDUS
'!': 'factorial',
'️\\pm': 'plusminus', // PLUS-MINUS SIGN
'\\mp': 'minusplus', // MINUS-PLUS SIGN
'\\land': 'and',
'\\wedge': 'and',
'\\lor': 'or',
'\\vee': 'or',
'\\oplus': 'xor',
'\\veebar': 'xor',
'\\lnot': 'not',
'\\neg': 'not',
'\\exists': 'exists',
'\\nexists': '!exists',
'\\forall': 'forAll',
'\\backepsilon': 'suchThat',
'\\therefore': 'therefore',
'\\because': 'because',
'\\nabla': 'nabla',
'\\circ': 'circle',
// '\\oplus': 'oplus',
'\\ominus': 'ominus',
'\\odot': 'odot',
'\\otimes': 'otimes',
'\\zeta': 'Zeta',
'\\Gamma': 'Gamma',
'\\min': 'min',
'\\max': 'max',
'\\mod': 'mod',
'\\lim': 'lim', // BIG OP
'\\sum': 'sum',
'\\prod': 'prod',
'\\int': 'integral',
'\\iint': 'integral2',
'\\iiint': 'integral3',
'\\Re': 'Re',
'\\gothicCapitalR': 'Re',
'\\Im': 'Im',
'\\gothicCapitalI': 'Im',
'\\binom': 'nCr',
'\\partial': 'partial',
'\\differentialD': 'differentialD',
'\\capitalDifferentialD': 'capitalDifferentialD',
'\\Finv': 'Finv',
'\\Game': 'Game',
'\\wp': 'wp',
'\\ast': 'ast',
'\\star': 'star',
'\\asymp': 'asymp',
// Function domain, limits
'\\to': 'to', // Looks like \rightarrow
'\\gets': 'gets', // Looks like \leftarrow
// Logic
'\\rightarrow': 'shortLogicalImplies',
'\\leftarrow': 'shortLogicalImpliedBy',
'\\leftrightarrow': 'shortLogicalEquivalent',
'\\longrightarrow': 'logicalImplies',
'\\longleftarrow': 'logicalImpliedBy',
'\\longleftrightarrow': 'logicalEquivalent',
// Metalogic
'\\Rightarrow': 'shortImplies',
'\\Leftarrow': 'shortImpliedBy',
'\\Leftrightarrow': 'shortEquivalent',
'\\implies': 'implies',
'\\Longrightarrow': 'implies',
'\\impliedby': 'impliedBy',
'\\Longleftarrow': 'impliedBy',
'\\iff': 'equivalent',
'\\Longleftrightarrow': 'equivalent',
}
const FUNCTION_TEMPLATE = {
// TRIGONOMETRY
'sin': '\\sin%_%^ %',
'cos': '\\cos%_%^ %',
'tan': '\\tan%_%^ %',
'cot': '\\cot%_%^ %',
'sec': '\\sec%_%^ %',
'csc': '\\csc%_%^ %',
'sinh': '\\sinh %',
'cosh': '\\cosh %',
'tanh': '\\tanh %',
'csch': '\\csch %',
'sech': '\\sech %',
'coth': '\\coth %',
'arcsin': '\\arcsin %',
'arccos': '\\arccos %',
'arctan': '\\arctan %',
'arccot': '\\arcctg %', // Check
'arcsec': '\\arcsec %',
'arccsc': '\\arccsc %',
'arsinh': '\\arsinh %',
'arcosh': '\\arcosh %',
'artanh': '\\artanh %',
'arcsch': '\\arcsch %',
'arsech': '\\arsech %',
'arcoth': '\\arcoth %',
// LOGARITHMS
'ln': '\\ln%_%^ %', // Natural logarithm
'log': '\\log%_%^ %', // General logarithm, e.g. log_10
'lg': '\\lg %', // Common, base-10, logarithm
'lb': '\\lb %', // Binary, base-2, logarithm
// Big operator
'sum': '\\sum%_%^ %',
// OTHER
'Zeta': '\\zeta%_%^ %', // Riemann Zeta function
'Gamma': '\\Gamma %', // Gamma function, such that Gamma(n) = (n - 1)!
'min': '\\min%_%^ %',
'max': '\\max%_%^ %',
'mod': '\\mod%_%^ %',
'lim': '\\lim%_%^ %', // BIG OP
'binom': '\\binom %',
'nabla': '\\nabla %',
'curl': '\\nabla\\times %',
'div': '\\nabla\\cdot %',
'floor': '\\lfloor % \\rfloor%_%^',
'ceil': '\\lceil % \\rceil%_%^',
'abs': '\\vert % \\vert%_%^',
'norm': '\\lVert % \\rVert%_%^',
'ucorner': '\\ulcorner % \\urcorner%_%^',
'lcorner': '\\llcorner % \\lrcorner%_%^',
'angle': '\\langle % \\rangle%_%^',
'group': '\\lgroup % \\rgroup%_%^',
'moustache':'\\lmoustache % \\rmoustache%_%^',
'brace': '\\lbrace % \\rbrace%_%^',
'sqrt': '\\sqrt[%^]{%}',
'lcm': '\\mathop{lcm}%',
'gcd': '\\mathop{gcd}%',
'erf': '\\mathop{erf}%',
'erfc': '\\mathop{erfc}%',
'randomReal': '\\mathop{randomReal}%',
'randomInteger': '\\mathop{randomInteger}%',
// Arithmetic operators
'*': '%0 \\times %1',
// Logic operators
'and': '%0 \\land %1',
'or': '%0 \\lor %1',
'xor': '%0 \\oplus %1',
'not': '%0 \\lnot %1',
// Other operators
'circle': '%0 \\circ %1',
'ast': '%0 \\ast %1',
'star': '%0 \\star %1',
'asymp': '%0 \\asymp %1',
'/': '\\frac{%0}{%1}',
'Re': '\\Re{%}',
'Im': '\\Im{%}',
'factorial': '%!',
'factorial2': '%!!',
}
// From www.w3.org/TR/MathML3/appendixc.html
const OP_PRECEDENCE = {
'degree': 880,
'nabla': 740,
'curl': 740, // not in MathML
'partial': 740,
'differentialD': 740, // not in MathML
'capitalDifferentialD': 740, // not in MathML
'odot': 710,
// Logical not
'not': 680,
// Division
'div': 660, // division sign
'solidus': 660,
'/': 660,
'setminus': 650, // \setminus, \smallsetminus
'%': 640,
'otimes': 410,
// Set operators
'union': 350, // \cup
'intersection': 350, // \cap
// Multiplication, division and modulo
'*': 390,
'ast': 390,
'.': 390,
'oplus': 300, // also logical XOR... @todo
'ominus': 300,
// Addition
'+': 275,
'-': 275,
'+-': 275, // \pm
'-+': 275, // \mp
// Most circled-ops are 265
'circle': 265,
'circledast': 265,
'circledcirc': 265,
'star': 265, // Different from ast
// Range
'..': 263, // Not in MathML
// Unit conversion
'to': 262, // Not in MathLM
'in': 262, // Not in MathML
// Relational
'=': 260,
'!=': 255,
'approx': 247,
'<': 245,
'>': 243,
'≥': 242,
'≤': 241,
// Set operator
'complement': 240,
'subset': 240, // \subset
'superset': 240, // \supset
// @todo and equality and neg operators
'elementof': 240, // \in
'!elementof': 240, // \notin
//
'exists': 230,
'!exists': 230,
'forall': 230,
// Logical operators
'and': 200,
'xor': 195, // MathML had 190
'or': 190,
// Note: 'not' is 680
// center, low, diag, vert ellipsis 150
// Composition/sequence
'suchThat': 110, // \backepsilon
':': 100,
// '..': 100,
// '...': 100,
// Conditional (?:)
// Assignement
':=': 80, // MathML had 260 (same with U+2254 COLON EQUALS)
'therefore': 70,
'because': 70,
// Arrows
// Note: MathML had 270 for the arrows, but this
// would not work for (a = b => b = a)
// See also https://en.wikipedia.org/wiki/Logical_connective#Order_of_precedence
// for a suggested precedence (note that in this page lower precedence
// has the opposite meaning as what we use)
'shortLogicalImplies': 52, // ->
'shortImplies': 51, // =>
'logicalImplies': 50, // -->
'implies': 49, // ==>
'shortLogicalImpliedBy': 48,// <-
'shortImpliedBy': 47, // <=
'logicalImpliedBy': 46, // <--
'impliedBy': 45, // <==
'shortLogicalEquivalent':44,// <->
'shortEquivalent': 43, // <=>
'logicalEquivalent':42, // <-->
'equivalent': 41, // <==>
',': 40,
';': 30
}
/**
* Given a canonical name, return its precedence
* @param {string} canonicalName, for example "and"
* @return {number}
*/
function getPrecedence(canonicalName) {
return canonicalName ? (OP_PRECEDENCE[canonicalName] || -1) : -1;
}
function getAssociativity(canonicalName) {
if (/=|=>/.test(canonicalName)) {
return 'right';
}
return 'left';
}
/**
*
* @param {string} name function canonical name
* @return {string}
*/
function getLatexTemplateForFunction(name) {
let result = FUNCTION_TEMPLATE[name];
if (!result) {
result = name.length > 1 ? '\\mathop{' + name + '} %' : (name + ' %');
}
return result;
}
/**
*
* @param {string} name symbol name
* @return {string}
*/
function getLatexForSymbol(name) {
let result = FUNCTION_TEMPLATE[name];
if (result) {
return result.replace('%1', '').replace('%0', '').replace('%', '');
}
const info = Definitions.getInfo('\\' + name, 'math');
if (info && info.type !== 'error' &&
(!info.fontFamily || info.fontFamily === 'main' || info.fontFamily === 'ams')) {
result = '\\' + name;
}
return result;
}
/**
*
* @param {string} name function or operator canonical name
* @return {string}
*/
function getLatexTemplateForOperator(name) {
let result = FUNCTION_TEMPLATE[name];
if (!result) {
result = '%0 \\mathbin{' + name + '} %1';
}
return result;
}
function isFunction(canonicalName) {
if (canonicalName === 'f' || canonicalName === 'g') return true;
let t = FUNCTION_TEMPLATE[canonicalName];
if (!t) return false;
// %0 and %1 are the lhs and rhs arguments. Remove those from the template
t = t.replace('%0', '').replace('%1', '');
// If we're left with a plain %, it's the argument list, and therefore
// this is a function.
if (/%/.test(t)) return true;
return false;
}
/**
*
* @param {string} latex, for example '\\times'
* @return {string} the canonical name for the input, for example '*'
*/
function getCanonicalName(latex) {
latex = (latex || '').trim();
let result = CANONICAL_NAMES[latex];
if (!result) {
if (latex.charAt(0) === '\\') {
const info = Definitions.getInfo(latex, 'math', {});
if (info && info.type !== 'error') {
result = info.value || latex.slice(1);
} else {
result = latex.slice(1);
}
} else {
result = latex;
}
}
return result;
}
/**
* Return the operator precedence of the atom
* or -1 if not an operator
* @param {*} atom
* @return {number}
*/
function opPrec(atom) {
if (!atom) return null;
const name = getCanonicalName(getString(atom));
const result = {
prec: getPrecedence(name),
assoc: getAssociativity(name)
}
if (result.prec <= 0) return null
return result;
}
function isOperator(atom) {
return opPrec(atom) !== null;
}
const DELIM_FUNCTION = {
'\\lfloor\\rfloor': 'floor',
'\\lceil\\rceil': 'ceil',
'\\vert\\vert': 'abs',
'\\lvert\\rvert': 'abs',
'||': 'abs',
'\\Vert\\Vert': 'norm',
'\\lVert\\rVert': 'norm',
'\\ulcorner\\urcorner': 'ucorner',
'\\llcorner\\lrcorner': 'lcorner',
'\\langle\\rangle': 'angle',
'\\lgroup\\rgroup': 'group',
'\\lmoustache\\rmoustache': 'moustache',
'\\lbrace\\rbrace': 'brace'
}
const POSTFIX_FUNCTION = {
'!': 'factorial',
'\\dag': 'dagger',
'\\dagger': 'dagger',
'\\ddager': 'dagger2',
'\\maltese': 'maltese',
'\\backprime': 'backprime',
'\\backdoubleprime': 'backprime2',
'\\prime': 'prime',
'\\doubleprime': 'prime2',
'\\$': '$',
'\\%': '%',
'\\_': '_',
'\\degree': 'degree'
}
const ASSOCIATIVE_FUNCTION = {
'+': '+',
'-': '+', // Substraction is add(), but it's
// handled specifically so that the
// argument is negated
'*': '*',
',': 'list',
';': 'list2',
'and': 'and',
'or': 'or',
'xor': 'xor',
'union': 'union',
// shortLogicalEquivalent and logicalEquivalent map to the same function
// they mean the same thing, but have a difference precedence.
'shortLogicalEquivalent': 'logicalEquivalent', // logical equivalent, iff, biconditional logical connective
'logicalEquivalent': 'logicalEquivalent', // same
// shortEquivalent and equivalent map to the same function
// they mean the same thing, but have a difference precedence.
'shortEquivalent': 'equivalent', // metalogic equivalent
'equivalent': 'equivalent', // same
}
const SUPER_ASSOCIATIVE_FUNCTION = {
',': 'list',
';': 'list2'
}
function getString(atom) {
if (atom.latex && atom.latex !== '\\mathop ' && atom.latex !== '\\mathbin ' &&
atom.latex !== '\\mathrel ' && atom.latex !== '\\mathopen ' &&
atom.latex !== '\\mathpunct ' && atom.latex !== '\\mathord ' &&
atom.latex !== '\\mathinner ' && atom.type !== 'font') {
return atom.latex.trim();
}
if (atom.type === 'leftright') {
return '';
}
if (typeof atom.body === 'string') {
return atom.body;
}
if (Array.isArray(atom.body)) {
let result = '';
for (const subAtom of atom.body) {
result += getString(subAtom);
}
return result;
}
return '';
}
/**
*
* @param {Object} expr -- Abstract Syntax Tree object
* @return {string} -- A string, the symbol, or undefined
*/
function asSymbol(expr) {
let result = expr;
if (typeof result !== 'string') {
result = expr !== undefined ? expr.sym : undefined;
}
if (result) {
const latex = getLatexForSymbol(result);
result = latex || result;
}
return result;
}
/**
*
* @param {Object} num -- Abstract Syntax Tree object
* @return {number} -- A Javascript number, the value of the AST or NaN
*/
function asMachineNumber(num) {
let result = undefined;
if (num !== undefined) {
if (num.num !== undefined) {
if (num.num.toString().match(/^[+-]?[0-9]*[.]?[0-9]*[eE]?[+-]?[0-9]?$/)) {
result = parseFloat(num.num);
}
} else if (typeof num === 'number') {
result = parseFloat(num);
}
}
return result;
}
function isNumber(expr) {
return typeof expr === 'number' ||
(expr !== undefined && expr.num !== undefined);
}
/**
* Return true if the current atom is of the specified type and value.
* @param {Object} expr
* @param {string} type
* @param {string} value
*/
function isAtom(expr, type, value) {
let result = false;
const atom = expr.atoms[expr.index];
if (atom && atom.type === type) {
if (value === undefined) {
result = true;
} else {
result = getString(atom) === value;
}
}
return result;
}
/**
* Return the negative of the expression. Usually {op:'-', lhs:expr}
* but for numbers, the negated number
* @param {*} expr
*/
function negate(expr) {
if (typeof expr === 'number') {
return -expr;
} else if (expr && typeof expr.num === 'number') {
expr.num = -expr.num;
return expr;
}
return {op:'-', lhs:expr};
}
/**
* Parse for a possible sup/sub at the current token location.
* Handles both sup/sub attached directly to the current atom
* as well as "empty" atoms with a sup/sub following the current
* atom.
* @param {Object} expr
*/
function parseSupsub(expr, options) {
let atom = expr.atoms[expr.index - 1];
// Is there a supsub directly on this atom?
if (!atom || !(atom.superscript || atom.subscript)) {
atom = null;
}
// Is the following atom a subsup atom?
if (!atom) {
atom = expr.atoms[expr.index];
if (isAtom(expr, 'msubsup') && (atom.superscript || atom.subscript)) {
expr.index += 1;
} else {
atom = null;
}
}
if (atom) {
if (typeof expr.ast === 'string') {