cejs
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A JavaScript module framework that is simple to use.
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JavaScript
/**
* @name CeL function for math application.
* @fileoverview 本檔案包含了生成 math application 的 functions。
* @since 2014/10/3
* @example <code>
CeL.run('application.math', function() {
// ..
});
* </code>
*/
'use strict';
if (typeof CeL === 'function')
CeL.run({
name : 'application.math',
// includes() @ data.code.compatibility.
require : 'data.code.compatibility.|data.math.',
// 為了方便格式化程式碼，因此將 module 函式主體另外抽出。
code : module_code
});
function module_code(library_namespace) {
/**
* null module constructor
*
* @class 出數學題目用的 functions
*/
var _// JSDT:_module_
= function() {
// null module constructor
};
/**
* for JSDT: 有 prototype 才會將之當作 Class
*/
_// JSDT:_module_
.prototype = {};
// ----------------------------------------------------- //
(function() {
runCode.setR = 0;
for (var i = 0, j, t, s, n_e; i < 10;) {
t = 2000 + 8000 * Math.random();
s = get_random_prime.get_different_number_set(3, t, t / 8);
if (s.LCM > 9999)
continue;
n_e = [];
n_e[s.GCD] = 1;
for (j = 0; j < s.length; j++)
if (n_e[s[j]])
continue;
else
n_e[s[j]] = 1;
sl([ s.GCD, s.LCM ] + '<b style="color:#c4a">;</b> ' + s);
i++;
}
});
// ----------------------------------------------------- //
// 中式短除法(Chinese short division)並非 short division.
// https://en.wikipedia.org/wiki/Short_division
function draw_short_division(naturals, layer, GCD_only) {
if (!Array.isArray(naturals))
if (isNaN(layer))
naturals = [ naturals ];
else
naturals = arguments, layer = null;
var i, length = naturals.length | 0, divisor, cell_width_em = 2,
//
natural_Array = [];
for (i = 0; i < length; i++) {
divisor = +naturals[i];
if (0 < divisor && divisor < Number.MAX_SAFE_INTEGER) {
natural_Array.push(divisor);
if (cell_width_em < String(divisor).length * .6)
cell_width_em = Math.ceil(String(divisor).length * .6);
}
}
length = (naturals = Array.prototype.slice.call(natural_Array)).length | 0;
var block = [], count = 0,
//
_GCD = library_namespace.GCD(natural_Array),
//
GCD = library_namespace.factorize(_GCD);
library_namespace
.debug(length + ' Naturals: ' + natural_Array + '.', 2);
if (GCD) {
// assert: _GCD > 1
if (_GCD !== (divisor = GCD.toString(true)))
_GCD += ' = ' + divisor;
// phase 1: 處理 GCD 部分。
for (divisor in GCD) {
divisor |= 0;
for (var j = 0; j < GCD[divisor] | 0; j++)
if (length !== 1 || natural_Array[0] !== divisor) {
block.push(draw_short_division.add_line(natural_Array,
cell_width_em, divisor, count++, true));
for (i = 0; i < length; i++)
natural_Array[i] = natural_Array[i] / divisor;
}
}
}
// phase 2: 處理 LCM 部分。
// TODO: 按大小排列。
GCD = 0;
do {
var LCM = natural_Array[0];
for (i = 1; i < length; i++)
if (natural_Array[i] > 1
&& (GCD = library_namespace.GCD(LCM, natural_Array[i])) > 1) {
divisor = +library_namespace.first_factor(GCD);
block.push(draw_short_division.add_line(natural_Array,
cell_width_em, divisor, count++));
for (i = 0; i < length; i++)
if (natural_Array[i] % divisor === 0)
natural_Array[i] = natural_Array[i] / divisor;
break;
}
} while (GCD > 1);
// 依照各種不同類之輸入，顯示不同備註標示。
if (length === 1) {
// 質因數分解。
block.push(draw_short_division.add_line(natural_Array,
cell_width_em), {
div : [ _GCD ]
});
} else {
i = library_namespace.LCM(naturals);
block.push(draw_short_division.add_line(natural_Array,
cell_width_em), {
div : [ 'GCD',
// '(', naturals.join(', '), ')',
' = ', _GCD ],
S : draw_short_division.GCD_style
},
{
div : [ 'LCM',
// '(', naturals.join(', '), ')',
' = ', i, ' = ',
library_namespace.factorize(i).toString(true) ]
});
}
// 最後收尾。
block = {
div : block,
style : 'width:'
+ (1 + (length + (1 < length ? 2 : 1)) * cell_width_em | 0)
+ 'em;background-color:#def',
C : 'short_division'
};
return layer ? new_node(block, layer) : block;
}
draw_short_division.GCD_style = 'color:#f79;';
draw_short_division.add_line = function(naturals, cell_width_em, divisor,
count, phase_GCD) {
library_namespace.debug(divisor + ': ' + naturals, 3,
'draw_short_division.add_line');
var line = [];
naturals.forEach(function(natural, index) {
line.push({
span : natural,
S :
//
'display:inline-block;text-align:right;padding-right:.2em;width:'
//
+ (cell_width_em + (index ? 0 : .5 - count / 5)).to_fixed(2)
+ 'em'
}, ' ');
});
line.pop();
if (divisor)
line = [ {
span : divisor,
S : 'text-align:right;padding-right:.2em;'
}, {
span : line,
S : 'border-left:1pt solid #88f;border-bottom:1pt solid #88f'
} ];
return {
div : line,
S : 'clear:both;text-align:right;'
+ (phase_GCD ? draw_short_division.GCD_style : '')
};
};
_.draw_short_division = draw_short_division;
/**
* <code>
CeL.run('application.math', function() {
CeL.draw_short_division([12], [ document.body, 2 ]);
CeL.draw_short_division([12, 18], [ document.body, 2 ]);
CeL.draw_short_division([12, 18, 24], [ document.body, 2 ]);
});
</code>
*/
// ----------------------------------------------------------------------------------------------
// //
var new_node = function() {
var func = library_namespace.DOM.new_node;
if (func)
return (new_node = func).apply(null, arguments);
},
//
check_MathML = function() {
var math_node = new_node({
div : {
span : 'normal'
},
S : 'line-height:1em;visibility:hidden'
}, document.body);
if (!math_node)
return;
new_node({
math : {
mfrac : [ {
mi : 'test'
}, {
mi : 'MathML'
} ]
}
}, math_node, 'mathml');
// Firefox/37.0 不需要 setTimeout()。
// setTimeout(check_MathML.check.bind(math_node), 0);
// return check_MathML.check.call(math_node, true);
return check_MathML.check.call(math_node);
};
// 2015/1/1: Firefox only. 僅 firefox 回傳 true。
check_MathML.check = function(no_remove) {
// library_namespace.debug(this);
Object.defineProperty(_, 'support_MathML', {
// method 1:
// 分數 2/3 之 2 的 offsetTop 應該比 3 更高一點。
// 但在 ff 中，沒有 .offsetTop。
// var mfrac = this.lastChild.firstChild;
// value : mfrac.firstChild.offsetTop < mfrac.lastChild.offsetTop;
// method 2: 因為插入 <mfrac>，<div> 應該比一般單行文字更高一點。但在 Chrome，兩者本身即有差別。
value : this.offsetHeight > this.firstChild.offsetHeight + 3
});
if (!_.support_MathML)
library_namespace
.debug('The browser does not support MathML. 您的瀏覽器不支援 MathML，或是 MathML 功能已被關閉。');
if (no_remove !== true) {
// library_namespace.remove_node(this);
document.body.removeChild(this);
}
return _.support_MathML;
};
// assert: support MathML 也必定 support Object.defineProperty().
Object.defineProperty(_, 'support_MathML', {
configurable : true,
get : check_MathML
});
// ----------------------------------------------------- //
/**
* 以 MathML 表現數學運算式。<br />
* 將 HTML 中 <math>expression</math> 皆轉為 MathML。<br />
* parse math expression & output MathML.<br />
*
* TODO: calculator, vector, ℕℤℚℝℂ, ∈∉
*
* @example <code>
// <script>
CeL.run([
// for new_node()
'interact.DOM', 'application.math' ], function() {
CeL.application.math.convert_MathML();
});
// <html>
<math>α=r×β</math><hr />
<math>5%*6=30%</math><hr />
<math>3*5/7</math><hr />
<math>3*(5/7)</math><hr />
<math>(4+5)/2</math><hr />
<math>5^4*3+2-4^2/5</math><hr />
<math>(a/b)/(c/d)</math><hr />
<math>資本收入=資本收益率×資本</math><hr />
<math>資本收入/國民年收入=資本收益率×(資本存量/國民年收入)</math><hr />
<math>
1/2+(1+2)/(2+3%)+((2+3))/((3+4))
</math><hr />
<math>
43+(54+5*(3+4)/3)*2
</math><hr />
<math>x_2^4</math><hr />
<math>x^2+y_1+z_12^34</math><hr />
<math>
x_2^4 = 3/2, y = 4/3, z = 5/4
</math><hr />
<math>
x_2^4 = 3/2
y = 4/3
z = 5/4
</math><hr />
<math>4^(1/7)</math><hr />
<math>√453</math><hr />
<math>√4e</math><hr />
<math>√-4e</math><hr />
<math>√(4e+3)</math><hr />
<math>∛45</math><hr />
<math>x=1/√3</math><hr />
<math>3<4</math><hr />
<math>log_4(45+2)</math><hr />
<math>log_4 452</math><hr />
<math>log_e 452</math><hr />
<math>sin(π/2) = sin(pi/2) = sin(90°)</math><hr />
<math>sin π/2 = (sin π)/2</math><hr />
<math>sin(34π) = sin 34π</math><hr />
<math>sin^-1(2π) = sin^-1 2π = sin^(-1)(2 pi)</math><hr />
<math>log_4^2 452</math><hr />
<math>log_4^2(34+2)</math><hr />
<math>2e+3^2π+4π</math><hr />
<math>-4e</math><hr />
<math>(5+3)⁄(5-4)</math><hr />
<math>7^(1/4) , 4√7</math><hr />
<math>x_y^2 x^2+2^(1/3)^8+4^(1/7)^6</math><hr />
<math>1+(b^2-4a c)^(1/5)</math><hr />
<math>x=(-b±√(b^2-4a c))/2a</math><hr />
<math>y=x(x^2-1)</math><hr />
<math>(^2)Fe</math><hr />
<math>(^12)C</math><hr />
<math>(_6^12)C</math><hr />
<math>(_6)C</math><hr />
<math>(_2^1)x_4^3</math><hr />
<math>(_2^1)x_4</math><hr />
<math>P(A∪B)=P((A))+P((B))-P(A∩B)</math>
<math>P(A|B)</math>
// TODO:
<math>{ a; b; c, d, e }</math><hr />
<math>{{4, 5, 6}, {7, 8, 9}, {1, 2, 3}}×((3,4,5),(5,6,7),(7,8,9))</math><hr />
<math>{{1,2},{3,4}}((5),(6))</math><hr />
<math>x_y^2 x^2 2^(1/3)^8 4^(1/7)^6</math><hr />
<math>(_(a+b))x</math><hr />
munderover
<math>∫_2^4 dy/dx</math><hr />
// reference
http://www.w3.org/TR/MathML/chapter3.html#id.3.1.3.2
https://developer.mozilla.org/en-US/docs/Web/MathML/Element
http://www.wolframalpha.com/examples/Math.html
http://reference.wolfram.com/language/ref/format/MathML.html
* </code>
*
* @see
*/
function convert_MathML(handler) {
if (!library_namespace.remove_all_child)
return;
// assert: library_namespace.DOM is loaded.
if (!_.support_MathML) {
library_namespace.warn('The browser does not support MathML!');
if (!library_namespace.is_WWW(true))
return;
}
// MathML nodes
var nodes = document.getElementsByTagName('math'), length = nodes.length, i = 0, node;
if (!handler)
handler = convert_MathML.handler['default'];
else if (handler in convert_MathML.handler)
handler = convert_MathML.handler[handler];
for (; i < length; i++) {
node = nodes[i];
if (!_.support_MathML) {
if (!node.title
&& node.getAttribute(convert_MathML.default_attribute)) {
// useless... Chrome 不會像 <span> 一般顯示 .title。
node.setAttribute('title', node
.getAttribute(convert_MathML.default_attribute));
}
continue;
}
if (false && typeof node.getAttribute !== 'function')
return;
var text;
if (node.childNodes.length !== 1
|| node.firstChild.nodeType !== document.TEXT_NODE
//
|| !(text = node.firstChild.nodeValue.trim()))
continue;
// temporary usage.
var attribute = convert_MathML.default_attribute,
//
structure = node.getAttribute(attribute)
|| node.getAttribute(attribute = 'title');
if (structure) {
// 當可以使用 <math> 時，把原先展示的內容物 .childNodes 轉而擺到 .title 去。
// 使用例： <math alt="e^(-)" title="e-">電子</math>, <math alt="H_2
// O" title="水 H2O">水分子</math>
// 避免覆蓋原先的 .title。.title 通常擺更詳細的資訊。
if (!node.getAttribute(attribute = 'title')) {
node.setAttribute('title', text);
}
text = '\n' + structure;
}
if (!node.getAttribute('xmlns')) {
node
.setAttribute('xmlns',
"http://www.w3.org/1998/Math/MathML");
}
// library_namespace.debug(node);
structure = convert_MathML.parse(text);
if (!structure[0]) {
// 若是所有 children 都是等式，則將之括弧起來。
var equalities = [ '{' ], j = 1, tmp;
for (; j < structure.length; j++) {
if (tmp = structure[j])
if (Array.isArray(tmp)
&& convert_MathML.RELATIONSHIP_PATTERN
.test(tmp[0])) {
equalities.push(tmp);
} else if (typeof tmp !== 'string' || tmp.trim()) {
equalities = null;
break;
}
}
if (equalities)
structure = equalities;
}
structure = convert_MathML.reduce(structure, node, handler);
// library_namespace.debug('convert_MathML: structure:');
// library_namespace.debug(structure);
library_namespace.remove_all_child(node);
new_node(structure, node, 'mathml');
}
}
_.convert_MathML = convert_MathML;
convert_MathML.default_attribute = 'alt';
convert_MathML.reduce_quote = function(operand) {
var row = operand.mrow;
if (!row || !Array.isArray(row) || row.length !== 3) {
return operand;
}
var operator = row[0].mo + row[2].mo;
if (operator === '{}' || operator === '()') {
// assert: Array.isArray(row[1].mrow)
return row[1];
}
return operand;
};
convert_MathML.handler = {
// toString()
// 運算元,運算子,運算元(操作符/算符/算子)
string : function(operand_1, operator, operand_2) {
if (!operator && Array.isArray(operand_1))
return operand_1.join(' ');
switch (operator) {
case '()':
return '(' + operand_1 + ')';
case 'm':
// 以表格呈現。
operand_1.forEach(function(row, index) {
operand_1[index] = '{' + row.join(',') + '}';
});
case '{}':
return '{' + operand_1 + '}';
case ',':
return operand_1.join(',');
case '{':
return operand_1.join('\n');
}
return operand_1 + (operator || '') + (operand_2 || '');
},
mathml : function(operand_1, operator, operand_2) {
if (!operator && Array.isArray(operand_1))
return operand_1;
switch (operator) {
case '{}':
case '()':
if (typeof operand_1 !== 'object') {
operand_1 = convert_MathML.parse_scalar(operand_1);
} else if (!operand_1.mfrac && Array.isArray(operand_1)) {
operand_1 = [ {
mo : operator === '{}' ? '{' : '('
}, {
mrow : operand_1
}, {
mo : operator === '{}' ? '}' : ')'
} ];
} else if (false && !operand_1.mfrac) {
// for !operand_1.mfrac: "(1/2)" → "1/2"
operand_1 = {
// deprecated MathML <mfenced> element
mfenced : operand_1,
separators : ''
};
if (operator === '{}') {
operand_1.open = '{';
operand_1.close = '}';
}
}
return operand_1;
case 'm':
// 以表格呈現矩陣。
operand_1.forEach(function(row, index) {
row.forEach(function(expression, index) {
row[index] = {
mtd : expression
};
});
operand_1[index] = {
mtr : row
};
});
operand_1 = {
mfenced : {
mtable : operand_1
}
};
if (operand_2 !== '()')
operand_1.open = '[', operand_1.close = ']';
return operand_1;
case '{':
// 以表格呈現方程式組。
operand_1.forEach(function(equality, index) {
operand_1[index] = {
mtr : {
mtd : equality
}
};
});
return {
mfenced : {
mtable : operand_1
},
open : '{',
close : ''
};
case ',':
case ';':
operand_2 = [];
operand_1.forEach(function(expression) {
operand_2.push(convert_MathML.parse_scalar(expression), {
mo : operator
});
});
operand_2.pop();
return operand_2;
case '/':
case '⁄':
// ↑ Fraction slash
case '∕':
// ↑ Division slash
operand_1 = convert_MathML.parse_scalar(operand_1);
operand_2 = convert_MathML.parse_scalar(operand_2);
// "(1)/(2)" → "1/(2)"
operand_1 = convert_MathML.reduce_quote(operand_1);
// "(1)/(2)" → "(1)/2"
operand_2 = convert_MathML.reduce_quote(operand_2);
if (false) {
if (operand_1.mfenced)
// "(1)/(2)" → "1/2"
operand_1 = convert_MathML
.parse_scalar(operand_1.mfenced);
if (operand_2.mfenced)
// "(1)/(2)" → "1/2"
operand_2 = convert_MathML
.parse_scalar(operand_2.mfenced);
}
// <mfrac> <mi>numerator</mi> <mi>denominator</mi> </mfrac>
/** {Boolean}分子或分母為分數 */
var content_hass_fraction = operand_1.mfrac || operand_2.mfrac;
operand_1 = {
mfrac : [ operand_1, operand_2 ]
};
// 除了這些外，皆當作分數，上下表示。
if (false && (operator === '⁄' || operator === '∕')) {
// @deprecated: https://github.com/w3c/mathml/issues/29
operand_1.bevelled = true;
}
if (false && content_hass_fraction) {
// chrome 不支援 width : "150%"。支援 width : "10px"。
operand_1.mfrac[0] = {
mpadded : operand_1.mfrac[0],
width : "2em",
lspace : "1em"
};
operand_1.mfrac[1] = {
mpadded : operand_1.mfrac[1],
width : "2em",
lspace : "1em"
};
}
if (false && content_hass_fraction) {
// chrome 的 width : "100%" 指螢幕寬度。
operand_1.style = "width: 2em";
}
return operand_1;
case '^':
operand_1 = convert_MathML.parse_scalar(operand_1);
operand_2 = convert_MathML.parse_scalar(operand_2);
if (operand_2.mfenced)
// 去除括號 "()"。
// "7^(2/3)" → "<msup>7 2/3</msup>"
operand_2 = convert_MathML.parse_scalar(operand_2.mfenced);
if (Array.isArray(operand_2.mfrac)
&& operand_2.mfrac[0].mn === 1) {
// 去除 operand_1 之括號 "()"。
if (operand_1.mfenced)
operand_1 = convert_MathML
.parse_scalar(operand_1.mfenced);
// (operand_1) 的 (operand_2.mfrac[1]) 次方根。
// "7^(1/3)" → "<mroot> 7 3 </mroot>"
return {
mroot : operand_1 ? [ operand_1, operand_2.mfrac[1] ]
: operand_2.mfrac[1]
};
}
return {
// 依照規定必須要有<mi>，不可以省略。 e.g., (^12)C
msup : [ operand_1 || {
none : null
}, operand_2 ]
};
case '√':
case '∛':
// 去除括號 "()"。
// "√(1+2)" → "<msqrt>1+2</msqrt>"
if (operand_1.mfenced)
operand_1 = operand_1.mfenced;
// (平)方根 / 立方根
return operator === '√' ? {
msqrt : operand_1
} : {
mroot : [ operand_1, {
mn : 3
} ]
};
}
operand_1 = convert_MathML.parse_scalar(operand_1);
if (!operator)
return operand_1;
operand_1 = [ operand_1, {
mo : operator
} ];
if (operand_2)
operand_1.push(convert_MathML.parse_scalar(operand_2));
return operand_1;
}
};
convert_MathML.handler['default'] = convert_MathML.handler.mathml;
// relationships, assignment, equalities
// https://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode
// https://zh.wikipedia.org/wiki/%E6%95%B0%E5%AD%A6%E8%BF%90%E7%AE%97%E7%AC%A6_(Unicode%E5%8C%BA%E6%AE%B5)
// [≁-⊋]:
// ≁≂≃≄≅≆≇≈≉≊≋≌≍≎≏≐≑≒≓≔≕≖≗≘≙≚≛≜≝≞≟≠≡≢≣≤≥≦≧≨≩≪≫≬≭≮≯≰≱≲≳≴≵≶≷≸≹≺≻≼≽≾≿⊀⊁⊂⊃⊄⊅⊆⊇⊈⊉⊊⊋
// [⋀-⋭]: ⋀⋁⋂⋃⋄⋅⋆⋇⋈⋉⋊⋋⋌⋍⋎⋏⋐⋑⋒⋓⋔⋕⋖⋗⋘⋙⋚⋛⋜⋝⋞⋟⋠⋡⋢⋣⋤⋥⋦⋧⋨⋩⋪⋫⋬⋭
// TODO: "~"
convert_MathML.RELATIONSHIP_PATTERN = '=><≪≫∝≁-⊋⋀-⋭';
// https://en.wikipedia.org/wiki/Plus_and_minus_signs#Character_codes
convert_MathML.non_scalar_chars = '(){}^√∛*\\/⁄∕×⋅÷+\\-−±∓'
+ convert_MathML.RELATIONSHIP_PATTERN + ',;\r\n';
// operator : [ pattern, handler, object_to_add ]
// 運算子優先順序最高到最低
// [[w:en:Mathematical operators and symbols in Unicode]]
(convert_MathML.operator = [
// parentheses
[ /\(([^()]+)\)/, function($0, $1) {
return [ '()', $1 ];
} ], [ /{([^{}]+)}/, function($0, $1) {
return [ '{}', $1 ];
} ], [ /\[([^[]]+)\]/, function($0, $1) {
return [ '[]', $1 ];
} ],
// exponents.
[ /(\S*)\^([+\-−±∓]?\S+)/, function($0, $1, $2) {
// [ , base, power ]
return [ '^', $1, $2 ];
} ], [ /([√∛])([+\-−±∓]?\S+)/, function($0, $1, $2) {
// [ , base, power ]
return [ $1, $2 ];
} ],
// multiplication and fraction.
[ /(\S+)([*\/⁄∕×⋅÷])(\S+)/, function($0, $1, $2, $3) {
if ($2 === '*')
$2 = '⋅';
// [ , numerator, denominator ]
return [ $2, $1, $3 ];
} ],
// addition and subtraction
[ /(\S+)([+\-−±∓])(\S+)/, function($0, $1, $2, $3) {
return [ $2, $1, $3 ];
} ],
// set theory
// TODO: [[w:en:Ordered set operators]]
[ /(\S+)([∪∩\|])(\S+)/, function($0, $1, $2, $3) {
return [ $2, $1, $3 ];
} ],
// relationships, assignment, equalities
[ new RegExp('(\\S+)([' + convert_MathML.RELATIONSHIP_PATTERN
//
+ '])(\\S+)'), function($0, $1, $2, $3) {
// console.trace([ $0, $1, $2, $3 ]);
return [ $2, $1, $3 ];
} ],
// terms
[ /\S+(?:,\S+)+/, function($0) {
($0 = $0.split(',')).unshift(',');
return $0;
} ],
// terms
[ /\S+(?:;\S+)+/, function($0) {
($0 = $0.split(';')).unshift(';');
return $0;
} ] ])
//
.forEach(function(term) {
// 不可用 'g'! e.g., 2+3-4+5
term[0] = new RegExp(term[0].source.replace(/\\S/g, '[^'
+ convert_MathML.non_scalar_chars + ']'), '');
// library_namespace.debug(term[0]);
});
convert_MathML.RELATIONSHIP_PATTERN = new RegExp('^['
+ convert_MathML.RELATIONSHIP_PATTERN + ']$');
convert_MathML.process = function(text, order, queue) {
library_namespace.debug('[' + text + '] (' + order + ')', 3,
'convert_MathML.process');
var changed, operator;
while (true) {
if (changed)
changed = false;
else if (!(operator = convert_MathML.operator[order++]))
break;
else {
library_namespace.debug('shift to ' + operator[0], 3,
'convert_MathML.process');
}
text = text.trim();
text = text.replace(operator[0], function($0, $1, $2, $3) {
// return [ type, text1, text2 ]
var expression = operator[1]($0, $1, $2, $3);
if (!expression) {
library_namespace.error('convert_MathML.process: '
+ "Cannot parse: '" + $0 + "'");
return $0;
}
changed = true;
// next order
expression.forEach(function(term, index) {
if (index > 0)
expression[index] = convert_MathML.resolve(
convert_MathML.process(term, order, queue),
queue);
});
queue.push(expression);
return (// queue.separator +
queue.prefix
// - 1: get the real index
+ (queue.length - 1) + queue.postfix
// + queue.separator
);
});
library_namespace.debug('→ [' + text + ']', 3,
'convert_MathML.process');
}
library_namespace.debug('return [' + text + ']', 3,
'convert_MathML.process');
return text;
};
// parse math expression.
convert_MathML.parse = function(text, queue) {
if (!queue) {
queue = [];
// assert: NOT space or operator.
queue.prefix = '［';
queue.postfix = '］';
while (text.includes(queue.prefix))
// 維持 open/close quote 相同的長度。
queue.prefix += '［', queue.postfix = '］' + queue.postfix;
while (text.includes(queue.postfix))
queue.prefix += '［', queue.postfix = '］' + queue.postfix;
// queue.separator = queue.prefix + queue.postfix;
queue.pattern = '\\' + queue.prefix.split('').join('\\') + '(\\d+)'
//
+ '\\' + queue.postfix.split('').join('\\');
// [ , index ]
queue.index_pattern = new RegExp('^\\s*' + queue.pattern + '\\s*$');
// [ , index || '' ]
queue.pattern = new RegExp(queue.pattern + '|$', 'g');
}
// 前期處理。
// TODO: °º⁺⁻⁼ ⁰¹²³⁴⁵⁶⁷⁸⁹⁽⁾ ±∓♥´ ₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎ ₐₑₒₓₔ½ ⅓⅔ ¼¾ ⅕⅖⅗⅘ ⅙⅚
// ⅛⅜⅝⅞
text = text.replace(/!=|<>/g, '≠').replace(/>=/g, '≥').replace(/<=/g,
'≤').replace(/⅟/g, '1⁄')
// ugly workaround for <math>a=1=1/1</math>
.replace(/\r?\n?([=≠≥≤])/g, '\n$1');
// TODO: ⁢ 用於表示乘法運算中被省略的乘號。
// https://zh.wikipedia.org/wiki/%E6%95%B0%E5%AD%A6%E7%BD%AE%E6%A0%87%E8%AF%AD%E8%A8%80#Presentation_MathML
if (false) {
text = text.replace(
// 處理數學常數。
// https://en.wikipedia.org/wiki/Mathematical_constant
// 3^2π → 3^(2⋅π)
/(\d+(?:\.\d+)?)\s*(pi|[a-z\u0370-\u03FF])([^\da-z\u0370-\u03FF]|$)/ig
// TODO: π
, '($1⋅$2)$3');
}
text = convert_MathML.process(text, 0, queue);
if (false) {
library_namespace.debug('convert_MathML.parse: [' + text + ']');
library_namespace.debug('convert_MathML.parse: queue [' + queue
+ ']');
}
text = convert_MathML.resolve(text, queue);
if (false) {
library_namespace.debug('convert_MathML.parse: return [' + text
+ ']');
library_namespace.debug('convert_MathML.parse: queue [' + queue
+ ']');
}
// console.trace(queue);
return text;
};
// (?:[+\-−±∓]?\d+(?:\.\d+)?[°∘%％‰‱]?|pi|PI|Pi|[eiKπδφγλΩ∞ℵ])
var PATTERN_numeric = /[+\-−±∓]?\d+(?:\.\d+)?[°∘%％‰‱]?/;
// [ , 純數, 識別元 ]
convert_MathML.PATTERN_numeric_prefix = new RegExp('^('
+ PATTERN_numeric.source + ')([^\d].*)?$' + '$');
convert_MathML.is_numeric_prefix = function(expression) {
return expression.match(convert_MathML.PATTERN_numeric_prefix);
};
convert_MathML.PATTERN_numeric = new RegExp('^' + PATTERN_numeric.source
+ '$');
// 傳回 {Boolean}，說明運算式是否可做為數字來評估。
convert_MathML.is_numeric = function(expression) {
return convert_MathML.PATTERN_numeric.test(expression);
};
// 解開 queue index。
// for: number, queue index, or the combination.
convert_MathML.resolve = function(text, queue) {
if (false) {
library_namespace.debug('convert_MathML.resolve: [' + text + ']');
library_namespace.debug('convert_MathML.resolve: queue ['
+ queue.join(';') + ']');
function is_index(token) {
return token.startsWith(queue.prefix)
&& token.endsWith(queue.postfix);
}
}
var matched = text.match(queue.index_pattern);
if (matched)
return queue[matched[1]];
if (convert_MathML.is_numeric(text))
return text;
library_namespace
.debug('convert_MathML.resolve: Parse combinated expression: ['
+ text + ']');
var array = [ null ], lastIndex = 0, changed, matched;
for (queue.pattern.lastIndex = 0;;) {
matched = queue.pattern.exec(text);
// 前導 text
var pre_text = null;
if (matched.index > lastIndex) {
pre_text = text.substring(lastIndex, matched.index);
if (/(?:^\s*[+\-−±∓]?|\s)\d+(?:\.\d+)?(?:\s|$)/.test(pre_text))
// e.g., "log 3.3"
changed = true, Array.prototype.push.apply(array, pre_text
.split(/\s+/));
else
array.push(pre_text);
}
lastIndex = queue.pattern.lastIndex;
// library_namespace.debug([ pre_text, matched[1], lastIndex ]);
if (matched[1])
changed = true, array.push(queue[matched[1]]);
else {
if (!changed && pre_text && convert_MathML.is_numeric(pre_text))
changed = true;
break;
}
}
// if (changed) library_namespace.debug(array);
return changed ? array : text;
};
// 處理純量與變數。
convert_MathML.parse_scalar = function(text, no_MathML) {
if (typeof text === 'object') {
return !no_MathML && Array.isArray(text) ? {
mrow : text
} : text;
}
if (no_MathML)
return text;
if (!(text = String(text).trim()))
return text;
if (/\s/.test(text)) {
text = text.split(/\s+/);
// 多項。 e.g., "2a 3b 4ac"
text.forEach(function(term, index) {
text[index] = convert_MathML.parse_scalar(term);
});
return text;
}
var is_numeric = convert_MathML.is_numeric(text);
// 純數。e.g., "1"
if (is_numeric)
return {
mn : text
};
// 純數 + 識別元。e.g., "2a", "3.3π"
if (is_numeric = convert_MathML.is_numeric_prefix(text))
return [ {
mn : is_numeric[1]
}, convert_MathML.parse_scalar(is_numeric[2]) ];
// 下標。e.g., "log_2"
if (is_numeric = text.match(/^([^_]*)_([^_]+)$/))
// <msub><mi>x</mi><mi>y</mi></msub>
return {
// 依照規定必須要有<mi>，不可以省略。 e.g., (_6)C
msub : [ convert_MathML.parse_scalar(is_numeric[1]) || {
// TODO: should use <none />
none : null
}, convert_MathML.parse_scalar(is_numeric[2]) ]
};
if (library_namespace.is_debug()
&&
// a-zA-Z: normal variable. 變量
// \u0370-\u03ff: mathematical constant. 數學常數/希臘字母變量. e.g., π
!/^[a-zA-Z\u0370-\u03ff∞ℵ\u2E80-\u30000][a-zA-Z\u0370-\u03ff∞ℵ\u2E80-\u30000\d]*$/
// \u2E80-\u30000: Unihan variable
.test(text)) {
library_namespace
.error("convert_MathML.parse_scalar: Cannot parse: '"
+ text + "'");
}
// 純識別元。e.g., "x"
return {
mi : text
};
};
// 將 convert_MathML.parse() 之結果，reduce 成所須的格式。
convert_MathML.reduce = function(structure, node, handler) {
function process_mprescripts(structure, postsuperscript) {
if (!structure[0]
&& Array.isArray(structure[1])
&& structure[1][0] === '()'
&& structure[2]
// e.g., (_2), (_2^1), (_(a+b)), (_(a+b)^(c+d))
&& (Array.isArray(matched = structure[1][1]) ? /^[^_]$/
.test(matched[0])
&& (!matched[1] || /^_/.test(matched[1]))
: !matched || /^_/.test(matched))) {
// <mprescripts />
// https://developer.mozilla.org/zh-TW/docs/Web/MathML/Element/mmultiscripts
// e.g., (_2^1)x, (_2^1)x_4^3, (_2^1)x_4^(3)
var mmultiscripts = convert_MathML.reduce(structure[2], node,
handler);
if (!Array.isArray(mmultiscripts)) {
if (mmultiscripts && Array.isArray(mmultiscripts.msub)) {
mmultiscripts = mmultiscripts.msub;
mmultiscripts.push(postsuperscript && {
mi : postsuperscript
} || {
none : null
});
} else {
mmultiscripts = [ mmultiscripts, {
none : null
}, {
none : null
} ];
}
}
mmultiscripts.push({
mprescripts : null
});
structure = structure[1][1];
if (!Array.isArray(structure)) {
structure = convert_MathML.reduce(structure, node, handler);
if (structure && Array.isArray(structure.msub)) {
structure = [ , structure.msub[1], structure.msub[0] ];
}
}
// presubscript
matched = convert_MathML.reduce(structure[1], node, handler);
if (!matched) {
matched = {
none : null
};
} else if (Array.isArray(matched.msub)
&& matched.msub.length === 2
&& ('none' in matched.msub[0])) {
matched = matched.msub[1];
}
mmultiscripts.push(
// presubscript
matched,
// presuperscript
convert_MathML.reduce(structure[2], node, handler));
return {
mmultiscripts : mmultiscripts
};
}
}
function operand_is_matrix(operand, index) {
if (index === 0)
// pass the operator
return true;
// 確認 array 型態相同。
if (operand[0] !== structure[0])
return false;
// 確認 operand 為 array。
if (Array.isArray(operand[1]) && operand[1][0] === ','
// 確認 array 大小皆同。
&& (!matrix.length || matrix[0].length === operand[1].length - 1)) {
// e.g., {{1,2},{3,4}}
var m = [];
operand[1].forEach(function(expression, index) {
if (index > 0)
m
.push(convert_MathML.reduce(expression, node,
handler));
});
// assert: true === !![].push(0)
return matrix.push(m);
}
// 確認 operand 為 array。
if (typeof operand[1] !== 'object'
// 確認 array 大小皆同。
&& (!matrix.length || matrix[0].length === 1))
// e.g., ((5),(6))
return matrix.push([ operand[1] ]);
if (library_namespace.is_debug()) {
library_namespace.debug('array 型態'
+ (operand[0] === structure[0] ? '相同' : '不同'));
library_namespace.debug(Array.isArray(operand[1])
&& operand[1][0] === ',' ? 'operand 為 array'
: 'operand 為 '
+ (Array.isArray(operand[1]) ? operand[1][0]
: operand[1]));
if (matrix[0])
library_namespace.debug('array 大小: ' + matrix[0].length
+ ' != ' + (operand[1].length - 1));
}
}
// library_namespace.debug(structure);
if (!Array.isArray(structure))
return handler(structure);
// structure = [ operator, operand_1, operand_2, .. ]
if ((structure[0] in {
'()' : true,
'{}' : true,
'[]' : true
})
// 矩陣。
&& structure.length === 2 && Array.isArray(structure[1])
&& structure[1][0] === ',') {
var matrix = [], i = 0, length = structure[1].length;
if (structure[1].every(operand_is_matrix))
return handler(matrix, 'm', structure[0]);
}
// 前期處理。
var matched;
if (structure[0] === '^') {
if (matched = process_mprescripts(structure[1], structure[2])) {
return matched;
}
// e.g., sin^-1(2π)
if (Array.isArray(structure[2]) && structure[2].length === 3
&& !structure[2][0]) {
structure[2][1] = [ '^', structure[1], structure[2][1] ];
structure = structure[2];
}
// e.g., sin^-1 2π
if (typeof structure[2] === 'string'
&& (matched = structure[2]
.match(/^([+\-−±∓]?\d+(?:\.\d+)?)\s+(\S+)$/))) {
structure[2] = matched[1];
structure = [ , structure, matched[2] ];
}
} else if (matched = process_mprescripts(structure)) {
return matched;
}
// TODO: <munderover />, <math>∫_2^4 dy/dx</math>
// need_preserve_quotes: e.g., <math>P((A))</math>
var need_preserve_quotes = Array.isArray(structure[1])
&& structure[0] === structure[1][0];
structure.forEach(function(operand, index) {
if (index > 0)
structure[index] = convert_MathML
.reduce(operand, node, handler);
});
return !need_preserve_quotes && structure[0] && !(structure[0] in {
'{' : true,
',' : true,
';' : true
}) ? handler(structure[1], structure[0], structure[2]) : handler(
structure.slice(1), structure[0]);
};
return (_// JSDT:_module_
);
}