Javascript的MathML生成算法。任何推薦的參考

Question

我想構建可以爲傳統數學輸入生成MathML的代碼。我正在使用JavaScript進行編碼。是否有任何參考文獻或推薦的閱讀材料可以幫助我們掌握所需的算法？我正在閱讀MathML的W3C標準，這是標準的參考，但不適用於算法。

例如，對於

sqrt 9 * 5 + 20 

樣本輸入我想要生成MATHML表達類似下面

<math xmlns='w3.org/1998/Math/MathML'>; <mrow> <mrow> <mn>5</mn> <mo>&#8290;</mo> <mn>9</mn> <mo>&#8290;</mo> <mi>SQRT</mi> </mrow> <mo>+</mo> <mn>20</mn> </mrow> </math> 

Answer 1

我找到了一個不錯的教程MATHML這裏：http://rypress.com/tutorials/mathml/basic-algebra.html並着手製定一個非常基本的代數分析器（例如4*sqrt(x+6)=(5-z)*y/7），其中包含一個處理括號的粗堆棧和一個示例sqrt函數。這是你以後的方向嗎？

的jsfiddle這裏：http://jsfiddle.net/alhambra1/bSJyE/

JavaScript代碼：

<script> 
document.write('<p><input id="input" size=50>') 
document.write('<button onclick="convertToMathML()">Convert</button></p>') 
document.write('<div id="output"></div>') 

function lex(str,ptr){ 
    var ascii = str.charCodeAt(ptr), 
     lexeme = {string: "", type: ""}, 
     operators = {"+": "+" 
        , "-": "-" 
        , "*": "&times;" 
        , "/": "&divide;" 
        , "=": "="}, 
     functions = {sqrt: "msqrt"} 

    //identify type 
    if (ascii == 41) 
     lexeme.type = "closeBracket" 
    else if (ascii == 40){ 
     lexeme.type = "func" 
     lexeme.func = "mfenced" 
    } 
    else if (ascii > 45 && ascii < 58 && ascii != 47) 
     lexeme.type = "mn" 
    else if ((ascii > 64 && ascii < 91) || (ascii > 96 && ascii < 123)){ 
     for (i in functions){ 
      if (str.substr(ptr,i.length).toLowerCase() == i){ 
       lexeme.type = "func" 
       lexeme.func = functions[i] 
       ptr += i.length - 1 
      } else 
       lexeme.type = "mi" 
     } 
    } else if (!operators[str.charAt(ptr)]) 
     return {string: str.charAt(ptr), type: "error", pointer: ptr} 
    else 
     lexeme.type = "mo" 

    switch (lexeme.type){ 
     case "mo": 
      lexeme.string = operators[str.charAt(ptr++)] 
      break 
     default: 
      lexeme.string = str.charAt(ptr++) 
      break 
    } 

    ascii = str.charCodeAt(ptr) 

    //identify numbers and functions 
    if (lexeme.type == "mn"){ 
     while (ptr < str.length && ascii > 45 && ascii < 58 && ascii != 47){ 
      lexeme.string += str.charAt(ptr) 
      ascii = str.charCodeAt(++ptr) 
     } 
    } else if (lexeme.type == "func" && lexeme.func != "mfenced"){ 
     while (ptr < str.length && str.substr(ptr).match(/^\s/)){ 
      ascii = str.charCodeAt(++ptr) 
     } 
     if (str.charAt(ptr) != "(") 
      return {string: str.charAt(ptr), type: "error", pointer: ptr} 
     else 
      ptr++ 
    } 

    lexeme["pointer"] = ptr 

    return lexeme 
} 

function markup(lexeme){ 
    return "<" + lexeme.type + ">\n" 
      + lexeme.string + "\n" 
      + "</" + lexeme.type + ">\n" 
} 

function convertToMathML(){ 
    var str = document.getElementById('input').value, 
     expression = "", 
     ptr = 0, 
     stack = [] 

    while (ptr < str.length){ 
     var currLexeme = lex(str,ptr) 

     if (currLexeme.type == "closeBracket"){ 
      if (stack.length == 0) 
       expression = "Extra bracket at: " + (currLexeme.pointer - 1) 
      else 
       expression += "</" + stack.pop().func + ">\n" 
          + "</mrow>"   
      ptr = currLexeme.pointer 
     } else if (currLexeme.type == "error"){ 
      expression = "Cannot parse \"" + currLexeme.string 
         + "\" at " + currLexeme.pointer 
      break 
     } else if (currLexeme.type == "func"){ 
      expression += "<" + currLexeme.func + ">\n" 
         + "<mrow>\n" 
      stack.push(currLexeme) 
      ptr = currLexeme.pointer 
     } else { 
      expression += markup (currLexeme) 
      ptr = currLexeme.pointer 
     } 
    } 

    if (ptr >= str.length && stack.length > 0) 
     expression = "Missing " + stack.length + " closing bracket/s." 

    expression = "<math xmlns='http://www.w3.org/1998/Math/MathML'>" 
       + expression + "</math>" 

    document.getElementById('output').innerHTML = expression 
} 
</script>