Added support in the expression parser for mathematical alphanumeric …

…symbols (see #265)

HISTORY.md

@@ -1,5 +1,12 @@
 # History
 
+## not yet released, version 2.4.0
+
+- Added support in the expression parser for mathematical alphanumeric symbols 
+  in the expression parser: unicode range \u{1D400} to \u{1D7FF} excluding 
+  invalid code points.
+
+
 ## 2015-09-19, version 2.3.0
 
 - Implemented function `distance`. Thanks @devanp92.

lib/expression/parse.js

@@ -314,8 +314,8 @@ function factory (type, config, load, typed) {
     }
 
     // check for variables, functions, named operators
-    if (isAlpha(c)) {
-      while (isAlpha(c) || isDigit(c)) {
+    if (currentIsAlpha()) {
+      while (currentIsAlpha() || isDigit(c)) {
         token += c;
         next();
       }
@@ -366,22 +366,40 @@ function factory (type, config, load, typed) {
   }
 
   /**
-   * checks if the given char c is:
-   * - a latin letter (upper or lower case)
-   * - a latin letter with accents
-   * - a greek letter
-   * - an underscore
-   * @param {string} c   a string with one character
+   * Checks whether the current character `c` is a valid alpha character:
+   *
+   * - A latin letter (upper or lower case) Ascii: a-z, A-Z
+   * - A underscore                         Ascii: _
+   * - A latin letter with accents          Unicode: \u00C0 - \u02AF
+   * - A greek letter                       Unicode: \u0370 - \u03FF
+   * - A mathematical alphanumeric symbol   Unicode: \u{1D400} - \u{1D7FF} excluding invalid code points
+   *
    * @return {boolean}
    * @private
    */
-  function isAlpha (c) {
+  function currentIsAlpha () {
     // http://unicode-table.com/en/
+    // http://www.wikiwand.com/en/Mathematical_operators_and_symbols_in_Unicode
     //
     // Note: In ES6 will be unicode aware:
     //   http://stackoverflow.com/questions/280712/javascript-unicode-regexes
     //   https://mathiasbynens.be/notes/es6-unicode-regex
-    return /^[a-zA-Z_\u00C0-\u02AF\u0370-\u03FF]$/.test(c);
+    var cPrev = expression.charAt(index - 1);
+    var cNext = expression.charAt(index + 1);
+
+    var isValidLatinOrGreek = function (p) {
+      return /^[a-zA-Z_\u00C0-\u02AF\u0370-\u03FF]$/.test(p);
+    };
+
+    var isValidMathSymbol = function (high, low) {
+      return /^[\uD835]$/.test(high) &&
+          /^[\uDC00-\uDFFF]$/.test(low) &&
+          /^[^\uDC55\uDC9D\uDCA0\uDCA1\uDCA3\uDCA4\uDCA7\uDCA8\uDCAD\uDCBA\uDCBC\uDCC4\uDD06\uDD0B\uDD0C\uDD15\uDD1D\uDD3A\uDD3F\uDD45\uDD47-\uDD49\uDD51\uDEA6\uDEA7\uDFCC\uDFCD]$/.test(low);
+    };
+
+    return isValidLatinOrGreek(c)
+        || isValidMathSymbol(c, cNext)
+        || isValidMathSymbol(cPrev, c);
   }
 
   /**

test/expression/parse.test.js

@@ -74,6 +74,16 @@ describe('parse', function() {
 
     math.eval('k\u00F6ln = 5', scope); // Combination of latin and unicode
     assert.strictEqual(scope['k\u00F6ln'], 5);
+
+    // test unicode characters in the astral plane (surrogate pairs
+    math.eval('\uD835\uDD38 = 1', scope); // double struck capital A
+    assert.strictEqual(scope['\uD835\uDD38'], 1);
+
+    // should not allow the "holes"
+    assert.throws(function () {
+      math.eval('\uD835\uDCA3 = 1', scope);
+    })
+
   });
 
   describe('multiline', function () {