Add optional arguments to \sqrt

Summary:
Use the TeX definitions of `\root` to get the optional `\sqrt`
argument in the right place. Also add the MathML version.

Fixes #48

Test Plan:
 - `make test`
 - See that the images look good

Reviewers: kevinb, alpert

Reviewed By: alpert

Differential Revision: https://phabricator.khanacademy.org/D17236

src/buildHTML.js

@@ -812,7 +812,37 @@ var groupTypes = {
             ], "firstBaseline", null, options);
         }
 
-        return makeSpan(["sqrt", "mord"], [delim, body]);
+        if (!group.value.index) {
+            return makeSpan(["sqrt", "mord"], [delim, body]);
+        } else {
+            // Handle the optional root index
+
+            // The index is always in scriptscript style
+            var root = buildGroup(
+                group.value.index,
+                options.withStyle(Style.SCRIPTSCRIPT));
+            var rootWrap = makeSpan(
+                [options.style.reset(), Style.SCRIPTSCRIPT.cls()],
+                [root]);
+
+            // Figure out the height and depth of the inner part
+            var innerHeight = Math.max(delim.height, body.height);
+            var innerDepth = Math.max(delim.depth, body.depth);
+
+            // The amount the index is shifted by. This is taken from the TeX
+            // source, in the definition of `\r@@t`.
+            var toShift = 0.6 * (innerHeight - innerDepth);
+
+            // Build a VList with the superscript shifted up correctly
+            var rootVList = buildCommon.makeVList(
+                [{type: "elem", elem: rootWrap}],
+                "shift", -toShift, options);
+            // Add a class surrounding it so we can add on the appropriate
+            // kerning
+            var rootVListWrap = makeSpan(["root"], [rootVList]);
+
+            return makeSpan(["sqrt", "mord"], [rootVListWrap, delim, body]);
+        }
     },
 
     sizing: function(group, options, prev) {

src/buildMathML.js

@@ -187,8 +187,17 @@ var groupTypes = {
     },
 
     sqrt: function(group) {
-        var node = new mathMLTree.MathNode(
-            "msqrt", [buildGroup(group.value.body)]);
+        var node;
+        if (group.value.index) {
+            node = new mathMLTree.MathNode(
+                "mroot", [
+                    buildGroup(group.value.body),
+                    buildGroup(group.value.index)
+                ]);
+        } else {
+            node = new mathMLTree.MathNode(
+                "msqrt", [buildGroup(group.value.body)]);
+        }
 
         return node;
     },

src/functions.js

@@ -71,16 +71,11 @@ var functions = {
     "\\sqrt": {
         numArgs: 1,
         numOptionalArgs: 1,
-        handler: function(func, optional, body, positions) {
-            if (optional != null) {
-                throw new ParseError(
-                    "Optional arguments to \\sqrt aren't supported yet",
-                    this.lexer, positions[1] - 1);
-            }
-
+        handler: function(func, index, body, positions) {
             return {
                 type: "sqrt",
-                body: body
+                body: body,
+                index: index
             };
         }
     },

static/katex.less

@@ -1,5 +1,8 @@
 @import "fonts.less";
 
+// The mu unit is defined as 1/18 em
+@mu: 1.0/18.0em;
+
 .katex-display {
     display: block;
     margin: 1em 0;
@@ -359,6 +362,13 @@
                 margin-top: -1px;
             }
         }
+
+        > .root {
+            // These values are taken from the definition of `\r@@t`,
+            // `\mkern 5mu` and `\mkern -10mu`.
+            margin-left: 5*@mu;
+            margin-right: -10*@mu;
+        }
     }
 
     .sizing, .fontsize-ensurer {

test/katex-spec.js

@@ -1210,8 +1210,8 @@ describe("An optional argument parser", function() {
         expect("\\rule[0.2em]{1em}{1em}").toParse();
     });
 
-    it("should fail on sqrts for now", function() {
-        expect("\\sqrt[3]{2}").toNotParse();
+    it("should work with sqrts with optional arguments", function() {
+        expect("\\sqrt[3]{2}").toParse();
     });
 
     it("should work when the optional argument is missing", function() {

test/screenshotter/ss_data.json

@@ -29,6 +29,7 @@
     "Sizing": "http://localhost:7936/test/screenshotter/test.html?m={\\Huge x}{\\LARGE y}{\\normalsize z}{\\scriptsize w}",
     "Spacing": "http://localhost:7936/test/screenshotter/test.html?m=^3+[-1][1-1]1=1(=1)\\lvert a\\rvert~b",
     "Sqrt": "http://localhost:7936/test/screenshotter/test.html?m=\\sqrt{\\sqrt{\\sqrt{x}}}_{\\sqrt{\\sqrt{x}}}^{\\sqrt{\\sqrt{\\sqrt{x}}}^{\\sqrt{\\sqrt{\\sqrt{x}}}}}",
+    "SqrtRoot": "http://localhost:7936/test/screenshotter/test.html?m=1+\\sqrt[3]{2}+\\sqrt[1923^234]{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^2}}}}}}}}}}}",
     "SupSubCharacterBox": "http://localhost:7936/test/screenshotter/test.html?m=a_2f_2{f}_2{aa}_2{af}_2",
     "SupSubHorizSpacing": "http://localhost:7936/test/screenshotter/test.html?m=x^{x^{x}}\\Big|x_{x_{x_{x_{x}}}}\\bigg|x^{x^{x_{x_{x_{x_{x}}}}}}\\bigg|",
     "SupSubOffsets": "http://localhost:7936/test/screenshotter/test.html?m=\\displaystyle \\int_{2+3}x f^{2+3}+3\\lim_{2+3+4+5}f",