UnicodeMath: write what reads back, and read two spaces after a comma

src/SharpEquations/Internal/UnicodeMath/UnicodeMathSerializer.cs

@@ -507,8 +507,9 @@ private string Binary(XElement node, string op)
             if (retd.Length == 0)
                 retd = "〖〗";
 
-            // a scripted base (𝑎_𝑏 under ^𝑐) is grouped, as 𝑎_𝑏^𝑐 is one subsup
-            if ((op == "^" || op == "_" || IsPrime(Text(Last(node)))) && IsScripted(First(node)) && functionName == null)
+            // a scripted base (𝑎_𝑏 under ^𝑐) is grouped, as 𝑎_𝑏^𝑐 is one subsup, and so is a matrix in brackets (⒨(…)),
+            // which a script after it would not apply to
+            if ((op == "^" || op == "_" || IsPrime(Text(Last(node)))) && (IsScripted(First(node)) || IsBracketedMatrix(First(node))) && functionName == null)
                 ret = "〖" + ret.TrimEnd(' ') + "〗";
             if (op == "^" && Name(Last(node)) == "msub" || op == "_" && Name(Last(node)) == "msup")
                 return ret + op + "(" + retd + ")";
@@ -522,6 +523,14 @@ private string Binary(XElement node, string op)
             // a script that applies a function (log_(𝑏⁡𝑎)): the space before the function name would end the script
             if ((op == "^" || op == "_") && Name(Last(node)) == "mrow" && Role(Last(node)) == ":function")
                 retd = "(" + retd.Trim(' ') + ")";
+            // a denominator that applies a function (𝑎/sin⁡𝛼): a space after the fraction bar would end the fraction
+            if (Name(node) == "mfrac" && Name(Last(node)) == "mrow" && Role(Last(node)) == ":function")
+                retd = retd.TrimStart(' ');
+            // a denominator that ends with a script, before an operand that follows the fraction (1/(4𝜋𝜀₀) 𝑞₁𝑞₂/𝑟²): the
+            // space after it would end the script, not the denominator (an operator after it ends both)
+            if (Name(node) == "mfrac" && op == "/" && EndsWithSpacedScript(Last(node)) && node.ElementsAfterSelf().FirstOrDefault() is { } next && Name(next) != "mo" &&
+                !(Ch(retd, 0) == "(" && RemoveOuterParens(retd) != retd))
+                retd = "(" + retd.Trim(' ') + ")";
             if (IsMathMLObject(node, false) && ChildCount(node) > 0)
             {
                 var attr = Role(Last(node));
@@ -757,10 +766,20 @@ private static bool EndsWithScript(XElement node)
             return Name(node) is "msub" or "msup" or "msubsup" or "mover" or "munder" or "munderover";
         }
 
+        private static bool IsBracketedMatrix(XElement node) => Name(node) == "mrow" && MatrixIntents.Any(m => m.Intent == Attr(node, "intent"));
+
+        // a script that a space after it ends, but not what is before it: all but the superscript digits (𝑥²)
+        private static bool EndsWithSpacedScript(XElement node)
+        {
+            while (Name(node) == "mrow" && ChildCount(node) > 0 && !HasAttr(node, "intent"))
+                node = Last(node);
+            return IsScripted(node) && !(Name(node) == "msup" && IsDigitArg(node));
+        }
+
         private string ScriptBase(XElement node)
         {
             var ret = Dump(node);
-            if (IsScripted(node) || Name(node) == "mrow" && ChildCount(node) > 1 && !HasAttr(node, "intent"))
+            if (IsScripted(node) || Name(node) == "mrow" && ChildCount(node) > 1 && !HasAttr(node, "intent") || IsBracketedMatrix(node))
                 ret = "〖" + ret.TrimEnd(' ') + "〗";
             return ret;
         }

src/SharpEquations/Internal/UnicodeMath/UnicodeMathTransform.cs

@@ -634,6 +634,13 @@ private static JsObject TransformSpaces(object value)
                 foreach (var space in spaceString)
                     spaces += "&#x" + ((int)space).ToString("x", CultureInfo.InvariantCulture) + ";";
             }
+            // a space of a width in eighteenths of an em (the ½ em of ",  "), as the character of that width; none for
+            // the width 0 of an empty cell
+            else if (value is JsObject width && Get(width, "space") is { } eighteenths && System.Convert.ToInt32(eighteenths, CultureInfo.InvariantCulture) > 0)
+            {
+                foreach (var space in UnicodeMathSerializer.UniSpaces[System.Convert.ToInt32(eighteenths, CultureInfo.InvariantCulture)])
+                    spaces += "&#x" + ((int)space).ToString("x", CultureInfo.InvariantCulture) + ";";
+            }
             return O("mo", NoAttr(spaces));
         }
 

tests/SharpEquations.Tests/Regression/WriterRoundTripTests.cs

@@ -35,6 +35,36 @@ public async Task UnicodeMathWritesWhatItReads(string mathML, string unicodeMath
             await Assert.That(RoundTrip(back, EquationFormat.UnicodeMath)).IsEqualTo(back);
         }
 
+        /// <summary>
+        /// UnicodeMath that reads to an equation the writer wrote as text that read back otherwise: a script of a matrix
+        /// in brackets (⒨(…)²), a function in a denominator (𝑎/ sin⁡𝛼), a denominator that ends with a script before
+        /// what follows the fraction (1/4𝜋𝜀₀ 𝑞₁𝑞₂/𝑟²), and the space after a comma that two spaces type (𝑎,  𝑏).
+        /// </summary>
+        [Test]
+        [Arguments("(■(a&b@c&d))^2")]
+        [Arguments("(■(a&b@c&d))^(-1)=1/(ad-bc) (■(d&-b@-c&a))")]
+        [Arguments("[■(a&b@c&d)]_ij")]
+        [Arguments("|■(a&b@c&d)|^2")]
+        [Arguments("a/sin⁡α")]
+        [Arguments("a/sin⁡α=b/sin⁡β=c/sin⁡γ")]
+        [Arguments("(sin⁡α)/a")]
+        [Arguments("1/(4πε_0) (q_1 q_2)/r^2")]
+        [Arguments("1/(x_1) y")]
+        [Arguments("1/(ab^2) c/d")]
+        [Arguments("A=√s,  s=2")]
+        [Arguments("f(x,  y)")]
+        public async Task UnicodeMathReadsBackWhatItWrites(string unicodeMath)
+        {
+            var equation = Equation.Parse(unicodeMath, EquationFormat.UnicodeMath);
+            await Assert.That(RoundTrip(equation, EquationFormat.UnicodeMath)).IsEqualTo(equation).Because(equation.ToString(EquationFormat.UnicodeMath));
+        }
+
+        [Test]
+        public async Task UnicodeMathReadsTwoSpacesAfterACommaAsASpace()
+        {
+            await Assert.That(Equation.Parse("a,  b", EquationFormat.UnicodeMath)).IsEqualTo(Equation.Parse("a,\u2002b", EquationFormat.UnicodeMath));
+        }
+
         [Test]
         [Arguments("<mrow><mo>[</mo><mi>a</mi><mo>|</mo><mi>b</mi><mo>]</mo></mrow>")]
         [Arguments("<mrow><mo>[</mo><mi>a</mi><mo>‖</mo><mi>b</mi><mo>]</mo></mrow>")]