Let a subscript have a subscript

BREAKING-CHANGES.md

@@ -42,6 +42,19 @@ A not-equal written `<>` is read as `not (a = b)`, and printed that way.
 
 ## Unreleased — since 2.6.0
 
+### A subscript may have a subscript
+
+**Not silent: what was a parse error is a name.** A name took at most one `_`, so `x_1_2` and `X_a_beta` were lexer
+errors. A subscript may now have one of its own: `X_a_beta` is one variable, `X` with the subscript `a_beta`, printed
+in LaTeX as `X_{a_{\beta}}`. `_` still neither begins nor ends a name, and two do not stand together
+([#524](https://github.com/asc-community/AngouriMath/issues/524)).
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `"X_a_beta + 10".ToEntity()` | an `UnhandledParseException` | `X_a_beta + 10` |
+| `MathS.Var("X_a_beta").Latexize()` | an `UnhandledParseException` | `X_{a_{\beta}}` |
+| `"x__1".ToEntity()` | an `UnhandledParseException` | an `UnhandledParseException` |
+
 ### A numerical definite integral is Gauss–Legendre, with the digits it knows
 
 **Silent: wrong answers, and values where there was NaN.** `Entity.DefiniteIntegral(x, a, b, steps)` was the mean of

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -711,7 +711,9 @@ BOOLEAN: ('true' | 'True' | 'false' | 'False') ;
 // otherwise be an identifier. https://github.com/asc-community/AngouriMath/issues/906
 NAN: 'NaN' ;
 
-VARIABLE: ('a'..'z'|'A'..'Z'|'\u0370'..'\u03FF'|'\u1F00'..'\u1FFF'|'\u0400'..'\u04FF'|'\u212F')+ ('_' ('a'..'z'|'A'..'Z'|'0'..'9'|'\u0370'..'\u03FF'|'\u1F00'..'\u1FFF'|'\u0400'..'\u04FF')+)? ;
+/* A subscript may have a subscript of its own: X_a_beta is X with the subscript a_beta, and prints as X_{a_{\beta}}.
+   https://github.com/asc-community/AngouriMath/issues/524 */
+VARIABLE: ('a'..'z'|'A'..'Z'|'\u0370'..'\u03FF'|'\u1F00'..'\u1FFF'|'\u0400'..'\u04FF'|'\u212F')+ ('_' ('a'..'z'|'A'..'Z'|'0'..'9'|'\u0370'..'\u03FF'|'\u1F00'..'\u1FFF'|'\u0400'..'\u04FF')+)* ;
 
 COMMENT: ('//' ~[\r\n]* ('\r'? '\n')? | '/*' .*? '*/') -> skip ;
 

Sources/AngouriMath/Docs/Usage/Syntax.md

@@ -142,12 +142,14 @@ is `pi` and the script `ℯ` is `e`, so `sin(π)` is `0` and `ln(ℯ)` is `1`. T
 they are variables that print like `e` and `x`, and `х + x` has two
 ([#1260](https://github.com/asc-community/AngouriMath/issues/1260)).
 
-Four things that look like names and are not:
+A subscript may have one of its own: `X_a_beta` is one name, `X` with the subscript `a_beta`, and in
+LaTeX it is `X_{a_{\beta}}` ([#524](https://github.com/asc-community/AngouriMath/issues/524)).
+
+Three things that look like names and are not:
 
 | written | what it is |
 |---|---|
-| `_x`, `x_` | a lexer error. `_` may neither begin a name nor end one |
-| `x_1_2` | a lexer error. At most one `_`, so subscripts do not nest ([#524](https://github.com/asc-community/AngouriMath/issues/524)) |
+| `_x`, `x_`, `x__1` | a lexer error. `_` may neither begin a name nor end one, and two do not stand together |
 | `x1` | `x ^ 1`. A digit is not a letter, and a name beside a number is a power — see below |
 | `sinx` | one name, spelled `sinx`. Letters written together are a single name, never a product of one-letter ones |
 

Sources/AngouriMath/Functions/Output/Latex/Latex.Classes.cs

@@ -59,9 +59,15 @@ static string LatexizePart(string symbol, bool upright)
                 }
                 // For variables with subscripts (e.g., "pi_2", "x_e", "e_pi")
                 // Both the main part and subscript are processed through LatexizePart,
-                // which handles upright formatting for "pi" and "e" consistently
+                // which handles upright formatting for "pi" and "e" consistently.
+                // A subscript may have one of its own, so X_a_beta is X_{a_{\beta}}.
+                // https://github.com/asc-community/AngouriMath/issues/524
+                static string LatexizeIndex(string index)
+                    => index.IndexOf('_') is var underscore && underscore == -1
+                    ? LatexizePart(index, IsNameLatexUprightFormatted(index))
+                    : $"{LatexizePart(index.Substring(0, underscore), IsNameLatexUprightFormatted(index.Substring(0, underscore)))}_{{{LatexizeIndex(index.Substring(underscore + 1))}}}";
                 return SplitIndex() is var (prefix, index)
-                    ? $"{LatexizePart(prefix, IsNameLatexUprightFormatted(prefix))}_{{{LatexizePart(index, IsNameLatexUprightFormatted(index))}}}"
+                    ? $"{LatexizePart(prefix, IsNameLatexUprightFormatted(prefix))}_{{{LatexizeIndex(index)}}}"
                     : LatexizePart(Name, IsOwnNameUpright);
             }
         }

Sources/Tests/UnitTests/Convenience/LatexTest.cs

@@ -65,6 +65,10 @@ void TestSimplify(string expected, Entity actual) =>
         [Fact] public void SubscriptSingle() => Test(@"c_{\mathrm{e}}", MathS.Var("c_e"));
         [Fact] public void SubscriptDuo() => Test(@"\Delta_{\mathrm{a2}}", MathS.Var("Delta_a2"));
         [Fact] public void SubscriptDuoPlus() => TestSimplify(@"6+\Delta_{\mathrm{a2}}", "Delta_a2+6");
+        // A subscript of a subscript. https://github.com/asc-community/AngouriMath/issues/524
+        [Fact] public void SubscriptNested() => Test(@"X_{a_{\beta}}", MathS.Var("X_a_beta"));
+        [Fact] public void SubscriptNestedThrice() => Test(@"x_{1_{2_{\mathrm{e}}}}", MathS.Var("x_1_2_e"));
+        [Fact] public void SubscriptNestedParsed() => Test(@"X_{a_{\beta}}+10", MathS.FromString("X_a_beta + 10"));
         [Fact] public void Square() => Test(@"{x}^{2}", MathS.Sqr(x));
         [Fact] public void TwoXSquare() => Test(@"2 {x}^{2}", 2 * MathS.Sqr(x));
         [Fact] public void MTwoXSquare() => Test(@"-2 \cdot {x}^{2}", -2 * MathS.Sqr(x));

Sources/Tests/UnitTests/Convenience/SyntaxDocumentedTest.cs

@@ -140,6 +140,9 @@ public void ALongerNameContainingNaNIsAVariable(string written) =>
         [InlineData("альфа")]
         [InlineData("x_ω")]
         [InlineData("sinx")]
+        // A subscript may have a subscript. https://github.com/asc-community/AngouriMath/issues/524
+        [InlineData("x_1_2")]
+        [InlineData("X_a_beta")]
         public void AName(string written)
         {
             var variable = Assert.IsType<Entity.Variable>(written.ToEntity());
@@ -154,7 +157,7 @@ public void AName(string written)
         [Theory]
         [InlineData("_x")]
         [InlineData("x_")]
-        [InlineData("x_1_2")]
+        [InlineData("x__1")]
         [InlineData("fi")]
         public void WhatIsNotAName(string written) =>
             Assert.Throws<UnhandledParseException>(() => written.ToEntity());