feat: support unicode superscript and subscript in latex parsing (strict and non-strict)

Author: arnog

CHANGELOG.md

@@ -1,20 +1,17 @@
 ### [Unreleased]
 
-- **Stochastic equality check for expressions with unknowns**: `expr.isEqual()`
-  now uses a stochastic fallback when symbolic methods (expand + simplify) can't
-  prove equality. Both expressions are evaluated at 50 sample points (9
-  well-known values + 41 random) and compared with relative+absolute tolerance,
-  including both real and imaginary parts. This detects equivalences like
-  `sin²(x) + cos²(x) = 1`, `(x+y)² = x²+2xy+y²`, and `sin(2x) = 2sin(x)cos(x)`
-  that were previously returned as `undefined`. Singularities (NaN at a sample
-  point) are skipped rather than treated as disagreements. The check also works
-  when the two expressions have different unknowns (e.g. `x - x + y` vs `y`).
-
 - **Non-strict parser supports exponents on bare functions**: In non-strict mode
-  (`strict: false`), bare function names like `sin`, `cos`, `tan` can now include
-  an exponent before the argument list. For example, `sin^2(x)` and `cos^{10}(x)`
-  are now correctly parsed as `["Power", ["Sin", "x"], 2]`, matching the behavior
-  of their LaTeX counterparts `\sin^2(x)` and `\cos^{10}(x)`.
+  (`strict: false`), bare function names like `sin`, `cos`, `tan` can now
+  include an exponent before the argument list. For example, `sin^2(x)` and
+  `cos^{10}(x)` are now correctly parsed as `["Power", ["Sin", "x"], 2]`,
+  matching the behavior of their LaTeX counterparts `\sin^2(x)` and
+  `\cos^{10}(x)`.
+
+- **Unicode superscript and subscript digit support**: The LaTeX parser now
+  recognizes Unicode superscript digits (`⁰¹²³⁴⁵⁶⁷⁸⁹⁻`) and subscript digits
+  (`₀₁₂₃₄₅₆₇₈₉₋`), converting them to `^{...}` and `_{...}` respectively.
+  This works in all parsing modes. For example, `x²` parses as `x^{2}`,
+  `sin²(x)` as `\sin^{2}(x)`, `x⁻²` as `x^{-2}`, and `x₁₂` as `x_{12}`.
 
 - **`.is()` now works with assigned variables**: Previously, `.is()` only
   evaluated expressions made entirely of declared constants (like `Pi`). Now it

src/compute-engine/latex-syntax/tokenizer.ts

@@ -7,6 +7,34 @@
 
 import { splitGraphemes } from '../../common/grapheme-splitter';
 
+const UNICODE_SUPERSCRIPT_MAP: Record<string, string> = {
+  '\u2070': '0', // ⁰
+  '\u00B9': '1', // ¹
+  '\u00B2': '2', // ²
+  '\u00B3': '3', // ³
+  '\u2074': '4', // ⁴
+  '\u2075': '5', // ⁵
+  '\u2076': '6', // ⁶
+  '\u2077': '7', // ⁷
+  '\u2078': '8', // ⁸
+  '\u2079': '9', // ⁹
+  '\u207B': '-', // ⁻
+};
+
+const UNICODE_SUBSCRIPT_MAP: Record<string, string> = {
+  '\u2080': '0', // ₀
+  '\u2081': '1', // ₁
+  '\u2082': '2', // ₂
+  '\u2083': '3', // ₃
+  '\u2084': '4', // ₄
+  '\u2085': '5', // ₅
+  '\u2086': '6', // ₆
+  '\u2087': '7', // ₇
+  '\u2088': '8', // ₈
+  '\u2089': '9', // ₉
+  '\u208B': '-', // ₋
+};
+
 // The 'special' tokens must be of length > 1 to distinguish
 // them from literals.
 // '<space>': whitespace
@@ -43,6 +71,24 @@ class Tokenizer {
     // Replace the Unicode minus sign (U+2212: MINUS SIGN) with a hyphen
     s = s.replace(/\u2212/g, '-');
 
+    // Replace Unicode superscript sequences with ^{...}
+    // Handles: ⁰¹²³⁴⁵⁶⁷⁸⁹ and ⁻ (superscript minus)
+    s = s.replace(/[⁰¹²³⁴⁵⁶⁷⁸⁹⁻]+/g, (m) => {
+      const digits = Array.from(m)
+        .map((c) => UNICODE_SUPERSCRIPT_MAP[c])
+        .join('');
+      return `^{${digits}}`;
+    });
+
+    // Replace Unicode subscript sequences with _{...}
+    // Handles: ₀₁₂₃₄₅₆₇₈₉ and ₋ (subscript minus)
+    s = s.replace(/[₀₁₂₃₄₅₆₇₈₉₋]+/g, (m) => {
+      const digits = Array.from(m)
+        .map((c) => UNICODE_SUBSCRIPT_MAP[c])
+        .join('');
+      return `_{${digits}}`;
+    });
+
     this.s = splitGraphemes(s);
     this.pos = 0;
   }