Refactor LaTeX syntax handling and improve parsing/serialization

- Updated `definitions-arithmetic.ts` to clarify handling of range and step-range notations.
- Removed outdated TODO comments in `definitions-core.ts` regarding Leibniz and Euler notations.
- Enhanced `definitions-other.ts` to support horizontal spacing commands (`\hspace`, `\hskip`, `\kern`) with appropriate parsing and serialization.
- Improved `definitions-sets.ts` to implement serialization for the complement operator and added support for set-builder notation.
- Introduced `serializeTabularBody` function in `definitions.ts` for better handling of matrix-like structures in LaTeX environments.
- Updated `_Parser` class in `parse.ts` to handle horizontal spacing commands and symbol-to-Unicode mapping.
- Modified `Serializer` class to prevent redundant wrapping of matchfix operators.
- Added comprehensive tests for new features and edge cases in `matchfix.test.ts`, `sets.test.ts`, `style.test.ts`, and `symbols.test.ts`.

Author: arnog

CHANGELOG.md

@@ -2,13 +2,48 @@
 
 #### Fixed
 
-- **LaTeX parsing: style, size, and color switch commands** —
-  `\displaystyle`, `\textstyle`, `\scriptstyle`, `\scriptscriptstyle`,
-  `\tiny`..`\Huge` (10 size commands), and `\color{...}` were silently
-  discarded during parsing. They now produce `Annotated` expressions that
-  preserve the styling information and round-trip correctly through
-  serialization. Added `\scriptstyle` / `\scriptscriptstyle` serialization
-  support (previously only `\displaystyle` and `\textstyle` were handled).
+- **LaTeX parsing: style, size, and color switch commands** — `\displaystyle`,
+  `\textstyle`, `\scriptstyle`, `\scriptscriptstyle`, `\tiny`..`\Huge` (10 size
+  commands), and `\color{...}` were silently discarded during parsing. They now
+  produce `Annotated` expressions that preserve the styling information and
+  round-trip correctly through serialization. Added `\scriptstyle` /
+  `\scriptscriptstyle` serialization support (previously only `\displaystyle`
+  and `\textstyle` were handled).
+
+- **LaTeX parsing: set-builder notation** — `\{x \in \R \mid x > 0\}` now parses
+  to `["Set", expr, ["Condition", cond]]`. Registered `\mid` as an infix
+  operator (`Divides`, precedence 160). The serializer round-trips set-builder
+  notation correctly.
+
+- **LaTeX serialization: `Complement`** — `["Complement", "A"]` now serializes
+  to `A^\complement` instead of falling back to the generic function form.
+  Removed stale `@todo` comments about a non-existent multi-argument case.
+
+- **LaTeX parsing: spacing commands** — `\hspace{dim}`, `\hspace*{dim}`,
+  `\hskip`, and `\kern` are now consumed during parsing (previously caused
+  "unexpected token" errors). These are treated as visual spacing and skipped.
+
+- **LaTeX serialization: `HorizontalSpacing` math classes** — the 2-argument
+  form `["HorizontalSpacing", expr, "'bin'"]` now serializes to `\mathbin{expr}`
+  (and similarly for `rel`, `op`, `ord`, `open`, `close`, `punct`, `inner`).
+  Previously the second argument was silently dropped.
+
+- **LaTeX serialization: redundant parens on matchfix operators** — `wrap()` no
+  longer adds parentheses around `Abs`, `Floor`, `Ceil`, `Norm`, and other
+  matchfix expressions that already have visible delimiters.
+
+- **LaTeX serialization: tabular environments** — default environment serializer
+  now renders matrix bodies (List of Lists) with `&` column separators and `\\`
+  row separators instead of nested function calls.
+
+- **LaTeX serialization: matchfix delimiter scaling** — default matchfix
+  serializer now respects `groupStyle` to choose between bare delimiters,
+  `\left..\right`, or `\bigl..\bigr` scaling.
+
+- **LaTeX parsing: Greek symbols in string groups** — `\alpha`, `\beta`, etc. in
+  `parseStringGroupContent()` (used by `\begin`/`\end`, color arguments) are now
+  interpreted as their Unicode equivalents instead of passing through as raw
+  LaTeX commands.
 
 ### 0.55.5 _2026-03-06_
 

docs/plans/2026-03-07-latex-todo-cleanup-design.md

@@ -0,0 +1,183 @@
+# LaTeX Parser @todo Cleanup — Design
+
+**Date**: 2026-03-07
+
+## Goal
+
+Address ~30 `@todo` comments across `src/compute-engine/latex-syntax/`, covering
+missing parse/serialize implementations (Category B) and presentation quality
+fixes (Category D).
+
+## Work Units
+
+### 1. Stale Derivative Comments (trivial)
+
+The `@todo` items at `definitions-core.ts:1365-1366` reference missing Leibniz
+and Euler derivative parsing. Investigation shows these are **already
+implemented**:
+
+- Leibniz ordinary: `definitions-arithmetic.ts:454-500` (outputs `D`)
+- Leibniz partial: `definitions-arithmetic.ts:420-451` (outputs
+  `PartialDerivative`)
+- Euler `D_x f`: `definitions-core.ts:1478-1518`
+- Euler partial `\partial_x f`: `definitions-other.ts:127-157`
+- Newton `\dot{x}`: `definitions-core.ts:1428-1476`
+- `D` serializer: `definitions-core.ts:1381-1425`
+
+**Action**: Remove the stale `@todo` comments.
+
+### 2. Set Operations (medium)
+
+#### 2a. Set Builder Parsing
+
+**File**: `definitions-sets.ts:364`
+
+The `{...}` matchfix parser only handles enumerated sets (`\{1,2,3\}`). Add
+detection of `\mid`, `|`, or `\colon` as a separator to produce set-builder
+notation.
+
+**Parsing**: `\{x \in \R \mid x > 0\}` →
+
+```json
+["Set", ["Element", "x", "RealNumbers"], ["Condition", ["Greater", "x", 0]]]
+```
+
+The serializer for this shape already exists at `definitions-sets.ts:571-581`.
+
+**Implementation**: Inside the matchfix parse handler, after parsing the body,
+check if the body contains a `\mid`/`|`/`\colon` separator. If so, split into
+expression + condition and wrap in `["Set", expr, ["Condition", cond]]`.
+
+The challenge: `|` is ambiguous (could be absolute value). Use `\mid` and
+`\colon` as unambiguous triggers. For bare `|`, only treat as separator when
+inside `\{...\}` matchfix context (which is already the case here).
+
+#### 2b. `Multiple` — Defer
+
+`Multiple` has no library definition (no entry in `sets.ts`). The latex-syntax
+entry has a name and an empty serialize stub. Since it's not a real operator in
+the engine, **defer** this until `Multiple` is defined in the library. Remove the
+empty serialize stub to avoid confusion.
+
+#### 2c. Multi-arg `CartesianProduct` / `Complement` Serialization
+
+**File**: `definitions-sets.ts:221,228`
+
+Currently these only handle the 2-arg infix case. Extend:
+
+- `CartesianProduct(A, B, C)` → `A \times B \times C`
+- `Complement(A, B)` — already works as postfix `A^\complement`; the multi-arg
+  comment may be stale. Verify and update/remove.
+
+### 3. BigOp Step Ranges — Update Comment (trivial)
+
+**File**: `definitions-arithmetic.ts:1712`
+
+The `Element` form (`i \in S`) is already handled at line 1720-1725. The
+step-range gap (`i=1..3..10`) is intentionally deferred — uncommon LaTeX
+notation. **Action**: Update the comment to reflect current state.
+
+### 4. Spacing Commands (small)
+
+#### 4a. Parse `\hspace`, `\hskip`, `\kern`
+
+**File**: `parse.ts:689`
+
+These take dimension arguments. Parse into
+`["HorizontalSpacing", "'<dimension>'"]` with the dimension as a string
+preserving unit.
+
+- `\hspace{1em}`, `\hspace*{1em}` — group argument
+- `\hskip 5pt`, `\kern-3mu` — inline glue (parse number + unit, ignore
+  plus/minus stretch)
+
+Register as expression triggers in `definitions-other.ts`. The parse handler
+reads the dimension and returns `["HorizontalSpacing", "'<value><unit>'"]`.
+
+#### 4b. Serialize `HorizontalSpacing` with Math Spacing Classes
+
+**File**: `definitions-other.ts:544`
+
+The 2-arg form `["HorizontalSpacing", expr, "'bin'"]` should serialize as:
+
+- `"bin"` → `\mathbin{expr}`
+- `"op"` → `\mathop{expr}`
+- `"rel"` → `\mathrel{expr}`
+- `"ord"` → `\mathord{expr}`
+- `"open"` → `\mathopen{expr}`
+- `"close"` → `\mathclose{expr}`
+- `"punct"` → `\mathpunct{expr}`
+
+Currently the second argument is silently dropped.
+
+### 5. Serializer Quality (medium)
+
+#### 5a. Skip Redundant Parens on Matchfix Operators
+
+**File**: `serializer.ts:90`
+
+`wrap()` adds parentheses around low-precedence expressions. But matchfix
+operators (`Abs`, `Floor`, `Ceil`, `Delimiter`) already have visible delimiters.
+Adding parens produces `\left(|x|\right)`.
+
+**Fix**: In `wrap()`, check if the expression is a matchfix operator with visible
+delimiters. If so, skip the wrapping. Identify matchfix by operator name:
+`Abs`, `Floor`, `Ceil`, `Norm`, and any `Delimiter` expression.
+
+#### 5b. `serializeTabular()` for Environments
+
+**File**: `definitions.ts:519`
+
+Environment entries use a generic serializer. When the body is a Matrix (List of
+Lists), serialize as tabular: `&` between columns, `\\` between rows.
+
+**Implementation**: Add a `serializeTabular()` helper that takes a matrix
+expression and produces `row1col1 & row1col2 \\ row2col1 & row2col2`. Wire it
+into the environment default serializer when the body matches a matrix shape.
+
+#### 5c. `groupStyle` for `\left..\right` in Matchfix
+
+**File**: `definitions.ts:531`
+
+Matchfix serialization currently emits raw delimiter strings. It should call
+`serializer.groupStyle(expr)` to choose between:
+
+- `"none"` → bare delimiters `(`, `)`
+- `"auto"` → `\left(`, `\right)`
+- `"big"` → `\bigl(`, `\bigr)`
+- etc.
+
+### 6. String Group Symbols (small)
+
+**File**: `parse.ts:1143`
+
+In `parseStringGroup()`, when encountering a `\`-prefixed token, check if it
+maps to a known Unicode symbol (Greek letters, common math symbols). Substitute
+the Unicode character instead of passing through the raw LaTeX command.
+
+Example: `\operatorname{\alpha-test}` → the string `"α-test"` instead of
+`"\\alpha-test"`.
+
+**Implementation**: Use the existing symbol dictionary to look up the mapping.
+Only substitute for symbols that have a single Unicode character representation
+(Greek letters, `\infty`, etc.). Leave unknown commands as-is.
+
+## Out of Scope
+
+- `Multiple` operator (no library definition)
+- Step ranges in BigOp indexing (uncommon notation)
+- Percent notation (`types.ts:618,693`)
+- Domain checks for `Abs`/`Norm` (`definitions-arithmetic.ts:877,1470,1479`)
+- Precedence corrections vs MathML (`definitions-other.ts:54,60,110`)
+
+## Testing Strategy
+
+Each work unit gets its own test block in the appropriate test file:
+
+- Set builder: `test/compute-engine/latex-syntax/sets.test.ts`
+- Spacing: `test/compute-engine/latex-syntax/style.test.ts`
+- Serializer quality: new tests alongside existing serialize tests
+- String groups: `test/compute-engine/latex-syntax/stefnotch.test.ts` or a new
+  `string-groups.test.ts`
+
+Round-trip tests (parse → serialize → parse) for all new parse/serialize pairs.