swiftui-math/MISSING_FEATURES.md

SwiftMath Missing Features - Implementation Status

This document lists LaTeX features that are not yet implemented in SwiftMath, based on comprehensive testing against the LaTeX Mathematics reference.

Summary

• Total Features Tested: 12
• Fully Implemented: 7 (58%)
• Partially Implemented: 0 (0%)
• Not Implemented: 5 (42%)

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HIGH PRIORITY Features (Not Implemented)

1. ✅ \displaystyle and \textstyle - IMPLEMENTED

Status: ✅ Working Description: Commands to force display or text style rendering within expressions

Test Results: All tests passed

• \displaystyle \sum_{i=1}^{n} x_i - ✅ Works
• \textstyle \int_{0}^{\infty} f(x) dx - ✅ Works
• Inline displaystyle fractions - ✅ Works

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2. ❌ \middle - Delimiter in Middle of Expression

Status: ❌ Not Implemented Error: Invalid command \middle

Description: Used with \left and \right to add delimiters in the middle of expressions

Examples:

\left( \frac{a}{b} \middle| \frac{c}{d} \right)
\left\{ x \middle\| y \right\}

Use Case: Set notation, conditional expressions, piecewise functions with multiple sections

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3. ✅ \substack - Multi-line Limits and Subscripts - IMPLEMENTED

Status: ✅ Working Description: Creates multi-line subscripts and limits for operators

Test Results: All tests passed

• \substack{a \\ b} - ✅ Works
• \sum_{\substack{0 \le i \le m \\ 0 < j < n}} P(i,j) - ✅ Works (nested in subscript)
• \prod_{\substack{p \text{ prime} \\ p < 100}} p - ✅ Works (nested in subscript)
• \substack{\frac{a}{b} \\ c} - ✅ Works (with nested commands)

Use Case: Complex summation/product limits, constrained expressions

Implementation: Uses buildInternal(true) pattern, handles implicit tables created by \\ within braces.

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4. ❌ Manual Delimiter Sizing: \big, \Big, \bigg, \Bigg

Status: ❌ Not Implemented Error: Invalid command \big

Description: Manually control delimiter sizes (4 levels beyond normal)

Examples:

\big( x \big)        % slightly larger
\Big[ y \Big]        % larger
\bigg\{ z \bigg\}    % even larger
\Bigg| w \Bigg|      % largest

Use Case: Fine control over delimiter appearance, nested expressions

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5. ❌ Spacing Commands: \,, \:, \;, \!

Status: ❌ Partially Not Implemented Error: Invalid command \: (and likely others)

Description: Fine-tuned horizontal spacing control

Command	Description	Width
\,	Thin space	3/18 em
\:	Medium space	4/18 em
\;	Thick space	5/18 em
\!	Negative thin space	-3/18 em

Examples:

a\,b                              % thin space
\int\!\!\!\int f(x,y) dx dy      % tight double integral
x \, y \: z \; w                  % mixed spacing

Use Case: Fine typography control, integral notation, custom spacing

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MEDIUM PRIORITY Features

6. ✅ Multiple Integral Symbols: \iint, \iiint, \iiiint - IMPLEMENTED

Status: ✅ Working Description: Special symbols for double, triple, and quadruple integrals

Test Results: All tests passed

• \iint f(x,y) dx dy - ✅ Works (double integral)
• \iiint f(x,y,z) dx dy dz - ✅ Works (triple integral)
• \iiiint f(w,x,y,z) dw dx dy dz - ✅ Works (quadruple integral)
• \iint_{D} f(x,y) dA - ✅ Works (with subscript limits)

Use Case: Multivariable calculus, surface and volume integrals

Implementation: Added U+2A0C (quadruple integral) Unicode character to operator definitions.

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7. ✅ \cfrac - Continued Fractions - IMPLEMENTED

Status: ✅ Working Description: Optimized layout for continued fractions

Test Results: All tests passed

• Simple \cfrac{1}{2} - ✅ Works
• Nested continued fractions - ✅ Works

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7b. ✅ \dfrac and \tfrac - Display/Text Style Fractions - IMPLEMENTED

Status: ✅ Working Description: Fractions with forced display or text style

Test Results: All tests passed

• \dfrac{1}{2} - ✅ Works (display-style fraction)
• \tfrac{a}{b} - ✅ Works (text-style fraction)
• y'=-\dfrac{2}{x^{3}} - ✅ Works (complex expression)
• Nested \dfrac and \tfrac - ✅ Works

Use Case:

• \dfrac forces display style (larger, more readable fractions)
• \tfrac forces text style (smaller, inline fractions)
• Useful when you want consistent fraction appearance regardless of context

Implementation: Prepends style atoms to numerator and denominator to force rendering style.

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8. ❌ \boldsymbol - Bold Greek Letters

Status: ❌ Not Implemented Error: Invalid command \boldsymbol

Description: Creates bold Greek letters (whereas \mathbf doesn't work for Greek)

Examples:

\boldsymbol{\alpha}        % bold alpha
\boldsymbol{\beta}         % bold beta
\boldsymbol{\Gamma}        % bold Gamma
\mathbf{x} + \boldsymbol{\mu}  % mix Roman and Greek bold

Use Case: Vectors with Greek symbols, bold emphasis for Greek letters

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9. ✅ Starred Matrix Environments: pmatrix*, bmatrix*, etc. - IMPLEMENTED

Status: ✅ Working Description: Matrix environments with optional column alignment

Test Results: All tests passed

• \begin{pmatrix*}[r] 1 & 2 \\ 3 & 4 \end{pmatrix*} - ✅ Works (right align)
• \begin{bmatrix*}[l] a & b \\ c & d \end{bmatrix*} - ✅ Works (left align)
• \begin{vmatrix*}[c] x & y \\ z & w \end{vmatrix*} - ✅ Works (center align)
• \begin{matrix*}[r] 10 & 20 \\ 30 & 40 \end{matrix*} - ✅ Works (no delimiters)

Alignment Options: [r] = right, [l] = left, [c] = center

Use Case: Financial tables, aligned numerical data in matrices

Implementation: Added readOptionalAlignment() function, modified readString() to accept asterisks, applies alignment to all columns.

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10. ✅ \smallmatrix Environment - IMPLEMENTED

Status: ✅ Working Description: Compact matrix for inline use (smaller than regular matrices)

Test Results: All tests passed

• \left( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \right) - ✅ Works (with delimiters)
• A = \left( \begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \right) - ✅ Works (identity matrix)
• \begin{smallmatrix} x \\ y \end{smallmatrix} - ✅ Works (column vector)

Use Case: Inline matrices, transformation matrices in text, compact notation

Implementation: Uses .script style for smaller font size, tighter column spacing (6 vs 18), no built-in delimiters.

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Implementation Priority Recommendations

Remaining High Priority Features

1. Spacing commands (\,, \:, \;, \!) - Used in almost all advanced math
2. Manual delimiter sizing (\big, etc.) - Common in published mathematics
3. \middle - Useful for conditional notation

Remaining Medium Priority Features

4. \boldsymbol - Important for vector notation with Greek letters

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Testing Coverage

All tests use the MTMathListBuilder.build(fromString:error:) API and automatically skip with XCTSkip when features are not implemented.

Test File: Tests/SwiftMathTests/MTMathListBuilderTests.swift Test Functions:

• testDisplayStyle() - ✅ Passed (IMPLEMENTED)
• testMiddleDelimiter() - ⏭️ Skipped (not implemented)
• testSubstack() - ✅ Passed (IMPLEMENTED)
• testManualDelimiterSizing() - ⏭️ Skipped (not implemented)
• testSpacingCommands() - ⏭️ Skipped (not implemented)
• testMultipleIntegrals() - ✅ Passed (IMPLEMENTED)
• testContinuedFractions() - ✅ Passed (IMPLEMENTED)
• testBoldsymbol() - ⏭️ Skipped (not implemented)
• testStarredMatrices() - ✅ Passed (IMPLEMENTED)
• testSmallMatrix() - ✅ Passed (IMPLEMENTED)

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Notes for Future Implementation

For \middle:

• Needs integration with existing \left...\right delimiter pairing system
• Should support all delimiter types that work with \left and \right

For Manual Sizing (\big, etc.):

• Needs 4 size levels beyond normal
• Each size approximately 1.2x the previous
• Should work with all delimiter types

For Spacing Commands:

• Need to insert proper MTMathSpace atoms
• Different space types: positive (\,, \:, \;) and negative (\!)
• Some might already be partially implemented

For \boldsymbol:

• Needs access to bold math font variants
• Should work with both Greek and other symbols
• Different from \mathbf (which changes font family)

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Generated: 2025-10-01 SwiftMath Version: Based on iosMath v0.9.5 Last Updated: 2025-10-01 - Implemented 4 major features: \substack, \smallmatrix, starred matrices, \iiiint