Texpr - Roadmap

Goal: Copy-paste LaTeX from academic sources and it just works.

---

Current State (v0.2.0)

✅ What Works

Parsing & Evaluation:

• Basic arithmetic, fractions, powers, roots
• 40+ mathematical functions (trig, hyperbolic, reciprocal, logarithmic, rounding)
• Complex number transcendental evaluation (sin, cos, tan, exp, ln for complex inputs)
• Symbolic differentiation with full calculus rules
• Symbolic integration (basic patterns)
• Numerical integration (Simpson's Rule)
• Matrix operations (determinant, inverse, transpose, trace)
• Summation (\sum), product (\prod), limit (\lim)
• Definite and indefinite integrals
• Multi-integrals (\iint, \iiint), closed integrals (\oint)

LaTeX Notation:

• Greek letters (lowercase, UPPERCASE, variants: \alpha, \Gamma, \varepsilon)
• Font commands (\mathbf, \mathcal, \mathrm, \boldsymbol)
• Delimiter sizing (\left, \right, \big, \Big, etc.)
• Spacing commands (\,, \;, \quad - ignored for evaluation)
• Partial derivatives (\partial), gradient (\nabla)
• Angle brackets (\langle, \rangle), set membership (\in)
• Blackboard bold (\mathbb{R})
• Comparison operators (\leq, \geq, \neq)

Academic Paper Compatibility (Tested):

• Heisenberg Uncertainty Principle
• Schrödinger Equation (time-dependent and time-independent)
• Maxwell's Equations (Gauss's Law, Ampère's Law)
• Navier-Stokes Equation
• Fourier Transform definition
• Cauchy-Schwarz Inequality
• Einstein Field Equations
• Normal distribution PDF

Test Coverage: 1,874 tests passing

---

Known Gaps

The following are known limitations discovered through testing:

1. Evaluation Limitations (Not Parsing)

Expression	Can Parse	Can Evaluate	Notes
\nabla{x^2 + y^2}	✅	✅	Concrete expressions with explicit vars
\nabla f (bare symbol)	✅	❌	Symbolic only; no structure to differentiate
\oint E \cdot dA	✅	❌	Line/surface integrals are symbolic only
Tensor notation (R_{\mu\nu})	✅	❌	Parsed as subscripted variable
Set notation (x \in \mathbb{R})	✅	❌	Parsed but not evaluated as constraint

2. Previously Missing LaTeX Commands ✅ Fixed

All commands below now parse successfully:

Command	Description	Status
\mapsto (↦)	Maps to arrow	✅
\Rightarrow (⇒)	Double arrow	✅
\approx (≈)	Approximately equal	✅
\propto (∝)	Proportional to	✅
\subset, \subseteq	Subset notation	✅
\cup, \cap	Set union/intersection	✅
\forall, \exists	Quantifiers	✅
\dot{x}, \ddot{x}	Time derivatives	✅
\bar{x}	Mean notation	✅

3. Syntax Variations ✅ Fixed

The following syntax variations are now automatically handled:

Academic LaTeX	Library Support	Notes
\frac12 (braceless)	✅ Works	Parses as \frac{1}{2}. Ambiguous cases like \frac123 error with clear message
sin(x) (no backslash)	✅ Works	Recognized when followed by (. Without (, remains as implicit mult
e^{ix}	✅ Works	Implicit multiplication inside exponents is handled

---

Roadmap

Phase 1: Parsing Completeness

Goal: Any valid mathematical LaTeX from a textbook or paper parses successfully.

Task	Status	Description
Add \approx, \bar, \dot, \ddot	✅	Common in physics papers
Add \Rightarrow, \Leftarrow, \Leftrightarrow	✅	Logic notation
Add \forall, \exists	✅	Quantifiers (parse as symbols)
Add \subset, \subseteq, \supset	✅	Set notation
Add \cup, \cap, \setminus	✅	Set operations
Add \propto, \mapsto	✅	Relation symbols
Test with 50+ real academic paper excerpts	✅	Validate "just works" claim

Phase 2: Common Use Case Evaluation

Goal: Expressions that can be numerically evaluated, are.

Task	Status	Description
Unicode input support	✅	Accept √, ∑, ∫, π directly
Improved implicit multiplication heuristics	✅	e^{ix} works, braces required for multi-char exponents
Better error messages for evaluation failures	✅	"Cannot evaluate gradient symbolically"

Phase 3: Developer Experience

Goal: Easy integration and debugging.

Task	Status	Description
JSON AST export	✅	For debugging and tooling
MathML export	✅	For web display
SymPy export	✅	For Python interoperability

---

Non-Goals

The following are explicitly not goals for this library:

1. Full Computer Algebra System (CAS) - We do pattern-based simplification, not canonical forms
2. Symbolic tensor calculus - Parsing tensor notation is supported; evaluation is not
3. Proof verification - Logic symbols are parsed but not reasoned about
4. Typesetting - Community already had it, we fill the gap with evaluation

---

How to Contribute

1. Find a LaTeX expression from an academic paper that fails to parse
2. Open an issue with the exact expression
3. We'll add support and tests

Phase 4: Performance & Optimization

Goal: Ensure 60fps performance on mobile devices.

Task	Status	Description
Standardized Comparison	✅	Cross-language comparison (Dart/JS/Python)
AOT Compilation Profile	📋	Verify performance in release builds
WebAssembly (Wasm)	📋	Investigate compiling to Wasm for web apps
Parallel Evaluation	📋	Evaluate independent sub-expressions in isolates

---

Last Updated: 2026-01-04