A GPU-accelerated, AI-integrated computer algebra system built in Rust.
65,000+ lines of Rust · 1,808 tests (0 failures) · 12 crates · 11 GPU modules
--- ## ✨ Why SymClaw? - 🚀 **GPU-Accelerated** — GPU polynomial GCD (Zippel), NTT polynomial multiply, Gröbner basis row reduction, Monte Carlo integration, ODE parameter sweeps — all via [CubeCL](https://github.com/tracel-ai/cubecl) - 🤖 **AI-Native** — OpenClaw skill bridge (22 JSON-RPC actions); every result includes LaTeX and confidence scores - 🌐 **Everywhere** — Rust library, Python (PyO3), WASM/browser (wasm-bindgen), C FFI, CLI REPL, WebSocket collab - 🔬 **Research-Grade** — Quantum computing (Pauli/ZX-calculus/UCCSD), systems biology (SIAN identifiability), quantum chemistry (Wick's theorem, Gaussian integrals), crystallography (space groups, structure factors) - ⚡ **Blazing Fast** — Packed polynomial representation (FORM-inspired), AVX2 Montgomery multiplication, E-graph equality saturation --- ## 🏗️ Architecture ``` symclaw-core — 32 modules: the complete symbolic math engine ├── Symbolic: parser · simplify · egraph · differentiate · integrate │ solve · series · limits · transforms · pattern · ode ├── Algebra: poly · modular_gcd · packed_poly · linalg · tensor │ number_theory · precision (BigFloat, GF(p)) ├── Novel: discover (symbolic regression) · units · proof · symbols └── Infra: codegen · streaming · simd_arith · eval · latex · cache symclaw-quantum — Pauli group · stabilizer tableau · circuits (30 gates) ZX-calculus (11 rewrite rules) · OpenQASM3/Qiskit/PennyLane/Cirq symclaw-bio — ODE models · SIAN structural identifiability reaction networks · Hardy-Weinberg · JC69/K80 · genome reversals symclaw-qchem — Wick's theorem (bitmask) · McMurchie-Davidson integrals Boys function · Clebsch-Gordan (Racah) · VQE/UCCSD symclaw-materials — 14 Bravais lattices · 32 point groups · 230 space groups structure factors · Cromer-Mann · BVS · Madelung/Born-Landé symclaw-gpu — NTT · FFT (Cooley-Tukey) · Gröbner (F4) · poly_gcd (Zippel) Monte Carlo · ODE sweeps · linalg · eval · SIMD batch ops symclaw-cli — Interactive REPL, 30+ commands (:diff, :integrate, :plot, :codegen, …) symclaw-python — PyO3 bindings with operator overloading symclaw-wasm — 24+ browser-ready exports via wasm-bindgen symclaw-ffi — C FFI for embedding in any language symclaw-skill — OpenClaw AI agent bridge (22 JSON-RPC actions) symclaw-collab — Multi-user WebSocket real-time collaboration ``` --- ## 🚀 Quick Start ### Python ```python # pip install symclaw (via maturin) from symclaw import Expression as E, S x = S("x") expr = (x + 1)**2 print(expr.simplify()) # x^2 + 2*x + 1 print(expr.diff("x")) # 2*x + 2 print(expr.integrate("x")) # x^3/3 + x^2 + x print(expr.to_latex()) # x^{2} + 2 x + 1 print(expr.to_code("python")) # x**2 + 2*x + 1 ``` ### CLI REPL ``` $ cargo run -p symclaw-cli symclaw> (x + 1)^2 x^2 + 2·x + 1 symclaw> :derive sin(x^2) x 2·x·cos(x²) symclaw> :integrate x^3 x x⁴/4 symclaw> :limit sin(x)/x x 0 1 symclaw> :taylor exp(x) x 4 0 1 + x + x²/2 + x³/6 + x⁴/24 symclaw> :codegen x^2 + 2*x + 1 rust x.powi(2) + 2.0 * x + 1.0 symclaw> :plot sin(x) x -6.28 6.28 60 [ASCII chart] ``` ### Rust ```rust use symclaw_core::{parser, simplify, differentiate, integrate, latex}; let expr = parser::parse("sin(x)^2 + cos(x)^2").unwrap(); let simplified = simplify::simplify(&expr); println!("{}", simplified); // 1 println!("{}", latex::to_latex(&simplified)); // 1 ``` ### WASM / JavaScript ```javascript import init, { simplify, differentiate, to_latex, eval_range } from 'symclaw-wasm'; await init(); console.log(simplify("sin(x)^2 + cos(x)^2")); // "1" console.log(differentiate("x^3 + 2*x", "x")); // "3·x² + 2" console.log(to_latex("1/2 + 1/3")); // "\\frac{5}{6}" // Evaluate over a range for plotting const pts = JSON.parse(eval_range("sin(x)", "x", 0, 6.28, 100)); ``` ### OpenClaw Skill (AI Agent) ```json // Request {"action": "differentiate", "expr": "x^3 + sin(x)", "var": "x"} // Response {"success": true, "result": "3·x² + cos(x)", "latex": "3 x^{2} + \\cos(x)", "confidence": 1.0} ``` --- ## 📦 What's Inside ### symclaw-core (32 modules, 1,279 unit tests) | Area | Modules | |------|---------| | **Parser & AST** | `parser`, `ast`, `interner` | | **Simplification** | `simplify`, `egraph` (equality saturation via egg) | | **Calculus** | `differentiate`, `integrate`, `series`, `limits`, `ode`, `transforms` | | **Algebra** | `solve`, `poly`, `modular_gcd`, `packed_poly`, `linalg`, `tensor` | | **Number theory** | `number_theory` (30+ functions), `precision` (BigFloat, GF(p)) | | **Advanced** | `pattern`, `discover` (symbolic regression), `units`, `proof`, `symbols` | | **Output** | `codegen` (7 languages), `latex`, `streaming`, `eval` | | **Infrastructure** | `cache`, `metrics`, `simd_arith`, `confidence` | ### symclaw-quantum (85 tests) - **Pauli group**: n-qubit operators, phase, commutators, weight, dagger - **Stabilizer tableau**: SympRow binary symplectic representation, H/CNOT/S gates - **Quantum circuits**: 30 gate types, depth, T-count, gate cancellation, state-vector simulator - **ZX-calculus**: diagram builder, 11 rewrite rules (spider fusion, π-copy, bialgebra, …), simplifier - **Codegen**: OpenQASM 3, Qiskit, PennyLane, Cirq - **Clifford gates**: CliffordGate1Q as Cl(3,0) algebra elements ### symclaw-bio (55 tests) - **ODE models**: state/parameter/output builder, Lie derivatives, input-output equations - **Identifiability**: SIAN structural identifiability via numerical Jacobian rank - **Reaction networks**: stoichiometry matrix, deficiency theorem, mass-action kinetics → ODEs - **Population genetics**: Hardy-Weinberg equilibrium, JC69 and K80 substitution models - **Genome algebra**: signed permutation reversals, breakpoints, greedy sorting; genetic code (64 codons) ### symclaw-qchem (53 tests) - **Second quantization**: FermionTerm/FermionOp, number-conserving operators - **Wick's theorem**: bitmask enumeration (iterative, no stack overflow), vacuum expectation values - **Molecular integrals**: GaussianBasis, normalization, Boys function F_m(x), McMurchie-Davidson E coefficients, overlap and kinetic energy integrals - **Angular momentum**: Pauli matrices, Clebsch-Gordan coefficients via Racah formula - **VQE**: parameter-shift gradient rule, HF reference state, UCCSD single/double excitations, Ansatz builder ### symclaw-materials (63 tests) - **Lattice**: all 14 Bravais lattice types, 7 crystal systems, lattice parameter constructors, unit cell volumes, primitive and reciprocal lattice vectors - **Groups**: all 32 crystallographic point groups (centrosymmetric=11, polar=10, chiral=11), SymOp (rotation matrix + fractional translation, compose, determinant), 230 space groups descriptor - **Structure**: CrystalStructure with built-in NaCl/Si/α-Fe, Cromer-Mann scattering factors, structure factors F(hkl), Debye-Waller factors, systematic absence detection - **Bonding**: Lennard-Jones 12-6 (Ar parameters), coordination environments, Bond Valence Sum (BVS) with R₀ table, Pauling electronegativity (30 elements) + ionicity, Madelung constants + Born-Landé lattice energy ### symclaw-gpu (101 tests) | Module | Algorithm | Backend | |--------|-----------|---------| | `ntt` | Number Theoretic Transform (NTT-friendly primes) | GPU/CPU | | `fft` | Cooley-Tukey radix-2 FFT; poly multiply via convolution | CPU | | `groebner` | Faugère F4 with sparse GF(p) matrix reduction | GPU/CPU | | `poly_gcd` | Zippel modular GCD batch evaluation | GPU/CPU | | `linalg` | Matrix multiply (f32 GPU), batch determinants, LU | GPU/CPU | | `monte_carlo` | LCG Monte Carlo integration, n-dimensional | CPU | | `ode` | RK4 parameter sweep (parallel runs) | CPU | | `eval` | Bytecode expression evaluator | CPU | | `simd` | Batch Horner eval, dot, norms, mat-vec, Lagrange, Welford stats | CPU | | `discover` | GPU symbolic regression | GPU/CPU | | `device` | Auto-detect: CUDA/ROCm/Metal/WebGPU/CPU | — | --- ## 📊 Test Coverage | Crate | Unit | Integration | Total | |-------|------|-------------|-------| | symclaw-core | 1,279 | 54 | **1,333** | | symclaw-quantum | 70 | 15 | **85** | | symclaw-bio | 40 | 15 | **55** | | symclaw-qchem | 38 | 15 | **53** | | symclaw-materials | 47 | 16 | **63** | | symclaw-gpu | 101 | — | **101** | | symclaw-cli | 36 | — | **36** | | symclaw-wasm | 11 | — | **11** | | symclaw-ffi | 8 | — | **8** | | symclaw-skill | 21 | — | **21** | | symclaw-collab | 42 | — | **42** | | **Total** | **1,693** | **115** | **1,808** | All 1,808 tests pass. 0 failures. No files exceed 1,250 lines. --- ## 🆚 vs Competition | Feature | SymClaw | Symbolica | Mathematica | SymPy | |---------|---------|-----------|-------------|-------| | GPU acceleration | ✅ 11 modules | ❌ | ❌ | ❌ | | E-graph simplification | ✅ | ❌ | ❌ | ❌ | | Symbolic regression (GPU) | ✅ | ❌ | ❌ | ❌ | | Quantum computing module | ✅ | ❌ | partial | partial | | Systems biology module | ✅ | ❌ | ❌ | ❌ | | Quantum chemistry module | ✅ | ❌ | partial | partial | | Crystallography module | ✅ | ❌ | partial | ❌ | | Dimensional type system | ✅ | ❌ | ✅ | ✅ | | Step-by-step proof traces | ✅ | ❌ | ❌ | ❌ | | AI agent integration | ✅ | ❌ | ❌ | ❌ | | Multi-user collab | ✅ | ❌ | ❌ | ❌ | | Browser / WASM | ✅ | ❌ | ❌ | ❌ | | C FFI | ✅ | ✅ | N/A | ❌ | | Python bindings | ✅ | ✅ | N/A | N/A | | Open source | ✅ MIT/Apache-2 | ❌ source-avail | ❌ commercial | ✅ BSD | --- ## 🛠️ Building ```bash git clone https://github.com/osobh/symclaw && cd symclaw # Build & test cargo build --release cargo test # runs all 1,808 tests # CLI cargo run -p symclaw-cli # Python wheel (requires maturin) cd crates/symclaw-python maturin develop # GPU backends (choose one at build time) cargo build -p symclaw-gpu --features cuda # NVIDIA cargo build -p symclaw-gpu --features wgpu # WebGPU / cross-platform (default) cargo build -p symclaw-gpu --features cpu # Software fallback (always available) ``` ### Requirements - **Rust** 1.75+ (MSRV) - **Python** 3.8+ (for symclaw-python) - **CUDA 12+** or **WebGPU-capable GPU** (optional, for GPU acceleration) --- ## 📄 License Dual-licensed under [MIT](LICENSE-MIT) and [Apache 2.0](LICENSE-APACHE). Choose whichever suits you. ## Acknowledgements - [**egg**](https://egraphs-good.github.io/) — E-graph equality saturation - [**CubeCL**](https://github.com/tracel-ai/cubecl) — Cross-platform GPU compute kernels - [**OpenClaw**](https://openclaw.com/) — Agentic AI platform and skill bridge - [**nom**](https://crates.io/crates/nom) — Parser combinator framework - [**PyO3**](https://pyo3.rs/) — Rust ↔ Python bindings ---Built with 🦀 in Rust · 1,808 tests · 0 failures