Solve any polynomial with exact rational arithmetic.
No radicals. No numerics. No complex numbers.
$ geode --coeffs "1, 0, 0, 0, -1, 1"
Polynomial: x⁵ − x + 1
Roots found: 1
x1 = -1.167303978261 (residual: 2.22e-16)Since Abel–Ruffini (1824), nobody had a closed-form rational solution for quintics. Hyper-Catalan series changes that.
No floating point in the solver path. BigInt coefficients, BigRational arithmetic. Truncate at any depth.
Compiles to WASM. Type a polynomial, get the answer. No server, no install, no account.
Quintic equations in cloth sim, Bézier intersection, implicit surfaces, and cryptographic analysis.
Since 1824, mathematicians knew that polynomials of degree 5 or higher cannot be solved with radicals (roots, square roots, etc.). This is the Abel–Ruffini theorem. For 200 years, the only options were:
In 2024, Norman Wildberger and Dean Rubine discovered that the Hyper-Catalan series gives a closed-form rational solution to any univariate polynomial equation.
x = Σₘ Cₘ · (a₁/a₀)^{m₁} · (a₂/a₀)^{m₂} · ...Cₘ are Hyper-Catalan numbers counting polygon dissections.
Truncation at depth d gives O(d) correct digits.
No radicals. No complex intermediates. Just exact rational arithmetic.
Quintic equations appear in cloth simulation, soft-body dynamics, and Bézier curve intersection. Get exact answers, not approximations.
Polynomial curves, surfaces, and ray-marching implicit surfaces all need polynomial solving. geode gives you exact rational roots.
A fundamental new method for computer algebra systems. Implement Hyper-Catalan series in your CAS for exact polynomial solving.
Analyze polynomial-based cryptographic primitives (Rainbow, MAYO). Exact arithmetic prevents rounding attacks.
CLI: Install with one command, solve from the terminal.
curl -sSf https://geode.jesed.dev/install.sh | shgeode --coeffs "1, 0, 0, 0, -1, 1"
Web: Open the demo, type coefficients, see results instantly.
Library: Use geode-poly in your Rust project for exact polynomial arithmetic.
The Hyper-Catalan series gives:
x = Σₘ Cₘ · (a₁/a₀)^{m₁} · (a₂/a₀)^{m₂} · ...where Cₘ are Hyper-Catalan numbers counting polygon dissections. Truncation at depth d gives O(d) correct digits.
curl -sSf https://geode.jesed.dev/install.sh | shcargo install geode-cli --git https://github.com/jesedv/geode.gitwasm-pack build crates/geode-wasm --target web
cd ui && npm install && npm run dev