Theory
Theory¶
The Start and Analysis sections describe the API. This section specifies what the library does underneath: how symbolic equations become native code, what equations the Lyapunov routines actually solve, and which conventions (shapes, time semantics, resolution orders) the implementation commits to. Read it when you need to check a result against your own derivation, or to predict what a sweep will cost.
| Page | What it covers |
|---|---|
| Compilation pipeline | Symbolic RHS → engine IR tape; structural vs. control parameters; the same lowering for maps; autogenerated Jacobians |
| Solvers | The kernel catalogue: explicit/implicit families, dt as an output grid, dense output and max_step, the v6 default tolerances |
| Backends | jit (the default), interp and reference — what each is for and how they relate bit-for-bit |
| Lyapunov exponents | Variational equations, QR re-orthonormalization, time-weighted averaging, the DDE caveat, the Kaplan–Yorke conjecture |
| Rigorous fixed points | The interval-Newton / Krawczyk enumerator: brackets every root in a box with a uniqueness certificate; the benchmark vs multi-start and the round-off caveat |
| Conventions | Time vs. steps, array shapes, IC resolution priority, map parameter order, metadata history semantics |
| Packaging | Why the project ships as one abi3 maturin wheel: the Python package plus the compiled engine |
See also¶
- The mental model — the prose introduction these pages formalize
- Reference — exact signatures of everything mentioned here