Module laplace 

Laplace transform L{f}(s) = ∫₀^∞ e^{−st} f(t) dt.

Two paths: a numerical transform by Simpson quadrature for any closure (general, always available), and a symbolic table transform over the CAS expression type. The current Expr algebra has no exp/trig variants, so the symbolic table covers the cases it can represent — constants, integer powers tⁿ, and their linear combinations — and fails closed (NotTransformable) on anything else rather than returning a wrong transform.

Enums

LaplaceError

Functions

laplace_numeric

Numerical Laplace transform of f at s, integrating to t_max with steps (even) Simpson panels. Requires s > 0, t_max > 0, steps ≥ 2 even.

laplace_table

Symbolic Laplace transform of expr in the time variable t, returning an Expr in the complex frequency variable s. Handles constants (c → c/s), powers (tⁿ → n!/s^{n+1}), negation, sums/differences, and scalar multiples; everything else fails closed.