Module expansion 

Expansions of the values of several infinitesimals in their smallest one.

A value of dx, declared much smaller than dt, that is no rational function of a root of dx over the values of dt — √(dt + dx), the state a loop stepped by dx leaves — is the sum of its expansion Σ c_k·dx^(k/q), each coefficient a value of dt and of the infinitesimals larger than it. An Expansion holds such a value as the operations that built it and computes coefficients on demand, each once: a rational function of a root of dx by power-series division; sums and products term by term; a reciprocal and a real root by the recurrences crate::germ reads one infinitesimal’s germs by. Every recurrence runs over any Coefficient ring, so the same expansion serves exact coefficients and coefficients that are themselves expansions.

Orders are integers in units of s^(1/q), q the expansion’s ramification; two expansions meet on the least grid both lie on, each refined to it.

Structs

Expansion

An expansion in the smallest infinitesimal of a value. See the module documentation.

Enums

ExpansionError

Why a coefficient or an operation of an expansion is not given.

Traits

Coefficient

The values an expansion’s coefficients are: a field with the operations the recurrences ask for, each refused in the coefficient’s own words when it cannot be done.

Source

A source of coefficients defined outside the operations here: a value of one infinitesimal read as a value of several, a flow’s state.