Expand description
Germs of several infinitesimals: a value of dx, declared much smaller than dt, known by its
expansion in dx whose coefficients are values of dt and of the infinitesimals larger than it,
not all of them exact — exp(dt + dx) = Σ (e^dt/k!)·dx^k, ln(1 + dt + dx), the state a loop
stepped by dx leaves when its rate is a value of dt.
A NestedGerm holds such a value as the recipe that built it and its Expansion over
Number coefficients, each computed once as a comparison or a printed term asks. The functions
are the recurrences one infinitesimal’s germs follow (crate::germ), one level down: exp(g) for
a g with no negative order starts at e^{g_0}, a coefficient’s own exponential; ln(g) for a g
of order 0 with a positive leading coefficient starts at ln(g_0). What is no germ is refused by
name: the exponential of a value infinite in the smallest infinitesimal lies beyond every power of
it, and the logarithm of a value of nonzero order carries the logarithm of that infinitesimal.
Signs are read from the first nonzero coefficient, through crate::germ::SIGN_ORDERS orders: a
coefficient that cannot be told from zero, or a germ whose first orders all vanish, is a loud
error, never a guess. Two germs whose recipes are the same are the same value, so a term both sides
of a difference share cancels exactly.
Structs§
- Nested
Germ - A germ of several infinitesimals at its smallest. See the module documentation.