pub fn real_fn<V: TowerValue>(f: RealFn, v: &V) -> Result<V, String>Expand description
f of v, exactly. A standard number goes in as the rational it denotes (a float as its dyadic
rational), an algebraic number or a computable real as itself, and the answer is held in its
smallest exact form: sqrt(4) is 2, sqrt(2) is √2, exp(0) is 1, ln(e) is 1. The
square root of a hyperreal or an infinite integer is its root in the real closure
(crate::puiseux): sqrt(dt) is √dt. Every other function of a value of the infinitesimal is
the germ of it (Germ): exp(dt) is 1 + dt + O(dt^2), ln(1 + dt) is
dt - (1/2)·dt^2 + O(dt^3), and the root of a germ is a germ. What is no germ is refused by name:
the exponential of an infinite value, beyond every power of dt, and the logarithm of a positive
infinitesimal or an infinite value, which carries ln(dt). A residue-dependent value is mapped
branch by branch and a provisional one keeps its evidence; a function of an ordinal has no exact
form.