Module jet_algebra 

The single shared Faà di Bruno / Leibniz combinatorial kernel (#1151).

Two jet representations live in this crate and historically each carried its own hand-written copy of the same calculus:

• crate::jet_tower::Tower4 — full dense derivative tensors (v, g, h, t3, t4) in K primary variables, with the Leibniz product and Faà di Bruno composition written out term-by-term per derivative order.
• crate::jet_partitions::MultiDirJet — bitmask-coefficient jet over distinct seeded directions, with the same two rules written as general submask / set-partition loops.

The data layouts are legitimately different (a complete small-K tower vs. a handful of directions of a large-K expression) and stay separate. What is identical is the combinatorics: for a group of differentiation slots, the Leibniz rule sums over subsets of those slots and the Faà di Bruno rule sums over their set-partitions. This module owns that combinatorics once, as a layout-agnostic [JetAlgebra] trait plus walkers parameterised by closures that read each representation’s own derivative for a slot-group. Both Tower4 and MultiDirJet route their mul / compose_unary through these walkers, so a fix to the rule is a fix to both — and a bit-exact equivalence test (see tests) proves the two layouts agree.

A “slot-group” is a list of positions 0..m (the differentiation arguments of one output coefficient). Each representation maps a group to a derivative:

• For a tensor index tuple (i, j, k, l), the positions 0..m carry axis labels [i, j, k, l]; a sub-group of positions selects the corresponding lower-order tensor entry (e.g. positions {0, 2} → h[i][k]).
• For a bitmask coefficient mask, the set bits are the slots; a sub-group of bits is itself a sub-mask read straight out of coeffs.

Functions

faa_di_bruno

Walk the multivariate Faà di Bruno rule for an output of m slots.