AlgebraCore

A tiny, dependency-free package that owns the generic verbs shared by symbolic algebra packages. It declares the functions (with their generic docstrings) but ships no methods: each algebra package imports and extends them for its own expression types, so the same verbs operate across different algebras.

Verbs

Verb	Meaning
simplify(s)	Structurally reduce an expression, returning the same kind of object.
substitute(s, pairs)	Replace named variables, staying symbolic; partial — unbound names are kept.
materialize(s, pairs)	Evaluate an expression to a concrete value.
pushforward(f, x, ẋ)	Forward-mode directional derivative (Jacobian–vector product).
differentiate(f, x)	Derivative / Jacobian, returning the same kind of object.

Extending

Add methods on your own types:

import AlgebraCore: differentiate

struct MyExpr end

differentiate(e::MyExpr, x) = ...   # your rule here

Consumers bring the verbs into scope with using AlgebraCore. Extending packages typically do not re-export them.

AlgebraCore itself contains only the function declarations, their generic docstrings, and the export list — no concrete methods and no dependencies.