eml-discover 0.2.0

Identify famous mathematical formulas from arbitrary SymPy expressions.

eml-discover

Stable beta. Patent pending. Source-available; see LICENSE.

Identify famous mathematical formulas from arbitrary SymPy expressions. Curated registry of ~17 formulas across statistics, ML activations, trig/hyperbolic identities, physics, and finance — each tagged with its Pfaffian-cost class for fast structural pre-filtering.

Installation

pip install eml-discover

eml-cost is installed as a dependency; sympy>=1.12 required.

Quick start

import sympy as sp
from eml_discover import identify

u = sp.Symbol("u")
matches = identify(1 / (1 + sp.exp(-u)))
for m in matches:
    print(m.formula.name, "—", m.confidence)
# sigmoid (canonical) — exact

matches = identify(sp.exp(-u**2 / 2) / sp.sqrt(2 * sp.pi))
print(matches[0].formula.name, matches[0].formula.description)
# Gaussian PDF (standardized) Standard normal probability density.

matches = identify("(log(S/K) + (r + vol**2/2)*T) / (vol*sqrt(T))")
print(matches[0].formula.citation)
# https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model

How it works

Two-stage match:

1. Fingerprint pre-filter (cheap, structural). Every registry template carries a Pfaffian fingerprint — p3-d2-w1-c0-h7f3a91 etc. Templates whose fingerprint axes don't match the user's expression are pruned in O(1) per template.
2. Symbolic equivalence (true match). Survivors are checked under SymPy variable rename: for each candidate template, try permutations of the user's free symbols, accept the rename if sp.simplify(template - user) == 0.

Returns a list of Match ordered by confidence: identical (Python equality, no rename) → exact (symbolic equivalence after rename) → axes (fingerprint axes match but no rename works).

Registry

Inspect what's registered:

from eml_discover import list_all, list_by_domain, by_name

list_all()                  # every Formula
list_by_domain("physics")   # Bessel J_0, Airy Ai, Boltzmann factor, ...
by_name("Black-Scholes d1") # the d1 Formula

Add a formula by appending to eml_discover.registry.FORMULAS — each entry is a small dataclass (name, expression_factory, domain, description, citation).

Use cases

• "Wait, that's Black-Scholes." Surface familiar formulas hiding in user code or auto-generated symbolic-regression output.
• Curriculum tools. Tag a notebook's expressions by their registry name → automatic pedagogy ("this cell uses softplus").
• Patent / claim analysis. Compare a candidate's formula against the public registry of named identities.

Links

• Project home: monogate.org
• Source: github.com/almaguer1986/eml-discover
• Companion: eml-cost, eml-rewrite

License

PROPRIETARY-PRE-RELEASE. See LICENSE.