Module analyze 

Layer D⁺ — post-discovery analysis of a recovered law via the oxieml computer-algebra system.

A discovered expression is a live oxieml::EmlTree, not a string, so the whole CAS applies to it directly: symbolic differentiation, antidifferentiation, series expansion, limits, and certified root finding (interval Newton/Krawczyk) — all in-ecosystem, with no round-trip through an external tool. This realizes phop’s “discover → analyze → verify” pipeline, which string-emitting symbolic-regression tools cannot offer without external glue.

Operations lower the tree to oxieml’s LoweredOp IR (EmlTree::lower) and delegate; the results are simplified and rendered to LaTeX. Certified roots come back as an oxieml::RootCertificate that proves unique existence / no root / indeterminacy in an interval enclosure.

Structs

Analysis

Rendered symbolic analysis of a discovered law (each form simplified, as LaTeX).

Functions

analyze

Differentiate, integrate, expand, and take the +∞ limit of tree with respect to variable wrt, rendering each canonical form to LaTeX. series_order is the Maclaurin truncation order.

certified_range

A guaranteed enclosure of the law’s range over an axis-aligned box, via interval arithmetic.

certified_root

Find a certified root of tree in [lo, hi] along variable wrt, with the other variables fixed to others (the wrt slot is overwritten by the search; pass &[] for a single-variable law). Uses oxieml’s interval Newton/Krawczyk verifier; the returned RootCertificate proves unique existence, absence, or indeterminacy within the interval enclosure.