Function presets (cp.catalog)

cp.catalog is a curated registry of complex functions, each described in a way that is both renderable (a Python callable) and serializable (plain dicts + an expression string + exact answer keys). It is the single source consumed by the gallery, the CLI and the STL object cards, and it is designed so that an independent implementation can be checked against the same records.

Not to be confused with cp.PlotPresets (capital P) — those are plot-config presets (resolution + colormap bundles). cp.catalog is the function registry.

Using the registry

import complexplorer as cp

cp.catalog.list()                              # -> sorted preset ids
p = cp.catalog.get("pole_flower_10")
cp.catalog.filter(tag="singularity-detective") # -> [FunctionPreset, …]

p.func(0.5 + 0.2j)        # the callable Complexplorer renders with
p.domain()                # a live Domain   (built from p.domain_spec)
p.colormap()              # a live Colormap (built from p.cmap_spec)
p.to_dict()               # JSON-ready record (everything except the callable)

The model

A FunctionPreset carries:

Field	Purpose
func	the callable Complexplorer renders with (not serialized)
expression	e.g. "z / (z**10 - 1)" — the function as a parseable string
domain_spec / cmap_spec / scaling_spec	plain dicts whose keys mirror the constructor kwargs
singularities	hand-authored, exact answer keys, one record per location
id / title / story / tags	metadata; tags group presets into sets

Serialization is the design center. Specs are dicts, not live objects, so a preset is a clean JSON record. Every complex value (a domain center, a singularity at) is an [re, im] pair, since JSON has no complex type. The factories domain_from_spec / cmap_from_spec rebuild live objects on demand; the core Domain/Colormap classes are untouched.

Singularity answer keys

Each singularities record is exact and author-provided (never detected numerically):

{"type": "pole", "at": [1.0, 0.0], "order": 1}          # type ∈ {zero, pole, essential, branch_point}

order is the multiplicity for zero/pole, the branching order for branch_point, and null for essential. Multivalued presets (sqrt, log, z**(1/3)) use numpy's principal branch and declare a branch_point, so the answer key and any independent implementation agree on the branch convention.