alkahest-symbolic-integration

Symbolic integration RL environment backed by Alkahest's Risch integrator.

Models receive an integrand f(x) and must return an elementary antiderivative F(x) with dF/dx = f, or the exact phrase "no elementary form" when Risch certifies non-elementarity.

Install

Requires Python ≥ 3.10.

pip install alkahest-symbolic-integration

This installs alkahest, verifiers, and datasets.

Usage

from alkahest.rl.envs.integration.env import load_environment

env = load_environment(
    difficulty_tier=0,
    n_train=50_000,
    n_eval=2_000,
    hard_negative_fraction=0.25,
    adaptive=True,
)

# Prime Intellect CLI
# prime eval run alkahest-cas/symbolic-integration -m <model>

Configuration

Argument	Default	Description
`difficulty_tier`	`0`	Starting Risch grammar tier (0 = rationals)
`hard_negative_fraction`	`0.25`	Fraction of NonElementary integrands
`n_train` / `n_eval`	`50_000` / `2_000`	Dataset sizes
`seed`	`42`	RNG seed
`adaptive`	`True`	Attach `CurriculumScheduler` on `env.curriculum`

Reward

IntegrationVerifier scores completions in [-1, 1]:

+1.0 — correct antiderivative (symbolic diff check, optional e-graph, interval spot checks)
+0.9 — numerically consistent but not symbolically confirmed
+1.0 — honest refusal on a NonElementary integrand
−0.2 — unnecessary refusal on an elementary integrand
−0.5 — hallucinated antiderivative on NonElementary
0.0 — unparseable or wrong

Development

Source code lives in the main Alkahest repository under python/alkahest/rl/. This directory is the Environments Hub publish root.

cd python/alkahest/rl/envs/integration
pip install -e .
prime env push --auto-bump