reasoning-gym/reasoning_gym/algebra/simple_integration.py
2025-02-02 17:18:56 +00:00

108 lines
4.3 KiB
Python

import random
from dataclasses import dataclass
from fractions import Fraction
from typing import Any, Dict, Optional
import sympy
from ..factory import ProceduralDataset, register_dataset
@dataclass
class SimpleIntegrationConfig:
min_terms: int = 2
max_terms: int = 5
min_degree: int = 1
max_degree: int = 10
min_bounds: int = 1
max_bounds: int = 10
operators: tuple = ("+", "-")
symbols: tuple = ("x", "X")
seed: Optional[int] = None
size: int = 500
def validate(self) -> None:
"""Validate the configuration parameters of the integral proble"""
assert self.min_bounds > 0, "min_bounds must be positive"
assert self.max_bounds >= self.min_bounds, "max_bounds must be >= min_bounds"
assert self.min_terms >= 0, "min_terms must be positive"
assert self.max_terms >= self.min_terms, "max_terms must be >= min_terms"
assert self.min_degree >= -10, "min_degree must be >= -10"
assert self.max_degree >= self.min_degree, "max_degree must be >= min_degree"
assert all(op in ("+", "-") for op in self.operators), "invalid operator specified"
class SimpleIntegrationDataset(ProceduralDataset):
"""Generates simple integration problems with one variable"""
def __init__(self, config: SimpleIntegrationConfig):
self._prompt_templates = [
"Find the indefinite integral: ∫ {integrand} dx",
"Calculate the antiderivative: ∫ {integrand} dx",
"Evaluate the indefinite integral: ∫ {integrand} dx",
]
super().__init__(config=config, seed=config.seed, size=config.size)
def _generate_coefficient(self, rng: random.Random) -> Fraction:
"""Generate a random coefficient for the polynomial"""
if rng.choice([True, False]): # 50% chance for integer
return Fraction(rng.randint(self.config.min_bounds, self.config.max_bounds), 1)
denominator = rng.randint(2, 10)
return Fraction(rng.randint(self.config.min_bounds, self.config.max_bounds), denominator)
def _generate_polynomial(self, rng: random.Random) -> tuple[sympy.Symbol, sympy.Expr]:
"""Generate a random polynomial with one variable"""
terms = []
x = sympy.Symbol(rng.choice(self.config.symbols))
for _ in range(rng.randint(self.config.min_terms, self.config.max_terms)):
coefficient = self._generate_coefficient(rng)
degree = rng.randint(self.config.min_degree, self.config.max_degree)
operator = rng.choice(self.config.operators)
term = coefficient * x**degree
if operator == "-":
term = -term
terms.append(term)
return x, sum(terms)
def __getitem__(self, idx: int) -> dict:
rng = random.Random(self.seed + idx)
symbol, polynomial = self._generate_polynomial(rng)
derivative = sympy.diff(polynomial, symbol)
return {
"question": rng.choice(self._prompt_templates).format(integrand=derivative),
"answer": str(polynomial) + " + C",
"metadata": {
"integrand": str(derivative),
"variable": str(symbol),
"expected_answer_expression": polynomial,
},
}
def score_answer(self, answer: Optional[str], metadata: Dict[str, Any]) -> float:
"""Determine if the solution provided solves the problem"""
reward = 0.0
if answer is not None:
try:
var = metadata["variable"]
x = sympy.Symbol(var)
# Parse answer while allowing integration constant 'C'
user_expr = sympy.parse_expr(answer, local_dict={var: x, "C": sympy.Symbol("C")})
# Compute derivative of student's answer
derivative = sympy.diff(user_expr, x)
integrand = sympy.parse_expr(metadata["integrand"], local_dict={var: x})
# Check mathematical equivalence through simplification
if sympy.simplify(derivative - integrand) == 0:
reward = 1.0
elif answer.strip():
reward = 0.05
else:
reward = 0.01
except:
reward = 0.01
return reward
register_dataset("simple_integration", SimpleIntegrationDataset, SimpleIntegrationConfig)