mirror of
https://github.com/open-thought/reasoning-gym.git
synced 2026-04-23 16:55:05 +00:00
165 lines
6.9 KiB
Python
165 lines
6.9 KiB
Python
import random
|
|
import warnings
|
|
from dataclasses import dataclass
|
|
from typing import Any, Dict, Optional, Tuple
|
|
|
|
import sympy as sp
|
|
from sympy.polys.monomials import itermonomials
|
|
|
|
from ..factory import ProceduralDataset, register_dataset
|
|
|
|
|
|
@dataclass
|
|
class PolynomialMultiplicationConfig:
|
|
"""
|
|
Configuration for polynomial multiplication task generation.
|
|
"""
|
|
|
|
min_terms: int = 2 # Minimum number of polynomial terms
|
|
max_terms: int = 4 # Maximum number of polynomial terms
|
|
min_value: int = 1 # Minimum value for coefficients
|
|
max_value: int = 100 # Maximum value for coefficients
|
|
min_degree: int = 0 # Minimum polynomial degree
|
|
max_degree: int = 3 # Maximum polynomial degree
|
|
min_polynomials: int = 2 # Minimum number of polynomials being multiplied
|
|
max_polynomials: int = 3 # Maximum number of polynomials being multiplied
|
|
variables: Tuple[str] = ("x", "y", "z") # Tuple of variable names, that will be chosen randomly
|
|
allow_cross_variable_product: bool = False # Generate tasks like "Multiply (x^2+3x-1)*(y^2-5)"
|
|
allow_multivariate_polynomials: bool = False # Generate multivariate tasks like "Multiply (2x^2 + 3y)*(5x^2+3x-1)"
|
|
operators: Tuple[str, ...] = (
|
|
"+",
|
|
"-",
|
|
) # Allowed operators between terms, Avoid adding '*' or '/' because they will affect the degree
|
|
seed: Optional[int] = None
|
|
size: int = 500
|
|
|
|
def validate(self) -> None:
|
|
"""Validate configuration parameters."""
|
|
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_value > 0, "min_value must be positive."
|
|
assert self.max_value >= self.min_value, "max_value must be >= min_value."
|
|
|
|
assert self.min_degree >= 0, "min_degree must be >= 0."
|
|
assert self.max_degree >= self.min_degree, "max_degree must be >= min_degree."
|
|
|
|
assert self.min_polynomials >= 2, "min_polynomials must be >= 2."
|
|
assert self.max_polynomials >= self.min_polynomials, "max_polynomials must be >= min_polynomials."
|
|
|
|
assert len(self.variables) > 0, "The variable tuple is empty."
|
|
assert not (
|
|
self.allow_multivariate_polynomials and not self.allow_cross_variable_product
|
|
), "Multivariate polynomials require cross product."
|
|
|
|
allowed_ops = {"+", "-"}
|
|
assert len(self.operators) > 0, "operators tuple cannot be empty."
|
|
assert all(op in allowed_ops for op in self.operators), "Invalid operator found. Must be a subset of {+, -}."
|
|
|
|
|
|
class PolynomialMultiplicationDataset(ProceduralDataset):
|
|
"""
|
|
Generates [min_polynomials, max_polynomials] random polynomials of degree in [min_degree, max_degree].
|
|
- The polynomial is formed by summing random terms of the form: coeff * x^exponent.
|
|
- Then we find "F = P_0 * ... * P_1" using Sympy.
|
|
"""
|
|
|
|
def __init__(self, config: PolynomialMultiplicationConfig):
|
|
self._prompt_templates = [
|
|
"Simplify this expression: {polynomial_expr}",
|
|
"Calculate the following: {polynomial_expr}",
|
|
]
|
|
super().__init__(config=config, seed=config.seed, size=config.size)
|
|
|
|
def __getitem__(self, idx: int) -> dict:
|
|
"""
|
|
Generate a single polynomial multiplication item.
|
|
|
|
Returns:
|
|
A dict with:
|
|
- question: str (e.g. "Multiply polynomials: (8x^3 + x + 2)*(x - 3)")
|
|
- answer: str (Product, e.g. "8x^4 - 24x^3 + x^2 - x - 6")
|
|
- metadata: dict with details (polynomial_expr, result, variables)
|
|
"""
|
|
|
|
rng = random.Random(self.seed + idx)
|
|
|
|
"""
|
|
Three Monomial States:
|
|
- allow_multivariate_polynomials == 1: list of multivariate monomials (e.g "xy" --> [x, y, xy, x**2, y**2])
|
|
- allow_cross_variable_product == 1: None. Will generate a unique list of single variable monomials for each term
|
|
- allow_cross_variable_product == 0: A shared list of monomials for each term (e.g "x" --> [x, x**2, 1])
|
|
"""
|
|
monomials = self._get_monomials(rng) if self.config.allow_cross_variable_product else None
|
|
monomials = None if self.config.allow_cross_variable_product else self._get_monomials(rng)
|
|
|
|
number_polynomials = rng.randint(self.config.min_polynomials, self.config.max_polynomials)
|
|
|
|
polynomial_terms = [self._generate_polynomial(rng, monomials) for _ in range(number_polynomials)]
|
|
polynomial_expr = sp.prod(polynomial_terms)
|
|
product = sp.expand(polynomial_expr)
|
|
|
|
return {
|
|
"question": rng.choice(self._prompt_templates).format(
|
|
polynomial_expr=polynomial_expr,
|
|
),
|
|
"answer": product,
|
|
"metadata": {
|
|
"polynomial_expr": str(polynomial_expr),
|
|
"result": str(product),
|
|
"variables": list(product.free_symbols),
|
|
},
|
|
}
|
|
|
|
def _get_monomials(self, rng: random.Random) -> str:
|
|
"""Get a list of monomials"""
|
|
if self.config.allow_multivariate_polynomials:
|
|
sym = sp.symbols(self.config.variables)
|
|
else:
|
|
sym = [sp.symbols(rng.choice(self.config.variables))]
|
|
monomials = list(itermonomials(sym, self.config.max_degree, self.config.min_degree))
|
|
return monomials
|
|
|
|
def _generate_polynomial(self, rng: random.Random, monomials: Optional[list]):
|
|
"""Generates a random polynomial, returns expression."""
|
|
# Choose the number of terms and their respective degrees
|
|
monomials = monomials if monomials else self._get_monomials(rng)
|
|
num_terms = rng.randint(self.config.min_terms, self.config.max_terms)
|
|
|
|
polynomial_expr = 0
|
|
for _ in range(num_terms):
|
|
# Pick a nonzero random coefficient between min_value and max_value.
|
|
coeff = rng.randint(self.config.min_value, self.config.max_value)
|
|
|
|
# Pick a random monomial
|
|
var = rng.choice(monomials)
|
|
|
|
# If '-' in operators, we can randomly flip the sign
|
|
if "-" in self.config.operators and rng.random() < 0.5:
|
|
coeff = -coeff
|
|
|
|
polynomial_expr += coeff * var
|
|
|
|
return polynomial_expr
|
|
|
|
def score_answer(self, answer: Optional[str], entry: Dict[str, Any]) -> float:
|
|
reward = 0.0
|
|
metadata = entry["metadata"]
|
|
if answer is not None:
|
|
try:
|
|
predicted_poly = sp.parse_expr(answer)
|
|
target_poly = sp.parse_expr(metadata["result"])
|
|
|
|
# Check if the difference simplifies to zero (i.e. they are equivalent).
|
|
if predicted_poly == target_poly:
|
|
reward = 1.0
|
|
elif answer.strip():
|
|
reward = 0.05
|
|
else:
|
|
reward = 0.01
|
|
except Exception:
|
|
reward = 0.01
|
|
return reward
|
|
|
|
|
|
register_dataset("polynomial_multiplication", PolynomialMultiplicationDataset, PolynomialMultiplicationConfig)
|