import random import string from dataclasses import dataclass from typing import Optional, Tuple import sympy from sympy import Eq, Symbol, solve from ..dataset import ProceduralDataset @dataclass class SimpleEquationsConfig: """Configuration for simple equation task generation""" min_terms: int = 2 # Minimum number of terms in expression max_terms: int = 4 # Maximum number of terms min_value: int = 1 # Minimum value for constants max_value: int = 100 # Maximum value for constants operators: tuple = ("+", "-", "*") # Allowed operators seed: Optional[int] = None size: int = 500 def validate(self): """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 len(self.operators) > 0, "must specify at least one operator" class SimpleEquationsDataset(ProceduralDataset): """Generates simple equations with one variable to solve""" def __init__(self, config: SimpleEquationsConfig): self.config = config self.config.validate() self._prompt_templates = [ "Find the value of {variable} in the equation: {equation}", "Solve for {variable}: {equation}", "Determine the value of {variable} that satisfies: {equation}", ] super().__init__(seed=config.seed, size=config.size) def __getitem__(self, idx: int) -> dict: """Generate a single equation task Returns: dict with keys: - question: str, the equation to solve (e.g. "3 * x = 12") - answer: str, the solution value (e.g. "4") - metadata: dict with generation parameters """ rng = random.Random(self.seed + idx) # Get variable and generate equation variable = self._get_variable(rng) equation, solution = self._generate_equation(rng, variable) return { "question": rng.choice(self._prompt_templates).format(variable=variable, equation=equation), "answer": str(solution), "metadata": { "equation": equation, "variable": variable, }, } def _get_variable(self, rng: random.Random) -> str: """Get a random lowercase variable name""" return rng.choice(string.ascii_lowercase) def _generate_equation(self, rng: random.Random, variable: str) -> Tuple[str, int]: """Generate an equation and its solution Args: rng: Random number generator variable: Variable symbol to use in equation Returns: Tuple of (equation string, solution integer) """ x = Symbol(variable) # Generate terms for left side num_terms = rng.randint(self.config.min_terms, self.config.max_terms) terms = [] # Generate all constant terms first for _ in range(num_terms): value = rng.randint(self.config.min_value, self.config.max_value) terms.append(value) # Replace one random term with the variable term var_pos = rng.randint(0, num_terms - 1) coef = rng.randint(self.config.min_value, self.config.max_value) terms[var_pos] = coef * x # Apply operators between terms expr = terms[0] for i in range(1, num_terms): op = rng.choice(self.config.operators) if op == "+": expr = expr + terms[i] elif op == "-": expr = expr - terms[i] else: # '*' expr = expr * terms[i] left_side = expr # Generate right side right_side = rng.randint(self.config.min_value, self.config.max_value) # Create equation equation = Eq(left_side, right_side) solutions = solve(equation, x) # Check if we found any solutions if not solutions: return self._generate_equation(rng, variable) solution = solutions[0] # Only return if solution is a positive integer if not (isinstance(solution, sympy.Integer) and solution > 0): return self._generate_equation(rng, variable) return f"{left_side} = {right_side}", int(solution) def simple_equations_dataset( min_terms: int = 2, max_terms: int = 5, min_value: int = 1, max_value: int = 100, operators: tuple = ("+", "-", "*"), seed: Optional[int] = None, size: int = 500, ) -> SimpleEquationsDataset: """Create a SimpleEquationsDataset with the given configuration""" config = SimpleEquationsConfig( min_terms=min_terms, max_terms=max_terms, min_value=min_value, max_value=max_value, operators=operators, seed=seed, size=size, ) return SimpleEquationsDataset(config)