reasoning-gym/tests/test_polynomial_equations.py
2025-02-08 10:19:20 +00:00

577 lines
25 KiB
Python

from reasoning_gym.curricula.algebra.polynomial_equations_curriculum import PolynomialEquationsCurriculum
from reasoning_gym.exercises.algebra.polynomial_equations import PolynomialEquationsExercise
import unittest
import random
from sympy import solve, Symbol, Eq, parse_expr
class TestPolynomialEquationsParsing(unittest.TestCase):
"""Test parsing of polynomial expressions and terms"""
def setUp(self):
self.exercise = PolynomialEquationsExercise()
def test_parse_expression(self):
"""Test parsing of polynomial expressions"""
test_metadata = {
'type': 'direct',
'executed_parts': {
'terms': ['2*x**2', '3*x', '1'],
'operators': ['+', '+'],
'variable': 'x'
}
}
parsed = test_metadata['executed_parts']
self.assertEqual(parsed["terms"], ["2*x**2", "3*x", "1"])
self.assertEqual(parsed["operators"], ["+", "+"])
self.assertEqual(parsed["variable"], "x")
def test_parse_negative_terms(self):
"""Test parsing of expressions with negative terms"""
test_metadata = {
'type': 'direct',
'executed_parts': {
'terms': ['-2*x**2', '4*x'],
'operators': ['+'],
'variable': 'x'
}
}
parsed = test_metadata['executed_parts']
self.assertEqual(parsed["terms"], ["-2*x**2", "4*x"])
self.assertEqual(parsed["operators"], ["+"])
self.assertEqual(parsed["variable"], "x")
class TestPolynomialEquationsEvaluation(unittest.TestCase):
"""Test evaluation of polynomial equations"""
def setUp(self):
self.exercise = PolynomialEquationsExercise()
def test_quadratic_equation(self):
"""Test evaluation of quadratic equations"""
parsed = {
"terms": ["x**2", "-5*x", "6"],
"operators": ["+", "+"],
"variable": "x"
}
result = self.exercise._evaluate_expression(parsed)
expected = "[2.0, 3.0]" # x^2 - 5x + 6 = 0 has roots at x = 2 and x = 3
self.assertEqual(result, expected)
def test_linear_equation(self):
"""Test evaluation of linear equations"""
parsed = {
"terms": ["2*x", "-4"],
"operators": ["+"],
"variable": "x"
}
result = self.exercise._evaluate_expression(parsed)
expected = "[2.0]" # 2x - 4 = 0 has root at x = 2
self.assertEqual(result, expected)
def test_no_real_solutions(self):
"""Test equations with no real solutions"""
parsed = {
"terms": ["x**2", "1"],
"operators": ["+"],
"variable": "x"
}
result = self.exercise._evaluate_expression(parsed)
expected = "[]" # x^2 + 1 = 0 has no real solutions
self.assertEqual(result, expected)
class TestPolynomialEquationsGeneration(unittest.TestCase):
"""Test problem generation"""
def setUp(self):
self.curriculum = PolynomialEquationsCurriculum()
self.exercise = PolynomialEquationsExercise()
self.rng = random.Random(42)
self.curriculum.rng = self.rng
def test_problem_structure(self):
"""Test that generated problems have the correct structure"""
problem = self.exercise.generate(self.curriculum)
# Check basic structure
self.assertIn("question", problem)
self.assertIn("answer", problem)
self.assertIn("metadata", problem)
# Check metadata structure
metadata = problem["metadata"]
self.assertEqual(metadata["type"], "direct")
self.assertIn("executed_parts", metadata)
executed_parts = metadata["executed_parts"]
self.assertIn("terms", executed_parts)
self.assertIn("operators", executed_parts)
self.assertIn("variable", executed_parts)
def test_term_generation(self):
"""Test generation of polynomial terms"""
# Set curriculum to basic settings
self.curriculum.set_attr_level("coefficient_value", 0) # 1-10
self.curriculum.set_attr_level("max_degree", 0) # degree 1
self.curriculum.set_attr_level("sign", 0) # No signs
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
# Check we have at least one term
self.assertTrue(len(executed_parts["terms"]) > 0)
# Check first term format
first_term = executed_parts["terms"][0]
self.assertTrue(isinstance(first_term, str))
self.assertTrue(first_term.replace('*', '').replace('x', '').replace('-', '').replace('.', '').isdigit() or
first_term == 'x')
def test_operator_generation(self):
"""Test generation of operators"""
self.curriculum.set_attr_level("operators", 1) # +, -
self.curriculum.set_attr_level("num_terms", 0) # 2 terms
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
# Check we have operators for n-1 terms
self.assertEqual(len(executed_parts["operators"]), len(executed_parts["terms"]) - 1)
# Check operator is valid
if executed_parts["operators"]:
self.assertIn(executed_parts["operators"][0], ["+", "-"])
class TestPolynomialEquationsComprehensive(unittest.TestCase):
"""Comprehensive tests for polynomial equations"""
def setUp(self):
self.curriculum = PolynomialEquationsCurriculum()
self.exercise = PolynomialEquationsExercise()
self.rng = random.Random(42)
self.curriculum.rng = self.rng
def test_variable_consistency(self):
"""Test that the same variable is used consistently throughout the equation"""
num_samples = 50
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
var_name = executed_parts["variable"]
# Check variable appears in question
self.assertIn(var_name, problem["question"])
# Check variable is used consistently in terms
for term in executed_parts["terms"]:
if var_name in term: # If term has a variable
self.assertIn(var_name, term)
def test_coefficient_ranges(self):
"""Test that coefficients are within expected ranges"""
self.curriculum.set_attr_level("coefficient_value", 0) # 1-10
num_samples = 50
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
for term in executed_parts["terms"]:
# Extract coefficient if term has one
if '*' in term:
coeff = term.split('*')[0]
if coeff and coeff != '-': # Skip if empty or just a minus sign
coeff = float(coeff)
self.assertLessEqual(abs(coeff), 10)
self.assertGreater(abs(coeff), 0)
def test_degree_constraints(self):
"""Test that polynomial degrees respect the curriculum settings"""
self.curriculum.set_attr_level("max_degree", 0) # Level 0 means max degree 1
num_samples = 50
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
max_degree = 0
for term in executed_parts["terms"]:
if "**" in term:
degree = int(term.split("**")[1])
max_degree = max(max_degree, degree)
elif executed_parts["variable"] in term: # Variable without exponent means degree 1
max_degree = max(max_degree, 1)
self.assertLessEqual(max_degree, 1)
def test_solution_validity(self):
"""Test that generated solutions are valid"""
num_samples = 50
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
# Parse the answer string to get solutions
solutions = eval(problem["answer"]) # Safe since we control the input
if solutions: # If there are real solutions
# Verify each solution satisfies the equation
var = Symbol(executed_parts["variable"])
expr = executed_parts["terms"][0]
# Reconstruct the expression
for i, term in enumerate(executed_parts["terms"][1:], 1):
expr += f" {executed_parts['operators'][i-1]} {term}"
# Verify each solution
sympy_expr = parse_expr(expr)
for sol in solutions:
result = abs(float(sympy_expr.subs(var, sol)))
self.assertAlmostEqual(result, 0, places=10)
def test_comprehensive_random_evaluation(self):
"""Test 1000 random problems across all levels to verify correct generation and evaluation"""
num_samples = 1000
# Statistics tracking
stats = {
'operator_counts': {}, # Count of each operator used
'degree_counts': {}, # Count of polynomial degrees
'term_counts': {}, # Distribution of number of terms
'variable_counts': {}, # Count of each variable used
'coefficient_stats': { # Track coefficient statistics
'min': float('inf'),
'max': float('-inf'),
'total': 0,
'count': 0,
'unique': set()
},
'solution_stats': { # Track solution statistics
'no_solutions': 0, # Count of equations with no real solutions
'one_solution': 0, # Count of equations with exactly one solution
'two_solutions': 0, # Count of equations with exactly two solutions
'min': float('inf'), # Minimum solution value
'max': float('-inf'), # Maximum solution value
},
'level_distribution': { # Track curriculum level usage
'max_degree': {},
'num_terms': {},
'coefficient_value': {},
'operators': {},
'sign': {},
'var_name': {}
}
}
for _ in range(num_samples):
# Randomly set curriculum levels
levels = {
'max_degree': self.rng.randint(0, 2),
'num_terms': self.rng.randint(0, 2),
'coefficient_value': self.rng.randint(0, 2),
'operators': self.rng.randint(0, 1),
'sign': self.rng.randint(0, 1),
'var_name': self.rng.randint(0, 2)
}
# Update level distribution stats
for attr, level in levels.items():
stats['level_distribution'][attr][level] = stats['level_distribution'][attr].get(level, 0) + 1
# Set curriculum levels
for attr, level in levels.items():
self.curriculum.set_attr_level(attr, level)
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
terms = executed_parts["terms"]
operators = executed_parts["operators"]
variable = executed_parts["variable"]
# Update operator statistics
for op in operators:
stats['operator_counts'][op] = stats['operator_counts'].get(op, 0) + 1
# Update term count statistics
num_terms = len(terms)
stats['term_counts'][num_terms] = stats['term_counts'].get(num_terms, 0) + 1
# Update variable statistics
stats['variable_counts'][variable] = stats['variable_counts'].get(variable, 0) + 1
# Calculate and update degree statistics
max_degree = 0
for term in terms:
if "**" in term:
degree = int(term.split("**")[1])
max_degree = max(max_degree, degree)
elif variable in term: # Variable without exponent means degree 1
max_degree = max(max_degree, 1)
stats['degree_counts'][max_degree] = stats['degree_counts'].get(max_degree, 0) + 1
# Update coefficient statistics
for term in terms:
if '*' in term:
coeff = term.split('*')[0]
if coeff and coeff not in ['-', '+']:
try:
value = abs(float(coeff))
stats['coefficient_stats']['min'] = min(stats['coefficient_stats']['min'], value)
stats['coefficient_stats']['max'] = max(stats['coefficient_stats']['max'], value)
stats['coefficient_stats']['total'] += value
stats['coefficient_stats']['count'] += 1
stats['coefficient_stats']['unique'].add(value)
except ValueError:
# Skip if coefficient is not a number (e.g., just a variable)
continue
# Update solution statistics
solutions = eval(problem["answer"]) # Safe since we control the input
num_solutions = len(solutions)
if num_solutions == 0:
stats['solution_stats']['no_solutions'] += 1
elif num_solutions == 1:
stats['solution_stats']['one_solution'] += 1
stats['solution_stats']['min'] = min(stats['solution_stats']['min'], solutions[0])
stats['solution_stats']['max'] = max(stats['solution_stats']['max'], solutions[0])
elif num_solutions == 2:
stats['solution_stats']['two_solutions'] += 1
stats['solution_stats']['min'] = min(stats['solution_stats']['min'], min(solutions))
stats['solution_stats']['max'] = max(stats['solution_stats']['max'], max(solutions))
# Verify solution correctness
if solutions: # If there are real solutions
var = Symbol(variable)
expr = terms[0]
for i, term in enumerate(terms[1:], 1):
expr += f" {operators[i-1]} {term}"
# Create local dict with the variable symbol
local_dict = {variable: var}
sympy_expr = parse_expr(expr, local_dict=local_dict)
for sol in solutions:
result = abs(float(sympy_expr.subs(var, sol)))
self.assertAlmostEqual(result, 0, places=10)
# Print comprehensive statistics
print("\nComprehensive Random Evaluation Statistics:")
print("-" * 50)
print("\nOperator Distribution:")
total_ops = sum(stats['operator_counts'].values())
for op, count in sorted(stats['operator_counts'].items()):
print(f" {op}: {count} ({count/total_ops*100:.1f}%)")
print("\nDegree Distribution:")
total_eqs = num_samples
for degree, count in sorted(stats['degree_counts'].items()):
print(f" Degree {degree}: {count} ({count/total_eqs*100:.1f}%)")
print("\nTerm Count Distribution:")
for terms, count in sorted(stats['term_counts'].items()):
print(f" {terms} terms: {count} ({count/total_eqs*100:.1f}%)")
print("\nVariable Distribution:")
total_vars = sum(stats['variable_counts'].values())
for var, count in sorted(stats['variable_counts'].items()):
print(f" {var}: {count} ({count/total_vars*100:.1f}%)")
print("\nCoefficient Statistics:")
print(f" Range: [{stats['coefficient_stats']['min']:.1f} to {stats['coefficient_stats']['max']:.1f}]")
if stats['coefficient_stats']['count'] > 0:
avg = stats['coefficient_stats']['total'] / stats['coefficient_stats']['count']
print(f" Average: {avg:.2f}")
print(f" Unique values: {len(stats['coefficient_stats']['unique'])}")
print("\nSolution Statistics:")
print(f" No real solutions: {stats['solution_stats']['no_solutions']} ({stats['solution_stats']['no_solutions']/total_eqs*100:.1f}%)")
print(f" One solution: {stats['solution_stats']['one_solution']} ({stats['solution_stats']['one_solution']/total_eqs*100:.1f}%)")
print(f" Two solutions: {stats['solution_stats']['two_solutions']} ({stats['solution_stats']['two_solutions']/total_eqs*100:.1f}%)")
if stats['solution_stats']['min'] != float('inf'):
print(f" Solution range: [{stats['solution_stats']['min']:.2f} to {stats['solution_stats']['max']:.2f}]")
print("\nCurriculum Level Distribution:")
for attr, levels in sorted(stats['level_distribution'].items()):
print(f"\n {attr}:")
for level, count in sorted(levels.items()):
print(f" Level {level}: {count} ({count/total_eqs*100:.1f}%)")
# Verify statistical properties
# 1. Check we see all operators when using operator level 1
if any(level == 1 for level in stats['level_distribution']['operators'].keys()):
self.assertTrue(all(op in stats['operator_counts'] for op in ["+", "-"]),
"Not all operators were generated")
# 2. Check degree distribution matches curriculum settings
max_possible_degree = max(stats['degree_counts'].keys())
self.assertLessEqual(max_possible_degree, 3, "Generated degree exceeds maximum allowed")
# 3. Check term count constraints
min_terms = min(stats['term_counts'].keys())
max_terms = max(stats['term_counts'].keys())
self.assertGreaterEqual(min_terms, 2, "Generated equations with too few terms")
self.assertLessEqual(max_terms, 4, "Generated equations with too many terms")
# 4. Check coefficient ranges
if stats['coefficient_stats']['count'] > 0:
self.assertGreater(len(stats['coefficient_stats']['unique']), 3,
"Too few unique coefficients generated")
self.assertGreater(stats['coefficient_stats']['min'], 0,
"Generated zero or negative coefficients")
self.assertLessEqual(stats['coefficient_stats']['max'], 100,
"Generated coefficients exceed maximum allowed")
# 5. Check solution distribution
total_with_solutions = stats['solution_stats']['one_solution'] + stats['solution_stats']['two_solutions']
if total_with_solutions > 0:
self.assertGreater(stats['solution_stats']['one_solution'], 0,
"No equations with exactly one solution generated")
self.assertGreater(stats['solution_stats']['two_solutions'], 0,
"No equations with exactly two solutions generated")
class TestPolynomialEquationsGenerate(unittest.TestCase):
"""Test the generate function with different curriculum settings"""
def setUp(self):
self.curriculum = PolynomialEquationsCurriculum()
self.exercise = PolynomialEquationsExercise()
self.rng = random.Random(42) # Fixed seed for reproducibility
self.curriculum.rng = self.rng
def test_generate_basic_linear(self):
"""Test generation of basic linear equations"""
# Configure curriculum for simple linear equations
self.curriculum.set_attr_level("max_degree", 0) # Linear equations
self.curriculum.set_attr_level("num_terms", 0) # 2 terms
self.curriculum.set_attr_level("coefficient_value", 0) # Small coefficients
self.curriculum.set_attr_level("sign", 0) # No signs
self.curriculum.set_attr_level("operators", 0) # Only +
problem = self.exercise.generate(self.curriculum)
# Verify structure
self.assertIn("question", problem)
self.assertIn("answer", problem)
self.assertIn("metadata", problem)
# Verify terms and operators
executed_parts = problem["metadata"]["executed_parts"]
self.assertTrue(len(executed_parts["terms"]) >= 2, "Not enough terms generated")
self.assertTrue(len(executed_parts["operators"]) >= 1, "No operators generated")
# Verify operator is addition
self.assertEqual(executed_parts["operators"][0], "+")
# Verify terms have correct degree
for term in executed_parts["terms"]:
self.assertNotIn("**", term, "Term should not have exponent > 1")
def test_generate_with_signs(self):
"""Test generation with positive/negative signs"""
self.curriculum.set_attr_level("operators", 0) # Only +
self.curriculum.set_attr_level("num_terms", 0) # 2 terms
self.curriculum.set_attr_level("sign", 1) # Allow -
self.curriculum.set_attr_level("max_degree", 0) # Linear equations
num_samples = 50
terms_seen = []
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
terms_seen.extend(executed_parts["terms"])
# Check we see both positive and negative terms
has_negative = any(term.startswith('-') for term in terms_seen)
has_positive = any(not term.startswith('-') for term in terms_seen)
self.assertTrue(has_positive, "No positive terms generated")
self.assertTrue(has_negative, "No negative terms generated")
def test_term_count_distribution(self):
"""Test that term counts follow the correct distribution"""
self.curriculum.set_attr_level("num_terms", 2) # 2-4 terms
num_samples = 100
term_counts = []
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
term_count = len(executed_parts["terms"])
term_counts.append(term_count)
self.assertTrue(2 <= term_count <= 4, f"Term count {term_count} outside valid range [2,4]")
# Verify we see different term counts
unique_counts = set(term_counts)
self.assertTrue(len(unique_counts) > 1, "Only one term count generated")
def test_operator_distribution(self):
"""Test distribution of operators"""
self.curriculum.set_attr_level("operators", 1) # +, -
num_samples = 100
operators_seen = []
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
operators_seen.extend(executed_parts["operators"])
# Check we see both operators
has_plus = "+" in operators_seen
has_minus = "-" in operators_seen
self.assertTrue(has_plus, "No + operators generated")
self.assertTrue(has_minus, "No - operators generated")
def test_variable_distribution(self):
"""Test distribution of variable names"""
self.curriculum.set_attr_level("var_name", 0) # x, y, z
num_samples = 100
variables_seen = set()
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
variables_seen.add(executed_parts["variable"])
# Check we see multiple variables
self.assertTrue(len(variables_seen) > 1, "Only one variable name generated")
self.assertTrue(all(var in "xyz" for var in variables_seen),
f"Invalid variables generated: {variables_seen}")
def test_coefficient_distribution(self):
"""Test distribution of coefficient values"""
self.curriculum.set_attr_level("coefficient_value", 0) # 1-10
num_samples = 100
coefficients = []
for _ in range(num_samples):
problem = self.exercise.generate(self.curriculum)
executed_parts = problem["metadata"]["executed_parts"]
for term in executed_parts["terms"]:
if '*' in term:
coeff = term.split('*')[0]
if coeff and coeff not in ['-', '+']:
coefficients.append(abs(float(coeff)))
# Check coefficient range
self.assertTrue(all(1 <= c <= 10 for c in coefficients),
"Coefficients outside valid range [1,10]")
# Check we see different values
unique_coeffs = set(coefficients)
self.assertTrue(len(unique_coeffs) > 3,
f"Too few unique coefficients: {unique_coeffs}")
def test_error_handling(self):
"""Test error handling in equation generation"""
# Test with invalid attribute level
with self.assertRaises(ValueError):
self.curriculum.set_attr_level("max_degree", 999)
# Test with invalid attribute name
with self.assertRaises(KeyError):
self.curriculum.set_attr_level("invalid_attr", 0)
if __name__ == '__main__':
unittest.main()