Symbolic Algebra MCP Server

import pytest from server import ( intro, introduce_expression, differentiate_expression, integrate_expression, create_coordinate_system, create_vector_field, calculate_curl, calculate_divergence, calculate_gradient, print_latex_expression, local_vars, expressions, coordinate_systems, ) from vars import Assumption # Add a fixture to reset global state between tests @pytest.fixture(autouse=True) def reset_globals(): # Clear global dictionaries before each test local_vars.clear() expressions.clear() coordinate_systems.clear() # Reset the expression counter import server server.expression_counter = 0 yield class TestDifferentiateExpressionTool: def test_differentiate_polynomial(self): # Introduce a variable intro("x", [Assumption.REAL], []) # Create an expression: x^3 expr_key = introduce_expression("x**3") # First derivative first_deriv_key = differentiate_expression(expr_key, "x") first_deriv_latex = print_latex_expression(first_deriv_key) # Should be 3x^2 assert "3" in first_deriv_latex assert "x^{2}" in first_deriv_latex # Second derivative second_deriv_key = differentiate_expression(expr_key, "x", 2) second_deriv_latex = print_latex_expression(second_deriv_key) # Should be 6x assert "6" in second_deriv_latex assert "x" in second_deriv_latex # Third derivative third_deriv_key = differentiate_expression(expr_key, "x", 3) third_deriv_latex = print_latex_expression(third_deriv_key) # Should be 6 assert "6" in third_deriv_latex def test_differentiate_trigonometric(self): # Introduce a variable intro("x", [Assumption.REAL], []) # Create sin(x) expression sin_key = introduce_expression("sin(x)") # Derivative of sin(x) is cos(x) deriv_key = differentiate_expression(sin_key, "x") deriv_latex = print_latex_expression(deriv_key) assert "\\cos" in deriv_latex def test_nonexistent_expression(self): intro("x", [Assumption.REAL], []) result = differentiate_expression("nonexistent_key", "x") assert "error" in result.lower() def test_nonexistent_variable(self): intro("x", [Assumption.REAL], []) expr_key = introduce_expression("x**2") result = differentiate_expression(expr_key, "y") assert "error" in result.lower() class TestIntegrateExpressionTool: def test_indefinite_integral_polynomial(self): # Introduce a variable intro("x", [Assumption.REAL], []) # Create expression: x^2 expr_key = introduce_expression("x**2") # Integrate integral_key = integrate_expression(expr_key, "x") integral_latex = print_latex_expression(integral_key) # Should be x^3/3 assert "x^{3}" in integral_latex assert "3" in integral_latex def test_indefinite_integral_trigonometric(self): # Introduce a variable intro("x", [Assumption.REAL], []) # Create expression: cos(x) expr_key = introduce_expression("cos(x)") # Integrate integral_key = integrate_expression(expr_key, "x") integral_latex = print_latex_expression(integral_key) # Should be sin(x) assert "\\sin" in integral_latex def test_nonexistent_expression(self): intro("x", [Assumption.REAL], []) result = integrate_expression("nonexistent_key", "x") assert "error" in result.lower() def test_nonexistent_variable(self): intro("x", [Assumption.REAL], []) expr_key = introduce_expression("x**2") result = integrate_expression(expr_key, "y") assert "error" in result.lower() class TestVectorOperations: def test_create_coordinate_system(self): # Create coordinate system result = create_coordinate_system("R") assert result == "R" assert "R" in coordinate_systems def test_create_custom_coordinate_system(self): # Create coordinate system with custom names result = create_coordinate_system("C", ["rho", "phi", "z"]) assert result == "C" assert "C" in coordinate_systems def test_create_vector_field(self): # Create coordinate system create_coordinate_system("R") # Introduce variables to represent components intro("x", [Assumption.REAL], []) intro("y", [Assumption.REAL], []) intro("z", [Assumption.REAL], []) # Create vector field F = (y, -x, z) vector_field_key = create_vector_field("R", "y", "-x", "z") # The key might be an error message if the test is failing if "error" not in vector_field_key.lower(): assert vector_field_key.startswith("vector_") else: assert False, f"Failed to create vector field: {vector_field_key}" def test_calculate_curl(self): # Create coordinate system create_coordinate_system("R") # Introduce variables intro("x", [Assumption.REAL], []) intro("y", [Assumption.REAL], []) # Create a simple vector field for curl calculation vector_field_key = create_vector_field("R", "y", "-x", "0") # Check if vector field was created successfully if "error" in vector_field_key.lower(): assert False, f"Failed to create vector field: {vector_field_key}" # Calculate curl curl_key = calculate_curl(vector_field_key) # Check if curl calculation was successful if "error" not in curl_key.lower(): assert curl_key.startswith("vector_") else: assert False, f"Failed to calculate curl: {curl_key}" def test_calculate_divergence(self): # Create coordinate system create_coordinate_system("R") # Introduce variables intro("x", [Assumption.REAL], []) intro("y", [Assumption.REAL], []) intro("z", [Assumption.REAL], []) # Create a simple identity vector field vector_field_key = create_vector_field("R", "x", "y", "z") # Check if vector field was created successfully if "error" in vector_field_key.lower(): assert False, f"Failed to create vector field: {vector_field_key}" # Calculate divergence - should be 0 because symbols have no dependency on coordinates div_key = calculate_divergence(vector_field_key) # Check if divergence calculation was successful if "error" in div_key.lower(): assert False, f"Failed to calculate divergence: {div_key}" div_latex = print_latex_expression(div_key) # Check result - should be 0 assert "0" in div_latex def test_calculate_gradient(self): # Create coordinate system create_coordinate_system("R") # Introduce variables intro("x", [Assumption.REAL], []) intro("y", [Assumption.REAL], []) intro("z", [Assumption.REAL], []) # Create a simple scalar field scalar_field_key = introduce_expression("x**2 + y**2 + z**2") # Calculate gradient grad_key = calculate_gradient(scalar_field_key) # Check if gradient calculation was successful if "error" not in grad_key.lower(): assert grad_key.startswith("vector_") else: assert False, f"Failed to calculate gradient: {grad_key}" def test_nonexistent_coordinate_system(self): result = create_vector_field("NonExistent", "x", "y", "z") assert "error" in result.lower() def test_nonexistent_vector_field(self): result = calculate_curl("nonexistent_key") assert "error" in result.lower()