GPT-4 User Use codegolf techniques but do not limit the length of the code. Write a very simple symbolic solver. Autogenerate operator metadata via trial. ChatGPT Building a simple symbolic solver with autogenerated operator metadata using a trial approach in Python can involve creating a system that tests operations and builds knowledge about them dynamically. Here is a simplified example. This symbolic solver can handle basic arithmetic operations and is written without strict code length constraints, while keeping the code relatively short and readable. The autogenerate operator metadata through trial involves using actual operations on sample data and storing their properties (e.g., commutative property). ```python import operator # Sample data for trial trial_data = [2, 3] # Operators to be tested and analyzed ops = { '+': operator.add, '-': operator.sub, '*': operator.mul, '/': operator.truediv, } # Autogenerate metadata meta_ops = {} for sym, op in ops.items(): # Trial operation a, b = trial_data try: r1, r2 = op(a, b), op(b, a) except ZeroDivisionError: continue # Skip division by zero # Check properties like commutativity is_commutative = r1 == r2 # Store metadata meta_ops[sym] = { 'func': op, 'commutative': is_commutative, } # Symbolic solver def simple_solve(expr, var, val): """ Solves an expression `expr` symbolically for a variable `var` given a value `val`. Example: simple_solve("x + 2", "x", 3) should return 5. """ try: # Replace variable with value and evaluate expr = expr.replace(var, str(val)) return eval(expr, {"__builtins__": None}, {}) except Exception as e: print(f"Error: {str(e)}") return None # Example usage expr = "x + y * z" var_values = {"x": 2, "y": 3, "z": 4} # Substituting variable values and solving for var, val in var_values.items(): expr = expr.replace(var, str(val)) result = simple_solve(expr, "", 0) print(f"Result: {result}") # Operator metadata for sym, meta in meta_ops.items(): print(f"Operator: {sym}, Commutative: {meta['commutative']}") ``` This code demonstrates a method of building a symbolic solver with autogenerated metadata for operators based on trial operations. The `simple_solve` function serves as a very basic symbolic solver that replaces variables with their corresponding values and evaluates the resulting expression. Note that using `eval` is generally not recommended for parsing expressions in a production environment due to security risks, and an expression parsing library or a safer evaluation method would be preferable in a more sophisticated implementation. The metadata for operations is dynamically generated by testing them on sample data (`trial_data`). It checks for properties such as commutativity (a+b == b+a) and could be expanded to check for other properties as needed. Keep in mind that this example is simplistic and a full-featured symbolic solver (like Sympy in Python) would require much more robust parsing, validation, and evaluation capabilities to handle a wide range of mathematical expressions and use-cases.