"""
Hamiltonian Mechanics Implementation

Provides tools for deriving Hamilton's equations of motion.
"""
from typing import Dict, List, Optional, Tuple
import sympy as sp

from ..base import PhysicsDomain
from ...utils import logger


class HamiltonianMechanics(PhysicsDomain):
    """
    Hamiltonian mechanics domain using Hamilton's equations.
    
    dq/dt = ∂H/∂p
    dp/dt = -∂H/∂q
    """
    
    def __init__(self, name: str = "hamiltonian_system"):
        super().__init__(name)
        self._hamiltonian: Optional[sp.Expr] = None
        self._symbol_cache: Dict[str, sp.Symbol] = {}
    
    def get_symbol(self, name: str, **assumptions) -> sp.Symbol:
        """Get or create a symbol with caching."""
        if name not in self._symbol_cache:
            default_assumptions = {'real': True}
            default_assumptions.update(assumptions)
            self._symbol_cache[name] = sp.Symbol(name, **default_assumptions)
        return self._symbol_cache[name]
    
    def set_hamiltonian(self, expr: sp.Expr) -> None:
        """Set the Hamiltonian directly."""
        self._hamiltonian = expr
    
    def define_lagrangian(self) -> sp.Expr:
        """
        Convert Hamiltonian to Lagrangian (inverse Legendre transform).
        
        L = Σ(p_i * q̇_i) - H
        """
        if self._hamiltonian is None:
            raise ValueError("Hamiltonian not defined")
        
        L = sp.S.Zero
        for q in self.coordinates:
            q_dot = self.get_symbol(f"{q}_dot")
            p = self.get_symbol(f"p_{q}")
            L += p * q_dot
        
        L = L - self._hamiltonian
        return L
    
    def define_hamiltonian(self) -> sp.Expr:
        """Return the Hamiltonian expression."""
        if self._hamiltonian is None:
            raise ValueError("Hamiltonian not defined")
        return self._hamiltonian
    
    def derive_equations_of_motion(self) -> Dict[str, sp.Expr]:
        """
        Derive Hamilton's equations of motion.
        
        Returns:
            Dictionary with q_dot and p_dot expressions
        """
        if self._hamiltonian is None:
            raise ValueError("Hamiltonian not defined")
        
        H = self._hamiltonian
        equations = {}
        
        for q in self.coordinates:
            q_sym = self.get_symbol(q)
            p_sym = self.get_symbol(f"p_{q}")
            
            # dq/dt = ∂H/∂p
            q_dot_expr = sp.diff(H, p_sym)
            equations[f"{q}_dot"] = sp.simplify(q_dot_expr)
            
            # dp/dt = -∂H/∂q
            p_dot_expr = -sp.diff(H, q_sym)
            equations[f"p_{q}_dot"] = sp.simplify(p_dot_expr)
        
        self.equations = equations
        self._is_compiled = True
        return equations
    
    def get_state_variables(self) -> List[str]:
        """Get state variables (q, p pairs) for ODE system."""
        state = []
        for q in self.coordinates:
            state.extend([q, f"p_{q}"])
        return state
    
    def get_conserved_quantities(self) -> Dict[str, sp.Expr]:
        """Hamiltonian is conserved for time-independent systems."""
        if self._hamiltonian is not None:
            return {'hamiltonian': self._hamiltonian}
        return {}
