use std::ops::{Add, Sub, Mul, Div, AddAssign};

#[derive(Clone, Copy, Debug)]
pub struct State<T> {
	pub q: T,
	pub p: T,
}

pub trait Hamiltonian {
	fn energy(&self) -> f64;
	fn dots(&self) -> Self;
}

impl<T: Add<Output = T>> Add for State<T> {
	type Output = Self;

	fn add(self, rhs: Self) -> Self {
		Self {
			q: self.q + rhs.q,
			p: self.p + rhs.p,
		}
	}
}

impl<T: Sub<Output = T>> Sub for State<T> {
	type Output = Self;

	fn sub(self, rhs: Self) -> Self {
		Self {
			q: self.q - rhs.q,
			p: self.p - rhs.p,
		}
	}
}

impl<T: Mul<f64, Output = T>> Mul<f64> for State<T> {
	type Output = Self;

	fn mul(self, rhs: f64) -> Self {
		Self {
			q: self.q * rhs,
			p: self.p * rhs,
		}
	}
}

impl<T: Div<f64, Output = T>> Div<f64> for State<T> {
	type Output = Self;

	fn div(self, rhs: f64) -> Self {
		Self {
			q: self.q / rhs,
			p: self.p / rhs,
		}
	}
}

impl<T: AddAssign> AddAssign for State<T> {
	fn add_assign(&mut self, other: Self) {
		self.q += other.q;
		self.p += other.p;
	}
}