#[macro_export]
macro_rules! ring_operation {
    ($field:ident, $p:ident, $g:ident, $r:ident, $r2:ident, $r3:ident, $inv:ident) => {
        group_operation!($field, $p, $g, $r, $r2, $r3, $inv);

        impl Ring for $field {
            const MULTIPLICATIVE_IDENTITY: $field = $field::one();

            fn one() -> Self {
                Self::MULTIPLICATIVE_IDENTITY
            }
        }

        impl Default for $field {
            fn default() -> Self {
                $field::one()
            }
        }

        impl PartialOrd for $field {
            fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
                Some(self.cmp(other))
            }

            fn lt(&self, other: &Self) -> bool {
                for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
                    if a != b {
                        return a < b;
                    }
                }
                false
            }

            fn le(&self, other: &Self) -> bool {
                for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
                    if a != b {
                        return a < b;
                    }
                }
                true
            }

            fn gt(&self, other: &Self) -> bool {
                for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
                    if a != b {
                        return a > b;
                    }
                }
                false
            }

            fn ge(&self, other: &Self) -> bool {
                for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
                    if a != b {
                        return a > b;
                    }
                }
                true
            }
        }

        impl Ord for $field {
            fn cmp(&self, other: &Self) -> Ordering {
                for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
                    if a < b {
                        return Ordering::Less;
                    } else if a > b {
                        return Ordering::Greater;
                    }
                }
                Ordering::Equal
            }
        }
    };
}

pub use ring_operation;