adic 0.5.1

Arithmetic and rootfinding for p-adic numbers
Documentation 
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use std::{
    fmt::Display,
    ops::{Div, Mul, MulAssign, Rem},
};
use num::{traits::Pow, BigUint};
use super::Prime;


/// Prime power p^n
#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
pub struct PrimePower(Prime, u32);

impl PrimePower {

    /// Prime `p`
    pub fn p(&self) -> Prime {
        self.0
    }

    /// Power of the prime `n`
    pub fn power(&self) -> u32 {
        self.1
    }

}



impl From<Prime> for PrimePower {
    fn from(value: Prime) -> Self {
        Self(value, 1)
    }
}

impl<P> From<(P, u32)> for PrimePower
where P: Into<Prime> {
    fn from(pp: (P, u32)) -> Self {
        Self(pp.0.into(), pp.1)
    }
}

impl<P> TryFrom<(P, usize)> for PrimePower
where P: Into<Prime> {
    type Error = <u32 as TryFrom<usize>>::Error;
    fn try_from(pp: (P, usize)) -> Result<Self, Self::Error> {
        let power32 = u32::try_from(pp.1)?;
        Ok(Self(pp.0.into(), power32))
    }
}

impl From<PrimePower> for u32 {
    fn from(pp: PrimePower) -> Self {
        u32::from(pp.0).pow(pp.1)
    }
}

impl From<&PrimePower> for u32 {
    fn from(pp: &PrimePower) -> Self {
        u32::from(pp.0).pow(pp.1)
    }
}

impl From<PrimePower> for BigUint {
    fn from(pp: PrimePower) -> Self {
        BigUint::from(pp.0).pow(pp.1)
    }
}

impl From<&PrimePower> for BigUint {
    fn from(pp: &PrimePower) -> Self {
        BigUint::from(pp.0).pow(pp.1)
    }
}

impl Display for PrimePower {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}^{}", self.0, self.1)
    }
}


impl Rem<&PrimePower> for u32 {
    type Output = Self;
    fn rem(self, rhs: &PrimePower) -> Self::Output {
        self % u32::from(rhs)
    }
}

impl Rem<PrimePower> for u32 {
    type Output = Self;
    fn rem(self, rhs: PrimePower) -> Self::Output {
        self.rem(&rhs)
    }
}

impl Div<&PrimePower> for u32 {
    type Output = Self;
    fn div(self, rhs: &PrimePower) -> Self::Output {
        self / u32::from(rhs)
    }
}

impl Div<PrimePower> for u32 {
    type Output = Self;
    fn div(self, rhs: PrimePower) -> Self::Output {
        self.div(&rhs)
    }
}


impl Mul for &PrimePower {
    type Output = PrimePower;

    // Ignore suspicious + in the Mul impl
    #[allow(clippy::suspicious_arithmetic_impl)]
    fn mul(self, rhs: Self) -> Self::Output {
        assert!(self.p() == rhs.p(), "Cannot multiply distinct PrimePowers");
        PrimePower(self.p(), self.power() + rhs.power())
    }

}
impl Mul<PrimePower> for &PrimePower {
    type Output = PrimePower;
    fn mul(self, rhs: PrimePower) -> Self::Output {
        self.mul(&rhs)
    }
}
impl Mul<&PrimePower> for PrimePower {
    type Output = PrimePower;
    fn mul(self, rhs: &PrimePower) -> Self::Output {
        (&self).mul(rhs)
    }
}
impl Mul<PrimePower> for PrimePower {
    type Output = PrimePower;
    fn mul(self, rhs: PrimePower) -> Self::Output {
        (&self).mul(&rhs)
    }
}

impl MulAssign for PrimePower {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl Pow<u32> for PrimePower {
    type Output = PrimePower;
    fn pow(self, power: u32) -> Self::Output {
        PrimePower(self.0, self.1 * power)
    }
}


#[cfg(test)]
mod tests {

    use crate::divisible::Modulus;
    use super::PrimePower;

    #[test]
    fn modular_methods() {
        let pp = PrimePower(5.into(), 2);

        assert_eq!(23, pp.mod_neg(2));
        assert_eq!(3, pp.mod_neg(22));

        assert_eq!(1, pp.mod_exp(5, 0));
        assert_eq!(5, pp.mod_exp(5, 1));
        assert_eq!(0, pp.mod_exp(5, 2));
        assert_eq!(0, pp.mod_exp(5, 3));
        assert_eq!(2, pp.mod_exp(3, 3));
        assert_eq!(6, pp.mod_exp(3, 4));
        assert_eq!(0, pp.mod_exp(0, 0));
        assert_eq!(0, pp.mod_exp(0, 3));
        assert_eq!(1, pp.mod_exp(1, 7));

    }

}