qfall-math 0.1.1

// Copyright © 2023 Phil Milewski, Marcel Luca Schmidt
//
// This file is part of qFALL-math.
//
// qFALL-math is free software: you can redistribute it and/or modify it under
// the terms of the Mozilla Public License Version 2.0 as published by the
// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.

//! Implementation of the [`Mul`] trait for [`PolyOverQ`] values.

use super::super::PolyOverQ;
use crate::{
    integer::PolyOverZ,
    macros::arithmetics::{
        arithmetic_assign_trait_borrowed_to_owned, arithmetic_trait_borrowed_to_owned,
        arithmetic_trait_mixed_borrowed_owned, arithmetic_trait_reverse,
    },
};
use flint_sys::fmpq_poly::fmpq_poly_mul;
use std::ops::{Mul, MulAssign};

impl MulAssign<&PolyOverQ> for PolyOverQ {
    /// Computes the multiplication of `self` and `other` reusing
    /// the memory of `self`.
    /// [`MulAssign`] can be used on [`PolyOverQ`] in combination with
    /// [`PolyOverQ`] and [`PolyOverZ`].
    ///
    /// Parameters:
    /// - `other`: specifies the polynomial to multiply to `self`
    ///
    /// Returns the product of both polynomials as a [`PolyOverQ`].
    ///
    /// # Examples
    /// ```
    /// use qfall_math::{rational::PolyOverQ, integer::PolyOverZ};
    /// use std::str::FromStr;
    ///
    /// let mut a = PolyOverQ::from_str("3  1 2/3 -3/4").unwrap();
    /// let b = PolyOverQ::from_str("5  1 2 -3 0 8/9").unwrap();
    /// let c = PolyOverZ::from_str("2  -1 2").unwrap();
    ///
    /// a *= &b;
    /// a *= b;
    /// a *= &c;
    /// a *= c;
    /// ```
    fn mul_assign(&mut self, other: &Self) {
        unsafe { fmpq_poly_mul(&mut self.poly, &self.poly, &other.poly) };
    }
}
impl MulAssign<&PolyOverZ> for PolyOverQ {
    /// Documentation at [`PolyOverQ::mul_assign`].
    fn mul_assign(&mut self, other: &PolyOverZ) {
        let other = PolyOverQ::from(other);

        self.mul_assign(other);
    }
}

arithmetic_assign_trait_borrowed_to_owned!(MulAssign, mul_assign, PolyOverQ, PolyOverQ);
arithmetic_assign_trait_borrowed_to_owned!(MulAssign, mul_assign, PolyOverQ, PolyOverZ);

impl Mul for &PolyOverQ {
    type Output = PolyOverQ;
    /// Implements the [`Mul`] trait for two [`PolyOverQ`] values.
    /// [`Mul`] is implemented for any combination of [`PolyOverQ`] and borrowed [`PolyOverQ`].
    ///
    /// Parameters:
    /// - `other`: specifies the value to multiply with `self`
    ///
    /// Returns the product of both polynomials as a [`PolyOverQ`].
    ///
    /// # Examples
    /// ```
    /// use qfall_math::rational::PolyOverQ;
    /// use std::str::FromStr;
    ///
    /// let a: PolyOverQ = PolyOverQ::from_str("3  1/7 2/5 -3").unwrap();
    /// let b: PolyOverQ = PolyOverQ::from_str("5  1/9 2/5 -3/17 0 8/9").unwrap();
    ///
    /// let c: PolyOverQ = &a * &b;
    /// let d: PolyOverQ = a * b;
    /// let e: PolyOverQ = &c * d;
    /// let f: PolyOverQ = c * &e;
    /// ```
    fn mul(self, other: Self) -> Self::Output {
        let mut out = PolyOverQ::default();
        unsafe {
            fmpq_poly_mul(&mut out.poly, &self.poly, &other.poly);
        }
        out
    }
}

arithmetic_trait_borrowed_to_owned!(Mul, mul, PolyOverQ, PolyOverQ, PolyOverQ);
arithmetic_trait_mixed_borrowed_owned!(Mul, mul, PolyOverQ, PolyOverQ, PolyOverQ);

impl Mul<&PolyOverZ> for &PolyOverQ {
    type Output = PolyOverQ;
    /// Implements the [`Mul`] trait for [`PolyOverQ`] and [`PolyOverZ`].
    /// [`Mul`] is implemented for any combination of owned and borrowed values.
    ///
    /// Parameters:
    /// - `other`: specifies the polynomial to multiply to `self`
    ///
    /// Returns the product of both polynomials as a [`PolyOverQ`].
    ///
    /// # Examples
    /// ```
    /// use qfall_math::rational::PolyOverQ;
    /// use qfall_math::integer::PolyOverZ;
    /// use std::str::FromStr;
    ///
    /// let a = PolyOverQ::from_str("4  1/2 0 3/7 1").unwrap();
    /// let b = PolyOverZ::from_str("4  2 0 3 1").unwrap();
    ///
    /// let c: PolyOverQ = &a * &b;
    /// ```
    fn mul(self, other: &PolyOverZ) -> Self::Output {
        let mut out = PolyOverQ::default();
        unsafe {
            fmpq_poly_mul(&mut out.poly, &self.poly, &PolyOverQ::from(other).poly);
        }
        out
    }
}

arithmetic_trait_reverse!(Mul, mul, PolyOverZ, PolyOverQ, PolyOverQ);

arithmetic_trait_borrowed_to_owned!(Mul, mul, PolyOverQ, PolyOverZ, PolyOverQ);
arithmetic_trait_borrowed_to_owned!(Mul, mul, PolyOverZ, PolyOverQ, PolyOverQ);
arithmetic_trait_mixed_borrowed_owned!(Mul, mul, PolyOverQ, PolyOverZ, PolyOverQ);
arithmetic_trait_mixed_borrowed_owned!(Mul, mul, PolyOverZ, PolyOverQ, PolyOverQ);

#[cfg(test)]
mod test_mul_assign {
    use super::PolyOverQ;
    use crate::integer::PolyOverZ;
    use std::str::FromStr;

    /// Ensure that `mul_assign` works for small numbers.
    #[test]
    fn correct_small() {
        let mut a = PolyOverQ::from_str("3  1/7 2/7 -3/7").unwrap();
        let b = PolyOverQ::from_str("5  1/11 2/11 5/11 1/11 2/11").unwrap();

        a *= b;

        assert_eq!(
            a,
            PolyOverQ::from_str("7  1/77 4/77 6/77 5/77 -11/77 1/77 -6/77").unwrap()
        );
    }

    /// Ensure that `mul_assign` works for large numbers.
    #[test]
    fn correct_large() {
        let mut a = PolyOverQ::from_str(&format!("2  {} {}", 2, i64::MIN)).unwrap();
        let b = PolyOverQ::from_str(&format!(
            "2  {}/{} {}/{}",
            u32::MAX,
            u128::MAX,
            i64::MAX,
            u128::MAX
        ))
        .unwrap();

        a *= b;

        assert_eq!(
            a,
            PolyOverQ::from_str(&format!(
                "3  {}/{} {}/{} {}/{}",
                2_u128 * u128::from(u32::MAX),
                u128::MAX,
                2_i128 * i128::from(i64::MAX) + i128::from(u32::MAX) * i128::from(i64::MIN),
                u128::MAX,
                i128::from(i64::MAX) * i128::from(i64::MIN),
                u128::MAX
            ))
            .unwrap()
        );
    }

    /// Ensure that `mul_assign` is available for all types.
    #[test]
    fn availability() {
        let mut a = PolyOverQ::from_str("3  1 2 -3").unwrap();
        let b = PolyOverQ::from_str("3  -1 -2 3").unwrap();
        let c = PolyOverZ::from_str("4  2 -1 2 3").unwrap();

        a *= &b;
        a *= b;
        a *= &c;
        a *= c;
    }
}

#[cfg(test)]
mod test_mul {
    use super::PolyOverQ;
    use std::str::FromStr;

    /// Testing multiplication for two [`PolyOverQ`]
    #[test]
    fn mul() {
        let a: PolyOverQ = PolyOverQ::from_str("3  1/7 2/7 -3/7").unwrap();
        let b: PolyOverQ = PolyOverQ::from_str("5  1/11 2/11 5/11 1/11 2/11").unwrap();
        let c: PolyOverQ = a * b;
        assert_eq!(
            c,
            PolyOverQ::from_str("7  1/77 4/77 6/77 5/77 -11/77 1/77 -6/77").unwrap()
        );
    }

    /// Testing multiplication for two borrowed [`PolyOverQ`]
    #[test]
    fn mul_borrow() {
        let a: PolyOverQ = PolyOverQ::from_str("3  1/7 2/7 -3/7").unwrap();
        let b: PolyOverQ = PolyOverQ::from_str("5  1/11 2/11 5/11 1/11 2/11").unwrap();
        let c: PolyOverQ = &a * &b;
        assert_eq!(
            c,
            PolyOverQ::from_str("7  1/77 4/77 6/77 5/77 -11/77 1/77 -6/77").unwrap()
        );
    }

    /// Testing multiplication for borrowed [`PolyOverQ`] and [`PolyOverQ`]
    #[test]
    fn mul_first_borrowed() {
        let a: PolyOverQ = PolyOverQ::from_str("3  1/7 2/7 -3/7").unwrap();
        let b: PolyOverQ = PolyOverQ::from_str("5  1/11 2/11 5/11 1/11 2/11").unwrap();
        let c: PolyOverQ = &a * b;
        assert_eq!(
            c,
            PolyOverQ::from_str("7  1/77 4/77 6/77 5/77 -11/77 1/77 -6/77").unwrap()
        );
    }

    /// Testing multiplication for [`PolyOverQ`] and borrowed [`PolyOverQ`]
    #[test]
    fn mul_second_borrowed() {
        let a: PolyOverQ = PolyOverQ::from_str("3  1/7 2/7 -3/7").unwrap();
        let b: PolyOverQ = PolyOverQ::from_str("5  1/11 2/11 5/11 1/11 2/11").unwrap();
        let c: PolyOverQ = a * &b;
        assert_eq!(
            c,
            PolyOverQ::from_str("7  1/77 4/77 6/77 5/77 -11/77 1/77 -6/77").unwrap()
        );
    }

    /// Testing multiplication with a constant [`PolyOverQ`]
    #[test]
    fn mul_constant() {
        let a: PolyOverQ = PolyOverQ::from_str("3  1/11 1/2 -7/3").unwrap();
        let b: PolyOverQ = PolyOverQ::from_str("1  4/7").unwrap();
        let c: PolyOverQ = a * b;
        assert_eq!(c, PolyOverQ::from_str("3  4/77 2/7 -4/3").unwrap());
    }

    /// Testing multiplication with `0`
    #[test]
    fn mul_zero() {
        let a: PolyOverQ = PolyOverQ::from_str("3  1/18 2/7 -3/10").unwrap();
        let b: PolyOverQ = PolyOverQ::default();
        let c: PolyOverQ = a * b;
        assert_eq!(c, PolyOverQ::default());
    }

    /// Testing multiplication for large [`PolyOverQ`]
    #[test]
    fn mul_large_numbers() {
        let a: PolyOverQ = PolyOverQ::from_str(&format!("2  {} {}", 2, i64::MIN)).unwrap();
        let b: PolyOverQ = PolyOverQ::from_str(&format!(
            "2  {}/{} {}/{}",
            u32::MAX,
            u128::MAX,
            i64::MAX,
            u128::MAX
        ))
        .unwrap();
        let c: PolyOverQ = a * b;

        assert_eq!(
            c,
            PolyOverQ::from_str(&format!(
                "3  {}/{} {}/{} {}/{}",
                2_u128 * u128::from(u32::MAX),
                u128::MAX,
                2_i128 * i128::from(i64::MAX) + i128::from(u32::MAX) * i128::from(i64::MIN),
                u128::MAX,
                i128::from(i64::MAX) * i128::from(i64::MIN),
                u128::MAX
            ))
            .unwrap()
        );
    }
}

#[cfg(test)]
mod test_mul_poly_over_z {
    use super::PolyOverQ;
    use crate::integer::PolyOverZ;
    use std::str::FromStr;

    /// Checks if polynomial multiplication works fine for both borrowed
    #[test]
    fn borrowed_correctness() {
        let poly_1 = PolyOverQ::from_str(&format!("1  1/{}", i64::MAX)).unwrap();
        let poly_2 = PolyOverZ::from_str("2  1 2").unwrap();
        let poly_cmp = PolyOverQ::from_str(&format!("2  1/{} 2/{}", i64::MAX, i64::MAX)).unwrap();

        let poly_1 = &poly_1 * &poly_2;

        assert_eq!(poly_cmp, poly_1);
    }

    /// Checks if multiplication works fine for different types
    #[test]
    fn availability() {
        let poly = PolyOverQ::from_str("3  1/2 2 3/7").unwrap();
        let z = PolyOverZ::from(2);

        _ = poly.clone() * z.clone();
        _ = z.clone() * poly.clone();
        _ = &poly * &z;
        _ = &z * &poly;
        _ = &poly * z.clone();
        _ = z.clone() * &poly;
        _ = &z * poly.clone();
        _ = poly.clone() * &z;
    }
}