algeo 0.1.0

Computer algebra, algebraic geometry, and related math.
Documentation 
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use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign};


/// integer type for fractions
pub type I = i64;

#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
pub struct Frac {
    pub numer: I,
    pub denom: I,
}

impl Frac {
    /// returns fraction numer/denom without simplifying
    /// 
    /// not for external use; fractions must always be created in simplest form
    const fn new_unchecked(numer: I, denom: I) -> Self {
        Frac {
            numer,
            denom,
        }
    }

    /// returns the zero element: 0/1
    pub const fn zero() -> Self {
        Frac::new_unchecked(0, 1)
    }

    /// returns the one element: 1/1
    pub const fn one() -> Self {
        Frac::new_unchecked(1, 1)
    }

    /// returns fraction numer/denom in simplest form
    pub fn new(numer: I, denom: I) -> Self {
        if denom == 0 { panic!("denominator cannot be zero") };

        let gcd = gcd(numer, denom);

        Frac::new_unchecked(
            numer * denom.signum() / gcd ,
            denom.abs() / gcd,
        )
    }

    /// for compatibility with Field trait
    pub fn powi(&self, n: i32) -> Self {
        Frac::new_unchecked(
            self.numer.pow(n as u32),
            self.denom.pow(n as u32)
        )
    }
}

impl Add for Frac {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        Frac::new(
            self.numer * other.denom + other.numer * self.denom,
            self.denom * other.denom,
        )
    }
}

impl Sub for Frac {
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        Frac::new(
            self.numer * other.denom - other.numer * self.denom,
            self.denom * other.denom,
        )
    }
}

impl Mul for Frac {
    type Output = Self;

    fn mul(self, other: Self) -> Self {
        Frac::new(
            self.numer * other.numer,
            self.denom * other.denom
        )
    }
}

impl Div for Frac {
    type Output = Self;
    
    fn div(self, other: Self) -> Self {
        Frac::new(
            self.numer * other.denom,
            self.denom * other.numer,
        )
    }
}

/// implements the given operation-assignment traits for fractions in the most
/// obvious way
/// 
/// for example if the operation in question is star, `⋆`, then `a ⋆= b`
/// is the same as `a = a ⋆ b`.
macro_rules! impl_op_assign_for_frac_simple {
    ($trait_name:ty, $op_ass_func:ident, $op_func:ident) => {
        impl $trait_name for Frac {
            #[inline]
            fn $op_ass_func(&mut self, other: Self) {
                *self = self.$op_func(other);
            }
        }
    };
}

impl_op_assign_for_frac_simple! { AddAssign, add_assign, add }
impl_op_assign_for_frac_simple! { SubAssign, sub_assign, sub }
impl_op_assign_for_frac_simple! { MulAssign, mul_assign, mul }
impl_op_assign_for_frac_simple! { DivAssign, div_assign, div }


impl std::fmt::Display for Frac {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}/{}", self.numer, self.denom)
    }
}

/// computes greatest common divisor using Euclidean algorithm
fn gcd(a: i64, b: i64) -> i64 {
    let mut a = a;
    let mut b = b;
    let mut t: i64;

    while b != 0 {
        t = b;
        b = a % b;
        a = t;
    }

    // return 
    a.abs()
}


#[cfg(test)]
mod tests {
    use super::gcd;
    use super::Frac;

    #[test]
    fn test_gcd() {
        assert_eq!(gcd(-10,-15), 5);
        assert_eq!(gcd(-5,-10), 5);
        assert_eq!(gcd(-0,-1), 1);
        assert_eq!(gcd(-5,-6), 1);
        assert_eq!(gcd(-80,-20), 20);
    }

    #[test]
    fn test_frac() {
        assert_eq!(Frac::new(0,1), Frac{ numer: 0, denom: 1});
        assert_eq!(Frac::new(1,1), Frac{ numer: 1, denom: 1});
        assert_eq!(Frac::new(2,2), Frac{ numer: 1, denom: 1});
        assert_eq!(Frac::new(1,2)+Frac::new(1,3), Frac{ numer: 5, denom: 6});
        assert_eq!(Frac::new(1,2)-Frac::new(1,3), Frac{ numer: 1, denom: 6});
        assert_eq!(Frac::new(1,2)*Frac::new(1,3), Frac{ numer: 1, denom: 6});
        assert_eq!(Frac::new(1,2)/Frac::new(1,3), Frac{ numer: 3, denom: 2});
    }
}