mathru 0.16.2

Fundamental algorithms for scientific computing in Rust
Documentation 
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//! Semigroup
use super::{
    magma::{Magma, MagmaAdd, MagmaMul},
    operator::{Addition, Multiplication, Operator},
};

/// A Semigroup is a pair $(\mathbb{S}, \circ)$, composed by a set
/// $\mathbb{S}$ and a binary inner operation $\circ$: # Definition
///
/// ```math
/// \circ: \mathbb{S} \times \mathbb{S} \rightarrow \mathbb{S} , (x, y) \mapsto x \circ y
/// ```
/// and is associative
/// $x, y, z \in \mathbb{S}$
/// $x \circ (y \circ z) = (x \circ y) \circ z$
pub trait Semigroup<O: Operator + Copy>: Magma<O> {
    fn is_associative(self, y: Self, z: Self) -> bool {
        self.clone().operate(y.clone()).operate(z.clone()) == self.operate(y.operate(z))
    }
}

macro_rules! impl_semigroup
(
    ($O:ty; $op: ident; $($T:ty),*) =>
    {
        $(
            impl Semigroup<$O> for $T
            {
            }
        )*
    }
);

impl_semigroup!(Addition; add; u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, f32, f64);
impl_semigroup!(Multiplication; mul; u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, f32, f64);

pub trait SemigroupAdd: Semigroup<Addition> + MagmaAdd {}

macro_rules! impl_semigroupadd
(
    ($($T:ty),*) =>
    {
        $(
            impl SemigroupAdd for $T
            {

            }
        )*
    }
);

impl_semigroupadd!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, f32, f64);

pub trait SemigroupMul: Semigroup<Multiplication> + MagmaMul {}

macro_rules! impl_semigroupmul
(
    ($($T:ty),*) =>
    {
        $(
            impl SemigroupMul for $T
            {

            }
        )*
    }
);

impl_semigroupmul!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, f32, f64);