alga/general/
specialized.rs

1use crate::general::{
2    AbstractField, AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma,
3    AbstractModule, AbstractMonoid, AbstractQuasigroup, AbstractRing, AbstractRingCommutative,
4    AbstractSemigroup, Additive, ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub,
5    Multiplicative,
6};
7use num::{One, Zero};
8
9macro_rules! specialize_structures(
10    // **With type parameters** for the trait being implemented.
11    ($specialized: ident, $abstract_trait: ident<$($ops: ident),*> : $($bounds: ident)*) => {
12        /// [Alias] Algebraic structure specialized for one kind of operation.
13        pub trait $specialized: $abstract_trait<$($ops),*> $(+ $bounds)* { }
14        impl<T: $abstract_trait<$($ops),*> $(+ $bounds)*> $specialized for T { }
15    };
16    // **Without type parameters** for the trait being implemented.
17    ($specialized: ident, $abstract_trait: ident : $($bounds: ident)*) => {
18        /// [Alias] Algebraic structure specialized for one kind of operation.
19        pub trait $specialized: $abstract_trait $(+ $bounds)* { }
20        impl<T: $abstract_trait $(+ $bounds)*> $specialized for T { }
21    }
22);
23
24specialize_structures!(AdditiveMagma,        AbstractMagma<Additive>        : );
25specialize_structures!(AdditiveQuasigroup,   AbstractQuasigroup<Additive>   : AdditiveMagma ClosedSub);
26specialize_structures!(AdditiveLoop,         AbstractLoop<Additive>         : AdditiveQuasigroup ClosedNeg Zero);
27specialize_structures!(AdditiveSemigroup,    AbstractSemigroup<Additive>    : AdditiveMagma ClosedAdd);
28specialize_structures!(AdditiveMonoid,       AbstractMonoid<Additive>       : AdditiveSemigroup Zero);
29specialize_structures!(AdditiveGroup,        AbstractGroup<Additive>        : AdditiveLoop AdditiveMonoid);
30specialize_structures!(AdditiveGroupAbelian, AbstractGroupAbelian<Additive> : AdditiveGroup);
31
32specialize_structures!(MultiplicativeMagma,      AbstractMagma<Multiplicative>      : );
33specialize_structures!(MultiplicativeQuasigroup, AbstractQuasigroup<Multiplicative> : MultiplicativeMagma ClosedDiv);
34specialize_structures!(MultiplicativeLoop,       AbstractLoop<Multiplicative>       : MultiplicativeQuasigroup One);
35specialize_structures!(MultiplicativeSemigroup,  AbstractSemigroup<Multiplicative>  : MultiplicativeMagma ClosedMul);
36specialize_structures!(MultiplicativeMonoid,     AbstractMonoid<Multiplicative>     : MultiplicativeSemigroup One);
37specialize_structures!(MultiplicativeGroup,      AbstractGroup<Multiplicative>      : MultiplicativeLoop MultiplicativeMonoid);
38specialize_structures!(MultiplicativeGroupAbelian, AbstractGroupAbelian<Multiplicative> : MultiplicativeGroup);
39
40specialize_structures!(Ring,            AbstractRing:            AdditiveGroupAbelian MultiplicativeMonoid);
41specialize_structures!(RingCommutative, AbstractRingCommutative: Ring);
42specialize_structures!(Field,           AbstractField:           RingCommutative MultiplicativeGroupAbelian);
43
44/// A module which overloads the `*` and `+` operators.
45pub trait Module:
46    AbstractModule<AbstractRing = <Self as Module>::Ring>
47    + AdditiveGroupAbelian
48    + ClosedMul<<Self as Module>::Ring>
49{
50    /// The underlying scalar field.
51    type Ring: RingCommutative;
52}
53
54// FIXME: unfortunately, Module cannot be auto-impl-ed.
55impl<N: RingCommutative + num::NumAssign> Module for num_complex::Complex<N> {
56    type Ring = N;
57}
58
59macro_rules! impl_module(
60    ($($T:ty),*) => {
61        $(impl Module for $T{
62            type Ring = $T;
63        })*
64    }
65);
66
67impl_module!(i8, i16, i32, i64, isize, f32, f64);
alga/general/specialized.rs

alga/general/
specialized.rs
