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// Copyright 2013-2014 The Algebra Developers. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. use general::{Magma, Op, Inverse, Additive, Multiplicative}; use cmp::ApproxEq; /// A magma with the divisibility property. /// /// Divisibility is a weak form of right and left invertibility: /// /// ```notrust /// ∀ a, b ∈ Self, ∃! r, l ∈ Self such that l ∘ a = b and a ∘ r = b /// ``` pub trait Quasigroup<O: Op> : Magma<O> + Inverse<O> { /// Returns `true` if latin squareness holds for the given arguments. fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where Self: ApproxEq { let (a, b) = (|| args.0.clone(), || args.1.clone()); a().approx_eq(&(a().operate(b().inv()).operate(b()))) && a().approx_eq(&(a().operate(b().operate(b().inv())))) // TODO: pseudo inverse? } } impl_marker!(Quasigroup<Additive>; i8, i16, i32, i64, f32, f64); impl_marker!(Quasigroup<Multiplicative>; f32, f64); #[cfg(test)] mod tests { macro_rules! check_int { ($($T:ident),* $(,)*) => { $(mod $T { use ops::Additive; use general::Quasigroup; #[quickcheck] fn prop_inv_is_latin_square(args: ($T, $T)) -> bool { Quasigroup::<Additive>::prop_inv_is_latin_square(args) } })+ } } //check_int!(u8); //check_int!(u16); //check_int!(u32); //check_int!(u64); check_int!(i8, i16, i32, i64); }