yui_core/abst/
ring.rs

1use crate::{AddGrp, AddGrpOps, Mon, MonOps, Sign};
2
3// Rings 
4
5pub trait RingOps<T = Self>: 
6    AddGrpOps<T> + 
7    MonOps<T>
8{}
9
10pub trait Ring: 
11    AddGrp + 
12    Mon + 
13    RingOps
14where
15    for<'a> &'a Self: RingOps<Self>
16{
17    fn from_sign(s: Sign) -> Self { 
18        if s.is_positive() { 
19            Self::one()
20        } else { 
21            -Self::one()
22        }
23    }
24
25    fn inv(&self) -> Option<Self>;
26    fn is_unit(&self) -> bool;
27    fn normalizing_unit(&self) -> Self;
28
29    fn normalized(&self) -> Self { 
30        self.clone().into_normalized()
31    }
32
33    fn into_normalized(self) -> Self { 
34        let u = self.normalizing_unit();
35        if u.is_one() { 
36            self
37        } else { 
38            self * u
39        }
40    }
41    
42    fn is_pm_one(&self) -> bool { 
43        self.is_one() || (-self).is_one()
44    }
45
46    // computational weight
47    fn c_weight(&self) -> f64 { 
48        if self.is_zero() { 
49            0.0
50        } else { 
51            1.0
52        }
53    }
54}
55
56#[cfg(test)]
57mod tests {
58    use crate::Ring;
59 
60    #[test]
61    fn is_pm_one() { 
62        assert!(1.is_pm_one());
63        assert!((-1).is_pm_one());
64        assert!(!2.is_pm_one());
65        assert!(!(-2).is_pm_one());
66    }
67
68    #[test]
69    fn normalized() {
70        assert_eq!(3.normalized(), 3);
71        assert_eq!((-3).normalized(), 3);
72    } 
73
74}
yui_core/abst/ring.rs

yui_core/abst/
ring.rs
