algebraeon_rings/integer/
modulo.rs

1use super::*;
2
3impl<
4    B: BorrowedStructure<IntegerCanonicalStructure>,
5    BE: BorrowedStructure<EuclideanRemainderQuotientStructure<IntegerCanonicalStructure, B, true>>,
6> CountableSetSignature
7    for MultiplicativeMonoidUnitsStructure<
8        EuclideanRemainderQuotientStructure<IntegerCanonicalStructure, B, true>,
9        BE,
10    >
11{
12    fn generate_all_elements(&self) -> impl Iterator<Item = Self::Set> + Clone {
13        self.list_all_elements().into_iter()
14    }
15}
16
17impl<
18    B: BorrowedStructure<IntegerCanonicalStructure>,
19    BE: BorrowedStructure<EuclideanRemainderQuotientStructure<IntegerCanonicalStructure, B, true>>,
20> FiniteSetSignature
21    for MultiplicativeMonoidUnitsStructure<
22        EuclideanRemainderQuotientStructure<IntegerCanonicalStructure, B, true>,
23        BE,
24    >
25{
26    fn list_all_elements(&self) -> Vec<Self::Set> {
27        let mut units = vec![];
28        let mut u = Integer::from(1);
29        while u < Abs::abs(self.monoid().modulus()) {
30            units.push(u.clone());
31            u += Integer::ONE;
32        }
33        units
34    }
35}
36
37impl<B: BorrowedStructure<IntegerCanonicalStructure>> FiniteFieldSignature
38    for EuclideanRemainderQuotientStructure<IntegerCanonicalStructure, B, true>
39{
40    fn characteristic_and_power(&self) -> (Natural, Natural) {
41        (Abs::abs(self.modulus()), Natural::ONE)
42    }
43}
44
45impl<B: BorrowedStructure<IntegerCanonicalStructure>, const IS_FIELD: bool> CountableSetSignature
46    for EuclideanRemainderQuotientStructure<IntegerCanonicalStructure, B, IS_FIELD>
47{
48    fn generate_all_elements(&self) -> impl Iterator<Item = Self::Set> + Clone {
49        (0usize..)
50            .map(Integer::from)
51            .take_while(|n| n < self.modulus())
52    }
53}
54
55impl<B: BorrowedStructure<IntegerCanonicalStructure>, const IS_FIELD: bool> FiniteSetSignature
56    for EuclideanRemainderQuotientStructure<IntegerCanonicalStructure, B, IS_FIELD>
57{
58    fn size(&self) -> usize {
59        Abs::abs(self.modulus()).try_into().unwrap()
60    }
61}
62
63#[cfg(test)]
64mod tests {
65    use super::*;
66
67    #[test]
68    fn count_elements() {
69        assert_eq!(
70            Integer::structure()
71                .into_quotient_ring(26.into())
72                .list_all_elements()
73                .len(),
74            26
75        );
76    }
77}
algebraeon_rings/integer/modulo.rs

algebraeon_rings/integer/
modulo.rs
