lambdaworks_math/
cyclic_group.rs

1use crate::unsigned_integer::traits::IsUnsignedInteger;
2
3pub trait IsGroup: Clone + PartialEq + Eq {
4    /// Returns the neutral element of the group. The equality
5    /// `neutral_element().operate_with(g) == g` must hold
6    /// for every group element `g`.
7    fn neutral_element() -> Self;
8
9    /// Check if an element the neutral element.
10    fn is_neutral_element(&self) -> bool {
11        self == &Self::neutral_element()
12    }
13
14    /// Applies the group operation `times` times with itself
15    /// The operation can be addition or multiplication depending on
16    /// the notation of the particular group.
17    fn operate_with_self<T: IsUnsignedInteger>(&self, mut exponent: T) -> Self {
18        let mut result = Self::neutral_element();
19        let mut base = self.clone();
20
21        while exponent != T::from(0) {
22            if exponent & T::from(1) == T::from(1) {
23                result = Self::operate_with(&result, &base);
24            }
25            exponent >>= 1;
26            base = Self::operate_with(&base, &base);
27        }
28        result
29    }
30
31    /// Applies the group operation between `self` and `other`.
32    /// The operation can be addition or multiplication depending on
33    /// the notation of the particular group.
34    fn operate_with(&self, other: &Self) -> Self;
35
36    /// Provides the inverse of the group element.
37    /// This is the unique y such that for any x
38    /// x.operate_with(y) returns the neutral element
39    fn neg(&self) -> Self;
40}
lambdaworks_math/cyclic_group.rs

lambdaworks_math/
cyclic_group.rs
