Trait FundamentalDiscriminant 

pub trait FundamentalDiscriminant: Discriminant {
    // Provided method
    fn inject<E: Element>(&self, element: impl Element, p: &impl Encoding) -> E
       where Self: NegativeDiscriminant { ... }
}

A fundamental (square-free) discriminant.

Provided Methods

fn inject<E: Element>(&self, element: impl Element, p: &impl Encoding) -> E

where Self: NegativeDiscriminant,

Available on crate feature alloc only.

Take an element of the class group with fundamental discriminant and apply the injection such that it is mapped to an element of the class group with non-fundamental discriminant.

This implements Algorithm 2, GoToNonMaxOrder. We specify it as follows for primitive forms of fundamental negative discriminants:

fn inject(a, b, c, p) {
  discriminant = (b * b) - (4 * a * c)
  (a, b) = coprime_form(a, b, c, p)
  return reduce(a, b * p, discriminant * p * p)
}

This is slightly different in that we do not specify the reduction of $b \mod 2 a$. Instead, we assume the existence of a reduction function, reduce, which inputs the a, b coefficients of an unreduced form and its discriminant before yielding a reduced form.

The resulting form is primitive however. First, the input is bound to be primitive. Second, coprime_form yields an equivalent form, where equivalence preserves primitivity. Finally, coprime_form yields a form whose a coefficient is coprime to p, so scaling the b coefficient by p won’t affect the greatest common divisor of a, b.

This function MAY panic or return an incorrect result if element is not of this discriminant. This function runs in time only variable to the discriminant, the length of the encoding of p, and E::a_b_c_discriminant (which may be implemented in constant-time).

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors

impl<Up, Udk> FundamentalDiscriminant for Cl15k<Up, Udk>