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use crate::elliptic_curve::traits::IsEllipticCurve;
use crate::field::element::FieldElement;
use core::fmt::Debug;

/// Trait to add elliptic curves behaviour to a struct.
pub trait IsMontgomery: IsEllipticCurve + Clone + Debug {
    fn a() -> FieldElement<Self::BaseField>;

    fn b() -> FieldElement<Self::BaseField>;

    /// Evaluates the short Weierstrass equation at (x, y z).
    /// Used for checking if [x: y: z] belongs to the elliptic curve.
    fn defining_equation(
        x: &FieldElement<Self::BaseField>,
        y: &FieldElement<Self::BaseField>,
    ) -> FieldElement<Self::BaseField> {
        (Self::b() * y.pow(2_u16)) - (x.pow(3_u16) + Self::a() * x.pow(2_u16) + x)
    }
}