Trait AdditiveGroup

Source

pub trait AdditiveGroup:
    Eq
    + 'static
    + Sized
    + Copy
    + Clone
    + Default
    + Send
    + Sync
    + Hash
    + Debug
    + Display
    + Zeroize
    + Zero
    + Neg<Output = Self>
    + Add<Self, Output = Self>
    + Sub<Self, Output = Self>
    + Mul<Self::Scalar, Output = Self>
    + AddAssign<Self>
    + SubAssign<Self>
    + MulAssign<Self::Scalar>
    + for<'a> Add<&'a Self, Output = Self>
    + for<'a> Sub<&'a Self, Output = Self>
    + for<'a> Mul<&'a Self::Scalar, Output = Self>
    + for<'a> AddAssign<&'a Self>
    + for<'a> SubAssign<&'a Self>
    + for<'a> MulAssign<&'a Self::Scalar>
    + for<'a> Add<&'a mut Self, Output = Self>
    + for<'a> Sub<&'a mut Self, Output = Self>
    + for<'a> Mul<&'a mut Self::Scalar, Output = Self>
    + for<'a> AddAssign<&'a mut Self>
    + for<'a> SubAssign<&'a mut Self>
    + for<'a> MulAssign<&'a mut Self::Scalar>
    + Sum<Self>
    + for<'a> Sum<&'a Self> {
    type Scalar: Field;

    const ZERO: Self;

    // Provided methods
    fn double(&self) -> Self { ... }
    fn double_in_place(&mut self) -> &mut Self { ... }
    fn neg_in_place(&mut self) -> &mut Self { ... }
}

Expand description

Defines an abstract group with additive notation. Support addition and subtraction with itself and multiplication by scalar. Scalar and group can be different types.

E.g., points on an elliptic curve define an additive group and can be multiplied by a scalar.