Trait un_algebra::group::mul_group::NumMulGroup

pub trait NumMulGroup: NumMulMonoid {
    fn invert(&self) -> Self;
    fn is_invertible(&self) -> bool;

    fn div(&self, other: &Self) -> Self { ... }
    fn axiom_left_invert(&self, eps: &Self::Error) -> bool { ... }
    fn axiom_right_invert(&self, eps: &Self::Error) -> bool { ... }
}

A "numeric" algebraic multiplicative group.

NumAddGroup trait is for types that only form multiplicative groups when "numeric" comparisons are used, e.g. floating point types.

Required Methods

fn invert(&self) -> Self

The unique multiplicative inverse of a group element. Inversion is only defined for invertible group elements.

fn is_invertible(&self) -> bool

Test for an invertible group element.

Provided Methods

fn div(&self, other: &Self) -> Self

The multiplicative "division" of two group elements.

fn axiom_left_invert(&self, eps: &Self::Error) -> bool

Numerically test the left axiom of inversion.

fn axiom_right_invert(&self, eps: &Self::Error) -> bool

Numerically test the right axiom of inversion.

Implementations on Foreign Types

impl NumMulGroup for f32

fn invert(&self) -> Self

Inversion is just floating point inversion.

fn is_invertible(&self) -> bool

Non-zero elements are invertible.

fn div(&self, other: &Self) -> Self

fn axiom_left_invert(&self, eps: &Self::Error) -> bool

fn axiom_right_invert(&self, eps: &Self::Error) -> bool

impl NumMulGroup for f64

fn invert(&self) -> Self

Inversion is just floating point inversion.

fn is_invertible(&self) -> bool

Non-zero elements are invertible.

fn div(&self, other: &Self) -> Self

fn axiom_left_invert(&self, eps: &Self::Error) -> bool

fn axiom_right_invert(&self, eps: &Self::Error) -> bool

impl<A: NumMulGroup> NumMulGroup for (A,)

1-tuples form a numeric multiplicative group if their corresponding items form numeric multiplicative groups.

fn invert(&self) -> Self

Inversion is by matching element.

fn is_invertible(&self) -> bool

Invertibility is across the tuple.

fn div(&self, other: &Self) -> Self

fn axiom_left_invert(&self, eps: &Self::Error) -> bool

fn axiom_right_invert(&self, eps: &Self::Error) -> bool

impl<A: NumMulGroup> NumMulGroup for (A, A)

Homogeneous 2-tuples form a numeric multiplicative group if their corresponding items form numeric multiplicative groups. We can only implement homogeneous tuples since numeric comparisons require a single numeric error type.

fn invert(&self) -> Self

Inversion is by matching element.

fn is_invertible(&self) -> bool

Invertibility is across the tuple.

fn div(&self, other: &Self) -> Self

fn axiom_left_invert(&self, eps: &Self::Error) -> bool

fn axiom_right_invert(&self, eps: &Self::Error) -> bool

impl<A: NumMulGroup> NumMulGroup for (A, A, A)

Homogeneous 3-tuples form a numeric multiplicative group if their corresponding items form numeric multiplicative groups. We can only implement homogeneous tuples since numeric comparisons require a single numeric error type.

fn invert(&self) -> Self

Inversion is by matching element.

fn is_invertible(&self) -> bool

Invertibility is across the tuple.

fn div(&self, other: &Self) -> Self

fn axiom_left_invert(&self, eps: &Self::Error) -> bool

fn axiom_right_invert(&self, eps: &Self::Error) -> bool

impl<T: Real> NumMulGroup for Complex<T>

Non-zero complex numbers (with real components) form a numeric multiplicative group.

fn invert(&self) -> Self

Inversion is just complex inversion.

fn is_invertible(&self) -> bool

Non-zero complex numbers are invertible.

fn div(&self, other: &Self) -> Self

fn axiom_left_invert(&self, eps: &Self::Error) -> bool

fn axiom_right_invert(&self, eps: &Self::Error) -> bool

Implementors