Trait un_algebra::group::mul_group::NumMulGroup

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

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

Test for an invertible group element.

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Provided methods

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

The multiplicative "division" of two group elements.

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

Numerically test the (left) axiom of inversion.

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

Numerically test the (right) axiom of inversion.

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Implementations on Foreign Types

impl NumMulGroup for f32

fn invert(&self) -> Self

Inversion is just floating point inversion.

fn is_invertible(&self, eps: &Self::Eps) -> bool

Non-zero elements are invertible.

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

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

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

impl NumMulGroup for f64

fn invert(&self) -> Self

Inversion is just floating point inversion.

fn is_invertible(&self, eps: &Self::Eps) -> bool

Non-zero elements are invertible.

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

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

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

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

1-tuples form a numeric multiplicative group when their items do.

fn invert(&self) -> Self

Inversion is by matching element.

fn is_invertible(&self, eps: &Self::Eps) -> bool

Invertibility is across the tuple.

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

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

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

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

Homogeneous 2-tuples form a numeric multiplicative group when their items do. Numeric comparisons require a common numeric error type.

fn invert(&self) -> Self

Inversion is by matching element.

fn is_invertible(&self, eps: &Self::Eps) -> bool

Invertibility is across the tuple.

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

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

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

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

Homogeneous 3-tuples form a numeric multiplicative group when their items do. Numeric comparisons require a common numeric error type.

fn invert(&self) -> Self

Inversion is by matching element.

fn is_invertible(&self, eps: &Self::Eps) -> bool

Invertibility is across the tuple.

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 0]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 1]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 2]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 3]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 4]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 5]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 6]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 7]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 8]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 9]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 10]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 11]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 12]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 13]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 14]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 15]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

impl<T: Copy + Default + NumMulGroup> NumMulGroup for [T; 16]

fn is_invertible(&self, eps: &Self::Eps) -> bool

fn invert(&self) -> Self

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

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

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

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Implementors

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