Trait un_algebra::group::add_group::NumAddGroup

pub trait NumAddGroup: NumAddMonoid {
    fn negate(&self) -> Self;

    fn sub(&self, other: &Self) -> Self { ... }
    fn axiom_left_negate(&self, eps: &Self::Eps) -> bool { ... }
    fn axiom_right_negate(&self, eps: &Self::Eps) -> bool { ... }
}

A "numeric" algebraic additive group.

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

Required methods

fn negate(&self) -> Self

The unique additive inverse of a group element.

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Provided methods

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

The additive "subtraction" of two group elements.

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

Numerically test the (left) axiom of negation.

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

Numerically test the (right) axiom of negation.

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Implementations on Foreign Types

impl NumAddGroup for f32

fn negate(&self) -> Self

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

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

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

impl NumAddGroup for f64

fn negate(&self) -> Self

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

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

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

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

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

fn negate(&self) -> Self

Negation is by element.

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

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

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

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

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

fn negate(&self) -> Self

Negation is by element.

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

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

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

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

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

fn negate(&self) -> Self

Negation is by element.

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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

fn negate(&self) -> Self

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

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

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

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Implementors

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