[−][src]Trait un_algebra::ring::ring::RingLaws

pub trait RingLaws: Ring {
    fn left_distributivity(&self, x: &Self, y: &Self) -> bool { ... }

    fn right_distributivity(&self, x: &Self, y: &Self) -> bool { ... }

    fn distributivity(&self, x: &Self, y: &Self) -> bool { ... }

    fn left_absorption(&self) -> bool { ... }

    fn right_absorption(&self) -> bool { ... }

    fn absorption(&self) -> bool { ... }

    fn left_negation(&self, x: &Self) -> bool { ... }

    fn right_negation(&self, x: &Self) -> bool { ... }

    fn negation(&self, x: &Self) -> bool { ... }

    fn left_zero_divisors(&self, x: &Self) -> bool { ... }

    fn right_zero_divisors(&self, x: &Self) -> bool { ... }

    fn zero_divisors(&self, x: &Self) -> bool { ... }
}

Laws (axioms and properties) of rings.

Provided methods

fn left_distributivity(&self, x: &Self, y: &Self) -> bool

The axiom of left distributivity (multiplication).

fn right_distributivity(&self, x: &Self, y: &Self) -> bool

The axiom of right distributivity (multiplication).

fn distributivity(&self, x: &Self, y: &Self) -> bool

The axiom of distributivity (multiplication).

fn left_absorption(&self) -> bool

The property of left zero absorption.

fn right_absorption(&self) -> bool

The property of right zero absorption.

fn absorption(&self) -> bool

The property of zero absorption.

fn left_negation(&self, x: &Self) -> bool

The property of left negation (multiplicative).

fn right_negation(&self, x: &Self) -> bool

The property of right negation (multiplicative).

fn negation(&self, x: &Self) -> bool

The property of negation (multiplicative).

fn left_zero_divisors(&self, x: &Self) -> bool

The property of left zero divisors.

fn right_zero_divisors(&self, x: &Self) -> bool

The property of right zero divisors.

fn zero_divisors(&self, x: &Self) -> bool

The property of zero divisors.

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Implementors

impl<R: Ring> RingLaws for R[src]

Blanket implementation of ring laws for ring implementations.

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