Trait OrderedRing 

pub trait OrderedRing: RingBase {
    // Required method
    fn cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering;

    // Provided methods
    fn abs_cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering { ... }
    fn is_leq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool { ... }
    fn is_geq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool { ... }
    fn is_lt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool { ... }
    fn is_gt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool { ... }
    fn is_neg(&self, value: &Self::Element) -> bool { ... }
    fn is_pos(&self, value: &Self::Element) -> bool { ... }
    fn abs(&self, value: Self::Element) -> Self::Element { ... }
    fn max<'a>(
        &self,
        fst: &'a Self::Element,
        snd: &'a Self::Element,
    ) -> &'a Self::Element { ... }
}

Trait for rings that have a total ordering on their elements. The ordering must be compatible with addition and multiplication in the usual sense.

In particular, this should only be implemented for rings that are subrings of the real numbers.

Required Methods

fn cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering

Returns whether lhs is Ordering::Less, Ordering::Equal or Ordering::Greater than rhs.

Provided Methods

fn abs_cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering

Returns whether abs(lhs) is Ordering::Less, Ordering::Equal or Ordering::Greater than abs(rhs).

fn is_leq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs <= rhs.

fn is_geq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs >= rhs.

fn is_lt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs < rhs.

fn is_gt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs > rhs.

fn is_neg(&self, value: &Self::Element) -> bool

Returns whether value < 0.

fn is_pos(&self, value: &Self::Element) -> bool

Returns whether value > 0.

fn abs(&self, value: Self::Element) -> Self::Element

Returns the absolute value of value, i.e. value if value >= 0 and -value otherwise.

fn max<'a>( &self, fst: &'a Self::Element, snd: &'a Self::Element, ) -> &'a Self::Element

Returns the larger one of fst and snd.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl OrderedRing for Real64Base

impl OrderedRing for MPZBase

Available on crate feature mpir only.

impl<'a, R> OrderedRing for IntegersWithLocalZnQuotient<'a, R>

where R: Sized + SelfIso + ZnRing + FromModulusCreateableZnRing + Clone,

impl<A: Allocator + Clone> OrderedRing for RustBigintRingBase<A>

impl<I> OrderedRing for RationalFieldBase<I>

where I: RingStore, I::Type: IntegerRing,

impl<T: PrimitiveInt> OrderedRing for StaticRingBase<T>