Module ordered

Traits for ordered structures

Traits

AddOrdered

A marker trait signifying that for x > y, x+z > x+z and z+x > z+x for all z

ArchimedeanDiv

Division with remainder using an ordering and the Archimedean Property

ArchimedeanProperty

The property that if x < y, there exists some natural n where n*x = x*...*x > y

MulOrdered

A marker trait signifying that for x > y, x*z > x*z and z*x > z*x for all z > 0

Ord

Trait for types that form a total order.

PartialOrd

Trait for types that form a partial order.

Sign

Helpful methods for manipulating an element’s order relative to 0

Signed

Helpful methods for measuring an element’s order relative to 0

Derive Macros

Ord

Derive macro generating an impl of the trait Ord. The behavior of this macro is described in detail here.

PartialOrd

Derive macro generating an impl of the trait PartialOrd. The behavior of this macro is described in detail here.

Trait Aliases

ArchAbelianGroup

An ordered abeliean group with the Archimedean property

ArchCommutativeRing

An ordered commutative ring with the Archimedean property and Archimedean division

ArchCommutativeSemiring

An ordered commutative semiring with the Archimedean property and Archimedean division

ArchDivisionRing

An ordered division ring with the Archimedean property and Archimedean division

ArchDivisionSemiring

An ordered division semiring with the Archimedean property and Archimedean division

ArchField

An ordered field ring with the Archimedean property and Archimedean division

ArchGroup

An ordered group with the Archimedean property

ArchMonoid

An ordered monoid with the Archimedean property

ArchRing

An ordered ring with the Archimedean property

ArchSemigroup

An ordered semigroup with the Archimedean property

ArchSemiring

An ordered semiring with the Archimedean property

ArchUnitalRing

An ordered unital ring with the Archimedean property and Archimedean division

ArchUnitalSemiring

An ordered unital semiring with the Archimedean property and Archimedean division

OrdAbelianGroup

An additive abelian group with an ordered addition operation

OrdCommutativeRing

A commutative ring with ordered addition and multiplication

OrdCommutativeSemiring

A commutative semiring with ordered addition and multiplication

OrdDivisionRing

A division ring with ordered addition and multiplication

OrdDivisionSemiring

A division semiring with ordered addition and multiplication

OrdField

A field with ordered addition and multiplication

OrdGroup

An additive group with an ordered addition operation

OrdLoop

An additive loop with an ordered addition operation

OrdMagma

An additive magma with an ordered addition operation

OrdMonoid

An additive monoid with an ordered addition operation

OrdRing

A ring with ordered addition and multiplication

OrdSemigroup

An additive semigroup with an ordered addition operation

OrdSemiring

A semiring with ordered addition and multiplication

OrdUnitalRing

A unital ring with ordered addition and multiplication

OrdUnitalSemiring

A unitial semiring with ordered addition and multiplication