OrderedMagma

catdef.spad line 954 [edit on github]

Magmas with compatible ordering, where both left and right multiplication is strictly increasing. Axioms: for all x, y, z x < y => x*z < y*z x < y => z*x < z*y.

*: (%, %) -> %

from Magma

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

latex: % -> String

from SetCategory

leftPower: (%, PositiveInteger) -> %

from Magma

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

negative?: % -> Boolean if % has SetWithZero

from OrderedSet

positive?: % -> Boolean if % has SetWithZero

from OrderedSet

rightPower: (%, PositiveInteger) -> %

from Magma

sign: % -> Integer if % has SetWithZero

from OrderedSet

smaller?: (%, %) -> Boolean

from Comparable

BasicType

CoercibleTo OutputForm

Comparable

Magma

OrderedSet

PartialOrder

SetCategory