OrderedMagmaWithZeroΒΆ

catdef.spad line 963 [edit on github]

Magmas with zero and compatible ordering. Axioms: for all x, y, z > 0 x < y => x*z < y*z x < y => z*x < z*y, for all x, y, z < 0 x < y => y*z < x*z x < y => z*y < z*x.

0: %

from SetWithZero

*: (%, %) -> %

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

from OrderedSet

positive?: % -> Boolean

from OrderedSet

rightPower: (%, PositiveInteger) -> %

from Magma

sample: %

from SetWithZero

sign: % -> Integer

from OrderedSet

smaller?: (%, %) -> Boolean

from Comparable

zero?: % -> Boolean

from SetWithZero

BasicType

CoercibleTo OutputForm

Comparable

Magma

MagmaWithZero

OrderedSet

PartialOrder

SetCategory

SetWithZero