AInterval R

ainterval.spad line 194 [edit on github]

• R: OrderedAbelianSemiGroup

AInterval(R) implements arithmetic with intervals.

0: % if R has OrderedSemiGroup and % has AbelianMonoid and R has SemiRng or R has OrderedMonoid and R has SemiRing or R has OrderedAbelianMonoid

from AIntervalCategory R

1: % if R has OrderedMonoid and R has SemiRing

from MagmaWithUnit

*: (%, %) -> % if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

from AIntervalCategory R

*: (Integer, %) -> % if % has AbelianGroup and R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing and % has AbelianGroup or R has OrderedAbelianGroup

from AIntervalCategory R

*: (NonNegativeInteger, %) -> % if R has OrderedSemiGroup and % has AbelianMonoid and R has SemiRng or R has OrderedMonoid and R has SemiRing or R has OrderedAbelianMonoid

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AIntervalCategory R

*: (R, %) -> % if R has OrderedSemiGroup and R has SemiRng

from AIntervalCategory R

+: (%, %) -> %

from AIntervalCategory R

+: (%, R) -> %

from AIntervalCategory R

-: % -> % if % has AbelianGroup and R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing and % has AbelianGroup or R has OrderedAbelianGroup

from AIntervalCategory R

-: (%, %) -> % if % has AbelianGroup and R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing and % has AbelianGroup or R has OrderedAbelianGroup

from AIntervalCategory R

/: (%, %) -> % if R has Field and R has OrderedRing

from AIntervalCategory R

=: (%, %) -> Boolean

from AIntervalCategory R

^: (%, NonNegativeInteger) -> % if R has OrderedMonoid and R has SemiRing

from AIntervalCategory R

^: (%, PositiveInteger) -> % if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

from AIntervalCategory R

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if R has OrderedAbelianGroup

from AIntervalCategory R

antiCommutator: (%, %) -> % if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

from NonAssociativeSemiRng

coerce: % -> List R

from AIntervalCategory R

coerce: % -> OutputForm

from CoercibleTo OutputForm

contains?: (%, %) -> Boolean

from AIntervalCategory R

contains?: (%, R) -> Boolean

from AIntervalCategory R

error?: % -> Boolean

from AIntervalCategory R

inf: % -> R

from AIntervalCategory R

interval: (R, R) -> %

from AIntervalCategory R

inv: % -> % if R has Field and R has OrderedRing

from AIntervalCategory R

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> % if R has OrderedMonoid and R has SemiRing

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> % if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

from Magma

leftRecip: % -> Union(%, failed) if R has OrderedMonoid and R has SemiRing

from MagmaWithUnit

negative?: % -> Boolean if R has OrderedAbelianMonoid

from AIntervalCategory R

one?: % -> Boolean if R has OrderedMonoid and R has SemiRing

from MagmaWithUnit

opposite?: (%, %) -> Boolean if R has OrderedSemiGroup and % has AbelianMonoid and R has SemiRng or R has OrderedMonoid and R has SemiRing or R has OrderedAbelianMonoid

from AbelianMonoid

positive?: % -> Boolean if R has OrderedAbelianMonoid

from AIntervalCategory R

qinterval: (R, R) -> %

from AIntervalCategory R

recip: % -> Union(%, failed) if R has OrderedMonoid and R has SemiRing

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> % if R has OrderedMonoid and R has SemiRing

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> % if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

from Magma

rightRecip: % -> Union(%, failed) if R has OrderedMonoid and R has SemiRing

from MagmaWithUnit

sample: % if R has OrderedSemiGroup and % has AbelianMonoid and R has SemiRng or R has OrderedMonoid and R has SemiRing or R has OrderedAbelianMonoid

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed) if % has AbelianGroup and R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing and % has AbelianGroup

from CancellationAbelianMonoid

sup: % -> R

from AIntervalCategory R

unit?: % -> Boolean if R has Field and R has OrderedRing

from AIntervalCategory R

width: % -> R if R has OrderedAbelianGroup

from AIntervalCategory R

zero?: % -> Boolean if R has OrderedSemiGroup and % has AbelianMonoid and R has SemiRng or R has OrderedMonoid and R has SemiRing or R has OrderedAbelianMonoid

from AIntervalCategory R

AbelianMonoid if R has OrderedAbelianMonoid or R has OrderedMonoid and R has SemiRing

AbelianSemiGroup

AIntervalCategory R

BasicType

BiModule(%, %) if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

CancellationAbelianMonoid if % has AbelianGroup and R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing and % has AbelianGroup

CoercibleTo OutputForm

LeftModule % if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

Magma if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

MagmaWithUnit if R has OrderedMonoid and R has SemiRing

Monoid if R has OrderedMonoid and R has SemiRing

NonAssociativeSemiRing if R has OrderedMonoid and R has SemiRing

NonAssociativeSemiRng if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

RightModule % if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

SemiGroup if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

SemiRing if R has OrderedMonoid and R has SemiRing

SemiRng if R has OrderedSemiGroup and R has SemiRng or R has OrderedMonoid and R has SemiRing

SetCategory