ModularRing(R, Mod, reduction, merge, exactQuo)

modring.spad line 1 [edit on github]

• R : CommutativeRing
• Mod : AbelianMonoid
• reduction : Mapping(R, R, Mod)
• merge : Mapping(Union(Mod, "failed"), Mod, Mod)
• exactQuo : Mapping(Union(R, "failed"), R, R, Mod)

These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See EuclideanModularRing , ModularField

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

associator : (%, %, %) -> %

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> R

coerce(x) is undocumented

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

exQuo : (%, %) -> Union(%, "failed")

exQuo(x, y) is undocumented

inv : % -> %

inv(x) is undocumented

latex : % -> String

from SetCategory

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

leftRecip : % -> Union(%, "failed")

from MagmaWithUnit

modulus : % -> Mod

modulus(x) is undocumented

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

recip : % -> Union(%, "failed")

recip(x) is undocumented

reduce : (R, Mod) -> %

reduce(r, m) is undocumented

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

rightRecip : % -> Union(%, "failed")

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

RightModule(%)

Rng

Monoid

Ring

SemiGroup

CancellationAbelianMonoid

LeftModule(%)

MagmaWithUnit

BasicType

unitsKnown

NonAssociativeRing

Magma

NonAssociativeSemiRng

SemiRing

AbelianGroup

NonAssociativeSemiRing

SetCategory

AbelianSemiGroup

AbelianMonoid

BiModule(%, %)

NonAssociativeRng

CoercibleTo(OutputForm)

SemiRng