ModularRing(R, Mod, reduction, merge, exactQuo)ΒΆ
modring.spad line 1 [edit on github]
Mod: AbelianMonoid
reduction: (R, Mod) -> R
merge: (Mod, Mod) -> Union(Mod, failed)
exactQuo: (R, R, Mod) -> Union(R, failed)
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
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from LeftModule %
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: % -> R
coerce(x)undocumented- coerce: Integer -> %
from NonAssociativeRing
- commutator: (%, %) -> %
from NonAssociativeRng
- exQuo: (%, %) -> Union(%, failed)
exQuo(x, y)undocumented
- inv: % -> %
inv(x)undocumented
- latex: % -> String
from SetCategory
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- modulus: % -> Mod
modulus(x)undocumented
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- recip: % -> Union(%, failed)
recip(x)undocumented
- reduce: (R, Mod) -> %
reduce(r, m)undocumented
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from AbelianMonoid
- subtractIfCan: (%, %) -> Union(%, failed)
- zero?: % -> Boolean
from AbelianMonoid
BiModule(%, %)