ResidueRing(F, Expon, VarSet, FPol, LFPol)

resring.spad line 1 [edit on github]

• F : Field
• Expon : OrderedAbelianMonoidSup
• VarSet : OrderedSet
• FPol : PolynomialCategory(F, Expon, VarSet)
• LFPol : List(FPol)

ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements

* : (%, %) -> %

from Magma

* : (%, F) -> %

from RightModule(F)

* : (F, %) -> %

from LeftModule(F)

* : (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 : % -> %

from Algebra(%)

coerce : F -> %

from Algebra(F)

coerce : FPol -> %

coerce(f) produces the equivalence class of f in the residue ring

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

latex : % -> String

from SetCategory

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

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

from MagmaWithUnit

lift : % -> FPol

lift(x) return the canonical representative of the equivalence class x

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(%)

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

from MagmaWithUnit

reduce : FPol -> %

reduce(f) produces the equivalence class of f in the residue ring

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(%)

Monoid

NonAssociativeSemiRing

SetCategory

Ring

SemiGroup

CancellationAbelianMonoid

LeftModule(%)

BasicType

unitsKnown

NonAssociativeAlgebra(F)

Module(%)

NonAssociativeRing

NonAssociativeAlgebra(%)

Rng

Magma

NonAssociativeSemiRng

SemiRing

Algebra(%)

Module(F)

AbelianGroup

AbelianSemiGroup

CommutativeRing

CommutativeStar

Algebra(F)

AbelianMonoid

LeftModule(F)

RightModule(F)

BiModule(%, %)

NonAssociativeRng

BiModule(F, F)

TwoSidedRecip

MagmaWithUnit

CoercibleTo(OutputForm)

SemiRng