ModMonic(R, Rep)

modmon.spad line 1 [edit on github]

• R : Ring
• Rep : UnivariatePolynomialCategory(R)

This domain implements quotient of ring of univariate polynomials by ideal generated by modulus polynomial. Modulus must be monic. Before performing any operations you need to set modulus, subsequent operations use this modulus.

* : (%, %) -> %

from Magma

* : (R, %) -> %

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

UnVectorise : Vector(R) -> %

UnVectorise(v) converts vector of coefficients to %.

Vectorise : % -> Vector(R)

Vectorise(x) returns vector of coefficients of lift(x).

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

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

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : % -> % if R has CommutativeRing

from Algebra(%)

coerce : R -> %

from CoercibleFrom(R)

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

convert : % -> InputForm if R has Finite

from ConvertibleTo(InputForm)

enumerate : () -> List(%) if R has Finite

from Finite

frobenius : % -> % if R has FiniteFieldCategory

frobenius(x) computes x^q where q is the size of R.

hash : % -> SingleInteger if R has Finite

from Hashable

hashUpdate! : (HashState, %) -> HashState if R has Finite

from Hashable

index : PositiveInteger -> % if R has Finite

from Finite

latex : % -> String

from SetCategory

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

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

from MagmaWithUnit

lift : % -> Rep

lift(x) returns x as a polynomial.

lookup : % -> PositiveInteger if R has Finite

from Finite

modulus : () -> Rep

modulus() returns current modulus.

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

plenaryPower : (%, PositiveInteger) -> % if R has CommutativeRing

from NonAssociativeAlgebra(%)

pow : () -> PrimitiveArray(%)

pow() returns precomputed array of powers of variable modulo current modulus from defree d up to degree 2*d -1, where d is degree of the modulus. Note: element at index 0 is variable to power d.

random : () -> % if R has Finite

from Finite

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

from MagmaWithUnit

reduce : Rep -> %

reduce(x) reduces x modulo current modulus.

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

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

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

setPoly : Rep -> Rep

setPoly(x) sets modulus for subsequent operations.

size : () -> NonNegativeInteger if R has Finite

from Finite

smaller? : (%, %) -> Boolean if R has Finite

from Comparable

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

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

Comparable

ConvertibleTo(InputForm)

CoercibleFrom(R)

RightModule(%)

Monoid

Algebra(%)

AbelianMonoid

CancellationAbelianMonoid

MagmaWithUnit

NonAssociativeRing

CommutativeStar

LeftModule(%)

LeftModule(R)

Finite

Module(%)

SetCategory

CoercibleTo(OutputForm)

Rng

CommutativeRing

TwoSidedRecip

Magma

SemiGroup

BiModule(%, %)

unitsKnown

AbelianGroup

AbelianSemiGroup

NonAssociativeSemiRing

NonAssociativeAlgebra(%)

NonAssociativeRng

Ring

SemiRng

NonAssociativeSemiRng

Hashable

BasicType

SemiRing