OrdinaryWeightedPolynomials(R, vl, wl, wtlevel)

wtpol.spad line 104 [edit on github]

• R : Ring
• vl : List(Symbol)
• wl : List(NonNegativeInteger)
• wtlevel : NonNegativeInteger

This domain represents truncated weighted polynomials over the "Polynomial" type. The variables must be specified, as must the weights. The representation is sparse in the sense that only non-zero terms are represented.

* : (%, %) -> %

from Magma

* : (%, R) -> % if R has CommutativeRing

from RightModule(R)

* : (R, %) -> % if R has CommutativeRing

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

/ : (%, %) -> Union(%, "failed") if R has Field

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

changeWeightLevel : NonNegativeInteger -> Void

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : R -> % if R has CommutativeRing

from Algebra(R)

coerce : Integer -> %

from NonAssociativeRing

coerce : Polynomial(R) -> %

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

coerce : % -> Polynomial(R)

commutator : (%, %) -> %

from NonAssociativeRng

latex : % -> String

from SetCategory

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

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

from MagmaWithUnit

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

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

from NonAssociativeAlgebra(R)

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

from MagmaWithUnit

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

NonAssociativeAlgebra(R)

Ring

SemiGroup

CancellationAbelianMonoid

LeftModule(%)

Algebra(R)

BasicType

unitsKnown

NonAssociativeRing

Rng

Magma

NonAssociativeSemiRng

SemiRing

LeftModule(R)

Module(R)

AbelianGroup

NonAssociativeSemiRing

SetCategory

AbelianSemiGroup

BiModule(R, R)

AbelianMonoid

BiModule(%, %)

NonAssociativeRng

MagmaWithUnit

RightModule(R)

CoercibleTo(OutputForm)

SemiRng