WeightedPolynomials(R, VarSet, E, P, vl, wl, wtlevel)

wtpol.spad line 1 [edit on github]

• R: Ring

• VarSet: OrderedSet

• E: OrderedAbelianMonoidSup

• P: PolynomialCategory(R, E, VarSet)

• vl: List VarSet

• wl: List NonNegativeInteger

• wtlevel: NonNegativeInteger

This domain represents truncated weighted polynomials over a general (not necessarily commutative) 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.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

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

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

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

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

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

x/y division (only works if minimum weight of divisor is zero, and if R is a Field)

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

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

from NonAssociativeRng

changeWeightLevel: NonNegativeInteger -> Void

changeWeightLevel(n) changes the weight level to the new value given: NB: previously calculated terms are not affected

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: % -> P

convert back into a "P", ignoring weights

coerce: Integer -> %

from NonAssociativeRing

coerce: P -> %

coerce(p) coerces p into Weighted form, applying weights and ignoring terms

coerce: R -> % if R has CommutativeRing

from Algebra 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

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %)

BiModule(R, R) if R has CommutativeRing

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule %

LeftModule R if R has CommutativeRing

Magma

MagmaWithUnit

Module R if R has CommutativeRing

Monoid

NonAssociativeAlgebra R if R has CommutativeRing

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule %

RightModule R if R has CommutativeRing

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown