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

wtpol.spad line 1 [edit on github]

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.

* : (%, %) -> %
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

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

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

characteristic : () -> NonNegativeInteger
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)
coerce : Integer -> %
from NonAssociativeRing
coerce : % -> P

convert back into a "P", ignoring weights

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
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(%)

Rng

Monoid

NonAssociativeAlgebra(R)

Ring

SemiGroup

CancellationAbelianMonoid

LeftModule(%)

Algebra(R)

BasicType

unitsKnown

NonAssociativeRing

Magma

NonAssociativeSemiRng

SemiRing

Module(R)

AbelianGroup

NonAssociativeSemiRing

SetCategory

AbelianSemiGroup

BiModule(R, R)

AbelianMonoid

BiModule(%, %)

NonAssociativeRng

MagmaWithUnit

RightModule(R)

CoercibleTo(OutputForm)

SemiRng

LeftModule(R)