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

wtpol.spad line 1

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
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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
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

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule %

RightModule R if R has CommutativeRing

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown