WeightedPolynomials(R, VarSet, E, P, vl, wl, wtlevel)ΒΆ
wtpol.spad line 1 [edit on github]
R: Ring
VarSet: OrderedSet
P: PolynomialCategory(R, E, VarSet)
vl: List VarSet
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/ydivision (only works if minimum weight of divisor is zero, and ifRis a Field)
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- 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)coercespinto 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)
- zero?: % -> Boolean
from AbelianMonoid
Algebra R if R has CommutativeRing
BiModule(%, %)
BiModule(R, R) if R has CommutativeRing
LeftModule R if R has CommutativeRing
Module R if R has CommutativeRing
NonAssociativeAlgebra R if R has CommutativeRing
RightModule R if R has CommutativeRing