# AntiSymm(R, lVar)¶

The domain of antisymmetric polynomials.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
associator: (%, %, %) -> %
characteristic: () -> NonNegativeInteger
coefficient: (%, %) -> R

coefficient(p, u) returns the coefficient of the term in p containing the basis term u if such a term exists, and 0 otherwise. Error: if the second argument u is not a basis element.

coerce: % -> OutputForm
coerce: Integer -> %
coerce: R -> %

from LeftAlgebra R

commutator: (%, %) -> %
degree: % -> NonNegativeInteger

degree(p) returns the homogeneous degree of p.

exp: List Integer -> %

exp([i1, ...in]) returns u_1\^{i_1} ... u_n\^{i_n}

generator: NonNegativeInteger -> %

generator(n) returns the nth multiplicative generator, a basis term.

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

homogeneous?: % -> Boolean

homogeneous?(p) tests if all of the terms of p have the same degree.

latex: % -> String

from SetCategory

leadingBasisTerm(p) returns the leading basis term of antisymmetric polynomial p.

leadingCoefficient(p) returns the leading coefficient of antisymmetric polynomial p.

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

map: (R -> R, %) -> %

map(f, p) changes each coefficient of p by the application of f.

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

reductum(p), where p is an antisymmetric polynomial, returns p minus the leading term of p if p has at least two terms, and 0 otherwise.

retract: % -> R

from RetractableTo R

retractable?: % -> Boolean

retractable?(p) tests if p is a 0-form, i.e. if degree(p) = 0.

retractIfCan: % -> Union(R, failed)

from RetractableTo R

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown