AntiSymm(R, lVar)ΒΆ

derham.spad line 93

The domain of antisymmetric polynomials.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (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: (%, %) -> %
from NonAssociativeSemiRng
associator: (%, %, %) -> %
from NonAssociativeRng
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
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
from CoercibleTo OutputForm
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
from RetractableTo R
commutator: (%, %) -> %
from NonAssociativeRng
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: % -> %
leadingBasisTerm(p) returns the leading basis term of antisymmetric polynomial p.
leadingCoefficient: % -> R
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)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftAlgebra R

LeftModule %

LeftModule R

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RetractableTo R

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown