AntiSymm(R, lVar)
derham.spad line 94
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The domain of antisymmetric polynomials.
- * : (%, %) -> %
- from Magma
- * : (R, %) -> %
- from LeftModule(R)
- * : (Integer, %) -> %
- from AbelianGroup
- * : (NonNegativeInteger, %) -> %
- from AbelianMonoid
- * : (PositiveInteger, %) -> %
- from AbelianSemiGroup
- + : (%, %) -> %
- from AbelianSemiGroup
- - : % -> %
- from AbelianGroup
- - : (%, %) -> %
- from AbelianGroup
- 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
- 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 : R -> %
- from LeftAlgebra(R)
- coerce : Integer -> %
- from NonAssociativeRing
- coerce : % -> OutputForm
- from CoercibleTo(OutputForm)
- 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.
- 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 : (Mapping(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)
- retractIfCan : % -> Union(R, "failed")
- from RetractableTo(R)
- retractable? : % -> Boolean
retractable?(p) tests if p is a 0-form, i.e. if degree(p) = 0.
- 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(%)
RetractableTo(R)
Monoid
Ring
SemiGroup
CancellationAbelianMonoid
LeftAlgebra(R)
CoercibleTo(OutputForm)
BasicType
unitsKnown
NonAssociativeRing
Rng
Magma
NonAssociativeSemiRng
SemiRing
LeftModule(%)
AbelianGroup
NonAssociativeSemiRing
SetCategory
CoercibleFrom(R)
AbelianSemiGroup
AbelianMonoid
BiModule(%, %)
NonAssociativeRng
LeftModule(R)
MagmaWithUnit
SemiRng