XDistributedPolynomial(vl, R)ΒΆ
xpoly.spad line 294 [edit on github]
vl: OrderedSet
R: Ring
This type supports distributed multivariate polynomials whose variables do not commute. The coefficient ring may be non-commutative too. However, coefficients and variables commute.
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from Magma
- *: (%, R) -> %
from RightModule R
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- *: (R, %) -> %
from LeftModule R
- *: (vl, %) -> %
from XFreeAlgebra(vl, R)
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- coef: (%, %) -> R
from XFreeAlgebra(vl, R)
- coef: (%, FreeMonoid vl) -> R
from XFreeAlgebra(vl, R)
- coefficient: (%, FreeMonoid vl) -> R
from FreeModuleCategory(R, FreeMonoid vl)
- coefficients: % -> List R
from FreeModuleCategory(R, FreeMonoid vl)
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: FreeMonoid vl -> %
from CoercibleFrom FreeMonoid vl
- coerce: Integer -> %
from NonAssociativeRing
- coerce: R -> %
from CoercibleFrom R
- coerce: vl -> %
from XFreeAlgebra(vl, R)
- commutator: (%, %) -> %
from NonAssociativeRng
- constant?: % -> Boolean
from XFreeAlgebra(vl, R)
- constant: % -> R
from XFreeAlgebra(vl, R)
- construct: List Record(k: FreeMonoid vl, c: R) -> %
from IndexedProductCategory(R, FreeMonoid vl)
- constructOrdered: List Record(k: FreeMonoid vl, c: R) -> % if FreeMonoid vl has Comparable
from IndexedProductCategory(R, FreeMonoid vl)
- degree: % -> NonNegativeInteger
from XPolynomialsCat(vl, R)
- latex: % -> String
from SetCategory
- leadingCoefficient: % -> R if FreeMonoid vl has Comparable
from IndexedProductCategory(R, FreeMonoid vl)
- leadingMonomial: % -> % if FreeMonoid vl has Comparable
from IndexedProductCategory(R, FreeMonoid vl)
- leadingSupport: % -> FreeMonoid vl if FreeMonoid vl has Comparable
from IndexedProductCategory(R, FreeMonoid vl)
- leadingTerm: % -> Record(k: FreeMonoid vl, c: R) if FreeMonoid vl has Comparable
from IndexedProductCategory(R, FreeMonoid vl)
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- linearExtend: (FreeMonoid vl -> R, %) -> R if R has CommutativeRing
from FreeModuleCategory(R, FreeMonoid vl)
- listOfTerms: % -> List Record(k: FreeMonoid vl, c: R)
from IndexedDirectProductCategory(R, FreeMonoid vl)
- lquo: (%, %) -> %
from XFreeAlgebra(vl, R)
- lquo: (%, FreeMonoid vl) -> %
from XFreeAlgebra(vl, R)
- lquo: (%, vl) -> %
from XFreeAlgebra(vl, R)
- map: (R -> R, %) -> %
from IndexedProductCategory(R, FreeMonoid vl)
- maxdeg: % -> FreeMonoid vl
from XPolynomialsCat(vl, R)
- mindeg: % -> FreeMonoid vl
from XFreeAlgebra(vl, R)
- mindegTerm: % -> Record(k: FreeMonoid vl, c: R)
from XFreeAlgebra(vl, R)
- mirror: % -> %
from XFreeAlgebra(vl, R)
- monomial?: % -> Boolean
from IndexedProductCategory(R, FreeMonoid vl)
- monomial: (R, FreeMonoid vl) -> %
from IndexedProductCategory(R, FreeMonoid vl)
- monomials: % -> List %
from FreeModuleCategory(R, FreeMonoid vl)
- numberOfMonomials: % -> NonNegativeInteger
from IndexedDirectProductCategory(R, FreeMonoid vl)
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- plenaryPower: (%, PositiveInteger) -> % if R has CommutativeRing
from NonAssociativeAlgebra R
- quasiRegular?: % -> Boolean
from XFreeAlgebra(vl, R)
- quasiRegular: % -> %
from XFreeAlgebra(vl, R)
- recip: % -> Union(%, failed)
from MagmaWithUnit
- reductum: % -> % if FreeMonoid vl has Comparable
from IndexedProductCategory(R, FreeMonoid vl)
- retract: % -> FreeMonoid vl
from RetractableTo FreeMonoid vl
- retract: % -> R
from RetractableTo R
- retractIfCan: % -> Union(FreeMonoid vl, failed)
from RetractableTo FreeMonoid vl
- retractIfCan: % -> Union(R, failed)
from RetractableTo R
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- rquo: (%, %) -> %
from XFreeAlgebra(vl, R)
- rquo: (%, FreeMonoid vl) -> %
from XFreeAlgebra(vl, R)
- rquo: (%, vl) -> %
from XFreeAlgebra(vl, R)
- sample: %
from AbelianMonoid
- sh: (%, %) -> % if R has CommutativeRing
from XFreeAlgebra(vl, R)
- sh: (%, NonNegativeInteger) -> % if R has CommutativeRing
from XFreeAlgebra(vl, R)
- smaller?: (%, %) -> Boolean if FreeMonoid vl has Comparable and R has Comparable
from Comparable
- subtractIfCan: (%, %) -> Union(%, failed)
- support: % -> List FreeMonoid vl
from FreeModuleCategory(R, FreeMonoid vl)
- trunc: (%, NonNegativeInteger) -> %
from XPolynomialsCat(vl, R)
- varList: % -> List vl
from XFreeAlgebra(vl, R)
- zero?: % -> Boolean
from AbelianMonoid
Algebra R if R has CommutativeRing
BiModule(%, %)
BiModule(R, R)
Comparable if FreeMonoid vl has Comparable and R has Comparable
FreeModuleCategory(R, FreeMonoid vl)
IndexedDirectProductCategory(R, FreeMonoid vl)
IndexedProductCategory(R, FreeMonoid vl)
Module R if R has CommutativeRing
NonAssociativeAlgebra R if R has CommutativeRing
noZeroDivisors if R has noZeroDivisors
XAlgebra R
XFreeAlgebra(vl, R)
XPolynomialsCat(vl, R)