XPolynomial RΒΆ
xpoly.spad line 797 [edit on github]
R: Ring
This type supports multivariate polynomials whose set of variables is Symbol. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However, coefficients and variables commute.
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from Magma
- *: (%, R) -> %
from XFreeAlgebra(Symbol, R)
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- *: (R, %) -> %
from LeftModule R
- *: (Symbol, %) -> %
from XFreeAlgebra(Symbol, 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(Symbol, R)
- coef: (%, FreeMonoid Symbol) -> R
from XFreeAlgebra(Symbol, R)
- coefficient: (%, FreeMonoid Symbol) -> R
from FreeModuleCategory(R, FreeMonoid Symbol)
- coefficients: % -> List R
from FreeModuleCategory(R, FreeMonoid Symbol)
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: FreeMonoid Symbol -> %
- coerce: Integer -> %
from NonAssociativeRing
- coerce: R -> %
from CoercibleFrom R
- coerce: Symbol -> %
from XFreeAlgebra(Symbol, R)
- commutator: (%, %) -> %
from NonAssociativeRng
- constant?: % -> Boolean
from XFreeAlgebra(Symbol, R)
- constant: % -> R
from XFreeAlgebra(Symbol, R)
- construct: List Record(k: FreeMonoid Symbol, c: R) -> %
from IndexedProductCategory(R, FreeMonoid Symbol)
- constructOrdered: List Record(k: FreeMonoid Symbol, c: R) -> %
from IndexedProductCategory(R, FreeMonoid Symbol)
- degree: % -> NonNegativeInteger
from XPolynomialsCat(Symbol, R)
expand: % -> XDistributedPolynomial(Symbol, R)
- latex: % -> String
from SetCategory
- leadingCoefficient: % -> R
from IndexedProductCategory(R, FreeMonoid Symbol)
- leadingMonomial: % -> %
from IndexedProductCategory(R, FreeMonoid Symbol)
- leadingSupport: % -> FreeMonoid Symbol
from IndexedProductCategory(R, FreeMonoid Symbol)
- leadingTerm: % -> Record(k: FreeMonoid Symbol, c: R)
from IndexedProductCategory(R, FreeMonoid Symbol)
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- linearExtend: (FreeMonoid Symbol -> R, %) -> R if R has CommutativeRing
from FreeModuleCategory(R, FreeMonoid Symbol)
- listOfTerms: % -> List Record(k: FreeMonoid Symbol, c: R)
from IndexedDirectProductCategory(R, FreeMonoid Symbol)
- lquo: (%, %) -> %
from XFreeAlgebra(Symbol, R)
- lquo: (%, FreeMonoid Symbol) -> %
from XFreeAlgebra(Symbol, R)
- lquo: (%, Symbol) -> %
from XFreeAlgebra(Symbol, R)
- map: (R -> R, %) -> %
from XFreeAlgebra(Symbol, R)
- maxdeg: % -> FreeMonoid Symbol
from XPolynomialsCat(Symbol, R)
- mindeg: % -> FreeMonoid Symbol
from XFreeAlgebra(Symbol, R)
- mindegTerm: % -> Record(k: FreeMonoid Symbol, c: R)
from XFreeAlgebra(Symbol, R)
- mirror: % -> %
from XFreeAlgebra(Symbol, R)
- monomial?: % -> Boolean
from XFreeAlgebra(Symbol, R)
- monomial: (R, FreeMonoid Symbol) -> %
from XFreeAlgebra(Symbol, R)
- monomials: % -> List %
from FreeModuleCategory(R, FreeMonoid Symbol)
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- plenaryPower: (%, PositiveInteger) -> % if R has CommutativeRing
from NonAssociativeAlgebra R
- quasiRegular?: % -> Boolean
from XFreeAlgebra(Symbol, R)
- quasiRegular: % -> %
from XFreeAlgebra(Symbol, R)
- recip: % -> Union(%, failed)
from MagmaWithUnit
- reductum: % -> %
from IndexedProductCategory(R, FreeMonoid Symbol)
RemainderList: % -> List Record(k: Symbol, c: %)
- retract: % -> FreeMonoid Symbol
- retract: % -> R
from RetractableTo R
- retractIfCan: % -> Union(FreeMonoid Symbol, failed)
- retractIfCan: % -> Union(R, failed)
from RetractableTo R
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- rquo: (%, %) -> %
from XFreeAlgebra(Symbol, R)
- rquo: (%, FreeMonoid Symbol) -> %
from XFreeAlgebra(Symbol, R)
- rquo: (%, Symbol) -> %
from XFreeAlgebra(Symbol, R)
- sample: %
from AbelianMonoid
- sh: (%, %) -> % if R has CommutativeRing
from XFreeAlgebra(Symbol, R)
- sh: (%, NonNegativeInteger) -> % if R has CommutativeRing
from XFreeAlgebra(Symbol, R)
- smaller?: (%, %) -> Boolean if R has Comparable
from Comparable
- subtractIfCan: (%, %) -> Union(%, failed)
- support: % -> List FreeMonoid Symbol
from FreeModuleCategory(R, FreeMonoid Symbol)
- trunc: (%, NonNegativeInteger) -> %
from XPolynomialsCat(Symbol, R)
unexpand: XDistributedPolynomial(Symbol, R) -> %
- varList: % -> List Symbol
from XFreeAlgebra(Symbol, R)
- zero?: % -> Boolean
from AbelianMonoid
Algebra R if R has CommutativeRing
BiModule(%, %)
BiModule(R, R)
CoercibleFrom FreeMonoid Symbol
Comparable if R has Comparable
FreeModuleCategory(R, FreeMonoid Symbol)
IndexedDirectProductCategory(R, FreeMonoid Symbol)
IndexedProductCategory(R, FreeMonoid Symbol)
Module R if R has CommutativeRing
NonAssociativeAlgebra R if R has CommutativeRing
noZeroDivisors if R has noZeroDivisors
RetractableTo FreeMonoid Symbol
XAlgebra R
XFreeAlgebra(Symbol, R)