# GeneralPolynomialSet(R, E, VarSet, P)ΒΆ

- R: Ring
- E: OrderedAbelianMonoidSup
- VarSet: OrderedSet
- P: RecursivePolynomialCategory(R, E, VarSet)

A domain for polynomial sets.

- #: % -> NonNegativeInteger
- from Aggregate
- =: (%, %) -> Boolean
- from BasicType
- ~=: (%, %) -> Boolean
- from BasicType
- any?: (P -> Boolean, %) -> Boolean
- from HomogeneousAggregate P
- coerce: % -> List P
- from CoercibleTo List P
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- collect: (%, VarSet) -> %
- from PolynomialSetCategory(R, E, VarSet, P)
- collectUnder: (%, VarSet) -> %
- from PolynomialSetCategory(R, E, VarSet, P)
- collectUpper: (%, VarSet) -> %
- from PolynomialSetCategory(R, E, VarSet, P)
- construct: List P -> %
- from Collection P
- convert: % -> InputForm
- from ConvertibleTo InputForm

- convert: List P -> %
`convert(lp)`

returns the polynomial set whose members are the polynomials of`lp`

.- copy: % -> %
- from Aggregate
- count: (P -> Boolean, %) -> NonNegativeInteger
- from HomogeneousAggregate P
- count: (P, %) -> NonNegativeInteger
- from HomogeneousAggregate P
- empty: () -> %
- from Aggregate
- empty?: % -> Boolean
- from Aggregate
- eq?: (%, %) -> Boolean
- from Aggregate
- eval: (%, Equation P) -> % if P has Evalable P
- from Evalable P
- eval: (%, List Equation P) -> % if P has Evalable P
- from Evalable P
- eval: (%, List P, List P) -> % if P has Evalable P
- from InnerEvalable(P, P)
- eval: (%, P, P) -> % if P has Evalable P
- from InnerEvalable(P, P)
- every?: (P -> Boolean, %) -> Boolean
- from HomogeneousAggregate P
- find: (P -> Boolean, %) -> Union(P, failed)
- from Collection P
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- headRemainder: (P, %) -> Record(num: P, den: R) if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- iexactQuo: (R, R) -> R if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- latex: % -> String
- from SetCategory
- less?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- mainVariable?: (VarSet, %) -> Boolean
- from PolynomialSetCategory(R, E, VarSet, P)
- mainVariables: % -> List VarSet
- from PolynomialSetCategory(R, E, VarSet, P)
- map!: (P -> P, %) -> %
- from HomogeneousAggregate P
- map: (P -> P, %) -> %
- from HomogeneousAggregate P
- member?: (P, %) -> Boolean
- from HomogeneousAggregate P
- members: % -> List P
- from HomogeneousAggregate P
- more?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- mvar: % -> VarSet
- from PolynomialSetCategory(R, E, VarSet, P)
- parts: % -> List P
- from HomogeneousAggregate P
- reduce: ((P, P) -> P, %) -> P
- from Collection P
- reduce: ((P, P) -> P, %, P) -> P
- from Collection P
- reduce: ((P, P) -> P, %, P, P) -> P
- from Collection P
- remainder: (P, %) -> Record(rnum: R, polnum: P, den: R) if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- remove: (P -> Boolean, %) -> %
- from Collection P
- remove: (P, %) -> %
- from Collection P
- removeDuplicates: % -> %
- from Collection P
- retract: List P -> %
- from RetractableFrom List P
- retractIfCan: List P -> Union(%, failed)
- from RetractableFrom List P
- rewriteIdealWithHeadRemainder: (List P, %) -> List P if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- rewriteIdealWithRemainder: (List P, %) -> List P if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- roughBase?: % -> Boolean if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- roughEqualIdeals?: (%, %) -> Boolean if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- roughSubIdeal?: (%, %) -> Boolean if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- roughUnitIdeal?: % -> Boolean if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- sample: %
- from Aggregate
- select: (P -> Boolean, %) -> %
- from Collection P
- size?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- sort: (%, VarSet) -> Record(under: %, floor: %, upper: %)
- from PolynomialSetCategory(R, E, VarSet, P)
- triangular?: % -> Boolean if R has IntegralDomain
- from PolynomialSetCategory(R, E, VarSet, P)
- trivialIdeal?: % -> Boolean
- from PolynomialSetCategory(R, E, VarSet, P)
- variables: % -> List VarSet
- from PolynomialSetCategory(R, E, VarSet, P)

Evalable P if P has Evalable P

InnerEvalable(P, P) if P has Evalable P

PolynomialSetCategory(R, E, VarSet, P)