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

polset.spad line 343 [edit on github]

R: Ring

VarSet: OrderedSet

P: RecursivePolynomialCategory(R, E, VarSet)

A domain for polynomial sets.

- #: % -> NonNegativeInteger
from Aggregate

- 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`

.

- count: (P -> Boolean, %) -> NonNegativeInteger
from HomogeneousAggregate P

- count: (P, %) -> NonNegativeInteger
from HomogeneousAggregate P

- 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

- max: % -> P if P has OrderedSet
from HomogeneousAggregate P

- max: ((P, P) -> Boolean, %) -> P
from HomogeneousAggregate P

- member?: (P, %) -> Boolean
from HomogeneousAggregate P

- members: % -> List P
from HomogeneousAggregate P

- min: % -> P if P has OrderedSet
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)

- 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)