GeneralPolynomialSet(R, E, VarSet, P)

polset.spad line 343 [edit on github]

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

A domain for polynomial sets.

# : % -> NonNegativeInteger

from Aggregate

= : (%, %) -> Boolean

from BasicType

any? : (Mapping(Boolean, P), %) -> 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 : List(P) -> %

convert(lp) returns the polynomial set whose members are the polynomials of lp.

convert : % -> InputForm

from ConvertibleTo(InputForm)

copy : % -> %

from Aggregate

count : (P, %) -> NonNegativeInteger

from HomogeneousAggregate(P)

count : (Mapping(Boolean, P), %) -> NonNegativeInteger

from HomogeneousAggregate(P)

empty : () -> %

from Aggregate

empty? : % -> Boolean

from Aggregate

eq? : (%, %) -> Boolean

from Aggregate

eval : (%, P, P) -> % if P has Evalable(P)

from InnerEvalable(P, P)

eval : (%, 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 : (%, List(Equation(P))) -> % if P has Evalable(P)

from Evalable(P)

every? : (Mapping(Boolean, P), %) -> Boolean

from HomogeneousAggregate(P)

find : (Mapping(Boolean, P), %) -> Union(P, "failed")

from Collection(P)

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 : (Mapping(P, P), %) -> %

from HomogeneousAggregate(P)

map! : (Mapping(P, P), %) -> %

from HomogeneousAggregate(P)

max : % -> P if P has OrderedSet

from HomogeneousAggregate(P)

max : (Mapping(Boolean, P, P), %) -> 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 : (Mapping(P, P, P), %) -> P

from Collection(P)

reduce : (Mapping(P, P, P), %, P) -> P

from Collection(P)

reduce : (Mapping(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, %) -> %

from Collection(P)

remove : (Mapping(Boolean, 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 : (Mapping(Boolean, P), %) -> %

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)

~= : (%, %) -> Boolean

from BasicType

PolynomialSetCategory(R, E, VarSet, P)

ConvertibleTo(InputForm)

Aggregate

RetractableFrom(List(P))

HomogeneousAggregate(P)

CoercibleTo(List(P))

InnerEvalable(P, P)

Evalable(P)

SetCategory

CoercibleTo(OutputForm)

finiteAggregate

shallowlyMutable

Collection(P)

BasicType