GeneralTriangularSet(R, E, V, P)ΒΆ
triset.spad line 474 [edit on github]
V: OrderedSet
P: RecursivePolynomialCategory(R, E, V)
A domain constructor of the category TriangularSetCategory. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists w.r.t. the main variables of their members but they are displayed in reverse order.
- #: % -> NonNegativeInteger
from Aggregate
- algebraic?: (V, %) -> Boolean
from TriangularSetCategory(R, E, V, P)
- algebraicVariables: % -> List V
from TriangularSetCategory(R, E, V, P)
- any?: (P -> Boolean, %) -> Boolean
from HomogeneousAggregate P
- autoReduced?: (%, (P, List P) -> Boolean) -> Boolean
from TriangularSetCategory(R, E, V, P)
- basicSet: (List P, (P, P) -> Boolean) -> Union(Record(bas: %, top: List P), failed)
from TriangularSetCategory(R, E, V, P)
- basicSet: (List P, P -> Boolean, (P, P) -> Boolean) -> Union(Record(bas: %, top: List P), failed)
from TriangularSetCategory(R, E, V, P)
- coerce: % -> List P
from CoercibleTo List P
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coHeight: % -> NonNegativeInteger if V has Finite
from TriangularSetCategory(R, E, V, P)
- collect: (%, V) -> %
from PolynomialSetCategory(R, E, V, P)
- collectQuasiMonic: % -> %
from TriangularSetCategory(R, E, V, P)
- collectUnder: (%, V) -> %
from PolynomialSetCategory(R, E, V, P)
- collectUpper: (%, V) -> %
from PolynomialSetCategory(R, E, V, P)
- construct: List P -> %
from Collection P
- convert: % -> InputForm
from ConvertibleTo InputForm
- count: (P -> Boolean, %) -> NonNegativeInteger
from HomogeneousAggregate P
- count: (P, %) -> NonNegativeInteger
from HomogeneousAggregate P
- degree: % -> NonNegativeInteger
from TriangularSetCategory(R, E, V, 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
- extend: (%, P) -> %
from TriangularSetCategory(R, E, V, P)
- extendIfCan: (%, P) -> Union(%, failed)
from TriangularSetCategory(R, E, V, P)
- find: (P -> Boolean, %) -> Union(P, failed)
from Collection P
- first: % -> Union(P, failed)
from TriangularSetCategory(R, E, V, P)
- headReduce: (P, %) -> P
from TriangularSetCategory(R, E, V, P)
- headReduced?: % -> Boolean
from TriangularSetCategory(R, E, V, P)
- headReduced?: (P, %) -> Boolean
from TriangularSetCategory(R, E, V, P)
- headRemainder: (P, %) -> Record(num: P, den: R)
from PolynomialSetCategory(R, E, V, P)
- iexactQuo: (R, R) -> R
from PolynomialSetCategory(R, E, V, P)
- infRittWu?: (%, %) -> Boolean
from TriangularSetCategory(R, E, V, P)
- initiallyReduce: (P, %) -> P
from TriangularSetCategory(R, E, V, P)
- initiallyReduced?: % -> Boolean
from TriangularSetCategory(R, E, V, P)
- initiallyReduced?: (P, %) -> Boolean
from TriangularSetCategory(R, E, V, P)
- initials: % -> List P
from TriangularSetCategory(R, E, V, P)
- last: % -> Union(P, failed)
from TriangularSetCategory(R, E, V, P)
- latex: % -> String
from SetCategory
- less?: (%, NonNegativeInteger) -> Boolean
from Aggregate
- mainVariable?: (V, %) -> Boolean
from PolynomialSetCategory(R, E, V, P)
- mainVariables: % -> List V
from PolynomialSetCategory(R, E, V, 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: % -> V
from PolynomialSetCategory(R, E, V, P)
- normalized?: % -> Boolean
from TriangularSetCategory(R, E, V, P)
- normalized?: (P, %) -> Boolean
from TriangularSetCategory(R, E, V, P)
- parts: % -> List P
from HomogeneousAggregate P
- quasiComponent: % -> Record(close: List P, open: List P)
from TriangularSetCategory(R, E, V, 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
- reduce: (P, %, (P, P) -> P, (P, P) -> Boolean) -> P
from TriangularSetCategory(R, E, V, P)
- reduceByQuasiMonic: (P, %) -> P
from TriangularSetCategory(R, E, V, P)
- reduced?: (P, %, (P, P) -> Boolean) -> Boolean
from TriangularSetCategory(R, E, V, P)
- remainder: (P, %) -> Record(rnum: R, polnum: P, den: R)
from PolynomialSetCategory(R, E, V, P)
- remove: (P -> Boolean, %) -> %
from Collection P
- remove: (P, %) -> %
from Collection P
- removeDuplicates: % -> %
from Collection P
- removeZero: (P, %) -> P
from TriangularSetCategory(R, E, V, P)
- rest: % -> Union(%, failed)
from TriangularSetCategory(R, E, V, P)
- retract: List P -> %
from RetractableFrom List P
- retractIfCan: List P -> Union(%, failed)
from RetractableFrom List P
- rewriteIdealWithHeadRemainder: (List P, %) -> List P
from PolynomialSetCategory(R, E, V, P)
- rewriteIdealWithRemainder: (List P, %) -> List P
from PolynomialSetCategory(R, E, V, P)
- rewriteSetWithReduction: (List P, %, (P, P) -> P, (P, P) -> Boolean) -> List P
from TriangularSetCategory(R, E, V, P)
- roughBase?: % -> Boolean
from PolynomialSetCategory(R, E, V, P)
- roughEqualIdeals?: (%, %) -> Boolean
from PolynomialSetCategory(R, E, V, P)
- roughSubIdeal?: (%, %) -> Boolean
from PolynomialSetCategory(R, E, V, P)
- roughUnitIdeal?: % -> Boolean
from PolynomialSetCategory(R, E, V, P)
- select: (%, V) -> Union(P, failed)
from TriangularSetCategory(R, E, V, P)
- select: (P -> Boolean, %) -> %
from Collection P
- size?: (%, NonNegativeInteger) -> Boolean
from Aggregate
- sort: (%, V) -> Record(under: %, floor: %, upper: %)
from PolynomialSetCategory(R, E, V, P)
- stronglyReduce: (P, %) -> P
from TriangularSetCategory(R, E, V, P)
- stronglyReduced?: % -> Boolean
from TriangularSetCategory(R, E, V, P)
- stronglyReduced?: (P, %) -> Boolean
from TriangularSetCategory(R, E, V, P)
- triangular?: % -> Boolean
from PolynomialSetCategory(R, E, V, P)
- trivialIdeal?: % -> Boolean
from PolynomialSetCategory(R, E, V, P)
- variables: % -> List V
from PolynomialSetCategory(R, E, V, P)
- zeroSetSplit: List P -> List %
from TriangularSetCategory(R, E, V, P)
- zeroSetSplitIntoTriangularSystems: List P -> List Record(close: %, open: List P)
from TriangularSetCategory(R, E, V, P)
Evalable P if P has Evalable P
InnerEvalable(P, P) if P has Evalable P
PolynomialSetCategory(R, E, V, P)
TriangularSetCategory(R, E, V, P)