RegularChain(R, ls)ΒΆ

zerodim.spad line 79 [edit on github]

A domain for regular chains (i.e. regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the RegularTriangularSet domain constructor.

#: % -> NonNegativeInteger

from Aggregate

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

algebraic?: (OrderedVariableList ls, %) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

algebraicCoefficients?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

algebraicVariables: % -> List OrderedVariableList ls

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

any?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Boolean, %) -> Boolean

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

augment: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

augment: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

augment: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

augment: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

autoReduced?: (%, (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Boolean) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

basicSet: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Boolean) -> Union(Record(bas: %, top: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)), failed)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

basicSet: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Boolean, (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Boolean) -> Union(Record(bas: %, top: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)), failed)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

coerce: % -> List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from CoercibleTo List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

coerce: % -> OutputForm

from CoercibleTo OutputForm

coHeight: % -> NonNegativeInteger

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

collect: (%, OrderedVariableList ls) -> %

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

collectQuasiMonic: % -> %

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

collectUnder: (%, OrderedVariableList ls) -> %

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

collectUpper: (%, OrderedVariableList ls) -> %

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

construct: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> %

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

convert: % -> InputForm if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has ConvertibleTo InputForm

from ConvertibleTo InputForm

copy: % -> %

from Aggregate

count: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Boolean, %) -> NonNegativeInteger

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

count: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> NonNegativeInteger

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

degree: % -> NonNegativeInteger

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

eq?: (%, %) -> Boolean

from Aggregate

eval: (%, Equation NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

eval: (%, List Equation NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

eval: (%, List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from InnerEvalable(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

eval: (%, NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from InnerEvalable(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

every?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Boolean, %) -> Boolean

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

extend: (%, NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> %

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

extend: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

extend: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

extend: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

extend: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

extendIfCan: (%, NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Union(%, failed)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

find: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Boolean, %) -> Union(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), failed)

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

first: % -> Union(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), failed)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

headReduce: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

headReduced?: % -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

headReduced?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

headRemainder: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Record(num: NewSparseMultivariatePolynomial(R, OrderedVariableList ls), den: R)

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

iexactQuo: (R, R) -> R

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

infRittWu?: (%, %) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

initiallyReduce: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

initiallyReduced?: % -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

initiallyReduced?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

initials: % -> List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

internalAugment: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

internalAugment: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

intersect: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

intersect: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

intersect: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

intersect: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

invertible?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

invertible?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List Record(val: Boolean, tower: %)

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

invertibleElseSplit?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Union(Boolean, List %)

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

invertibleSet: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

last: % -> Union(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), failed)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

lastSubResultant: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List Record(val: NewSparseMultivariatePolynomial(R, OrderedVariableList ls), tower: %)

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

lastSubResultantElseSplit: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Union(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), List %)

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

latex: % -> String

from SetCategory

less?: (%, NonNegativeInteger) -> Boolean

from Aggregate

mainVariable?: (OrderedVariableList ls, %) -> Boolean

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

mainVariables: % -> List OrderedVariableList ls

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

map!: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> %

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

map: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> %

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

max: % -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls) if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has OrderedSet

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

max: ((NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Boolean, %) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

member?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

members: % -> List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

min: % -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls) if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has OrderedSet

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

mvar: % -> OrderedVariableList ls

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

normalized?: % -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

normalized?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

parts: % -> List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

purelyAlgebraic?: % -> Boolean

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

purelyAlgebraic?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

purelyAlgebraicLeadingMonomial?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

purelyTranscendental?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

quasiComponent: % -> Record(close: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), open: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

reduce: ((NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

reduce: ((NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %, NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

reduce: ((NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %, NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

reduce: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %, (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls), (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Boolean) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

reduceByQuasiMonic: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

reduced?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %, (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Boolean) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

remainder: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Record(rnum: R, polnum: NewSparseMultivariatePolynomial(R, OrderedVariableList ls), den: R)

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

remove: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Boolean, %) -> %

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

remove: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> %

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

removeDuplicates: % -> %

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

removeZero: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

rest: % -> Union(%, failed)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

retract: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> %

from RetractableFrom List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

retractIfCan: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Union(%, failed)

from RetractableFrom List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

rewriteIdealWithHeadRemainder: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

rewriteIdealWithRemainder: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

rewriteSetWithReduction: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %, (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls), (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) -> Boolean) -> List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

roughBase?: % -> Boolean

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

roughEqualIdeals?: (%, %) -> Boolean

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

roughSubIdeal?: (%, %) -> Boolean

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

roughUnitIdeal?: % -> Boolean

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

sample: %

from Aggregate

select: (%, OrderedVariableList ls) -> Union(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), failed)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

select: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> Boolean, %) -> %

from Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

sort: (%, OrderedVariableList ls) -> Record(under: %, floor: %, upper: %)

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

squareFreePart: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> List Record(val: NewSparseMultivariatePolynomial(R, OrderedVariableList ls), tower: %)

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

stronglyReduce: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

stronglyReduced?: % -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

stronglyReduced?: (NewSparseMultivariatePolynomial(R, OrderedVariableList ls), %) -> Boolean

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

triangular?: % -> Boolean

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

trivialIdeal?: % -> Boolean

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

variables: % -> List OrderedVariableList ls

from PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

zeroSetSplit: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), Boolean) -> List %

from RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

zeroSetSplit: (List NewSparseMultivariatePolynomial(R, OrderedVariableList ls), Boolean, Boolean) -> List %

zeroSetSplit(lp, clos?, info?) returns a list lts of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with lp. Moreover, if clos? is false then the union of the regular zero set of the ts (for ts in lts) equals this variety. If info? is true then some information is displayed during the computations. See zeroSetSplit.

zeroSetSplit: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> List %

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

zeroSetSplitIntoTriangularSystems: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls) -> List Record(close: %, open: List NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

from TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

Aggregate

BasicType

CoercibleTo List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

CoercibleTo OutputForm

Collection NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

ConvertibleTo InputForm if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has ConvertibleTo InputForm

Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls) if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

finiteAggregate

HomogeneousAggregate NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

InnerEvalable(NewSparseMultivariatePolynomial(R, OrderedVariableList ls), NewSparseMultivariatePolynomial(R, OrderedVariableList ls)) if NewSparseMultivariatePolynomial(R, OrderedVariableList ls) has Evalable NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

PolynomialSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

RegularTriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))

RetractableFrom List NewSparseMultivariatePolynomial(R, OrderedVariableList ls)

SetCategory

shallowlyMutable

TriangularSetCategory(R, IndexedExponents OrderedVariableList ls, OrderedVariableList ls, NewSparseMultivariatePolynomial(R, OrderedVariableList ls))