SquareFreeRegularSetDecompositionPackage(R, E, V, P, TS)

sregset.spad line 862 [edit on github]

• R : GcdDomain
• E : OrderedAbelianMonoidSup
• V : OrderedSet
• P : RecursivePolynomialCategory(R, E, V)
• TS : SquareFreeRegularTriangularSetCategory(R, E, V, P)

A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu, Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set, or how two quasi-components are compared (by an inclusion-test), or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain TS and the packages QCMPPK(R, E, V, P, TS) and RSETGCD(R, E, V, P, TS). The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call directly any operation of this package since they can be accessed by the domain TS. Thus, the operations of this package are not documented.

KrullNumber : (List(P), List(TS)) -> NonNegativeInteger

algebraicDecompose : (P, TS) -> Record(done : List(TS), todo : List(Record(val : List(P), tower : TS)))

convert : Record(val : List(P), tower : TS) -> String

decompose : (List(P), List(TS), Boolean, Boolean) -> List(TS)

decompose : (List(P), List(TS), Boolean, Boolean, Boolean, Boolean, Boolean) -> List(TS)

internalDecompose : (P, TS) -> Record(done : List(TS), todo : List(Record(val : List(P), tower : TS)))

internalDecompose : (P, TS, NonNegativeInteger) -> Record(done : List(TS), todo : List(Record(val : List(P), tower : TS)))

internalDecompose : (P, TS, NonNegativeInteger, Boolean) -> Record(done : List(TS), todo : List(Record(val : List(P), tower : TS)))

numberOfVariables : (List(P), List(TS)) -> NonNegativeInteger

printInfo : (List(Record(val : List(P), tower : TS)), NonNegativeInteger) -> Void

transcendentalDecompose : (P, TS) -> Record(done : List(TS), todo : List(Record(val : List(P), tower : TS)))

transcendentalDecompose : (P, TS, NonNegativeInteger) -> Record(done : List(TS), todo : List(Record(val : List(P), tower : TS)))

upDateBranches : (List(P), List(TS), List(Record(val : List(P), tower : TS)), Record(done : List(TS), todo : List(Record(val : List(P), tower : TS))), NonNegativeInteger) -> List(Record(val : List(P), tower : TS))