QuasiComponentPackage(R, E, V, P, TS)¶

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

A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets.

algebraicSort: List TS -> List TS: algebraicSort(lts) sorts lts w.r.t supDimElseRittWu?.

branchIfCan: (List P, TS, List P, Boolean, Boolean, Boolean, Boolean, Boolean) -> Union(Record(eq: List P, tower: TS, ineq: List P), failed): branchIfCan(leq, ts, lineq, b1, b2, b3, b4, b5) is an internal subroutine, exported only for development.

infRittWu?: (List P, List P) -> Boolean: infRittWu?(lp1, lp2) is an internal subroutine, exported only for development.

internalInfRittWu?: (List P, List P) -> Boolean: internalInfRittWu?(lp1, lp2) is an internal subroutine, exported only for development.

internalSubPolSet?: (List P, List P) -> Boolean: internalSubPolSet?(lp1, lp2) returns true iff lp1 is a sub-set of lp2 assuming that these lists are sorted increasingly w.r.t. infRittWu?.

internalSubQuasiComponent?: (TS, TS) -> Union(Boolean, failed): internalSubQuasiComponent?(ts, us) returns a boolean b value if the fact that the regular zero set of us contains that of ts can be decided (and in that case b gives this inclusion) otherwise returns "failed".

moreAlgebraic?: (TS, TS) -> Boolean: moreAlgebraic?(ts, us) returns false iff ts and us are both empty, or ts has less elements than us, or some variable is algebraic w.r.t. us and is not w.r.t. ts.

prepareDecompose: (List P, List TS, Boolean, Boolean) -> List Record(eq: List P, tower: TS, ineq: List P): prepareDecompose(lp, lts, b1, b2) is an internal subroutine, exported only for development.

removeSuperfluousCases: List Record(val: List P, tower: TS) -> List Record(val: List P, tower: TS): removeSuperfluousCases(llpwt) is an internal subroutine, exported only for development.

removeSuperfluousQuasiComponents: List TS -> List TS: removeSuperfluousQuasiComponents(lts) removes from lts any ts such that subQuasiComponent?(ts, us) holds for another us in lts.

startTable!: (String, String, String) -> Void: startTableGcd!(s1, s2, s3) is an internal subroutine, exported only for development.

stopTable!: () -> Void: stopTableGcd!() is an internal subroutine, exported only for development.

subCase?: (Record(val: List P, tower: TS), Record(val: List P, tower: TS)) -> Boolean: subCase?(lpwt1, lpwt2) is an internal subroutine, exported only for development.

subPolSet?: (List P, List P) -> Boolean: subPolSet?(lp1, lp2) returns true iff lp1 is a sub-set of lp2.

subQuasiComponent?: (TS, List TS) -> Boolean: subQuasiComponent?(ts, lus) returns true iff subQuasiComponent?(ts, us) holds for one us in lus.

subQuasiComponent?: (TS, TS) -> Boolean: subQuasiComponent?(ts, us) returns true iff internalSubQuasiComponent? returns true.

subTriSet?: (TS, TS) -> Boolean: subTriSet?(ts, us) returns true iff ts is a sub-set of us.

supDimElseRittWu?: (TS, TS) -> Boolean: supDimElseRittWu(ts, us) returns true iff ts has less elements than us otherwise if ts has higher rank than us w.r.t. Riit and Wu ordering.