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 with respect to 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 with respect to 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 with respect to us and is not with respect to 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 with respect to Riit and Wu ordering.