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

sregset.spad line 32 [edit on github]

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

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

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

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. Ritt and Wu ordering.