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

regset.spad line 341

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 developement.
infRittWu?: (List P, List P) -> Boolean
infRittWu?(lp1, lp2) is an internal subroutine, exported only for developement.
internalInfRittWu?: (List P, List P) -> Boolean
internalInfRittWu?(lp1, lp2) is an internal subroutine, exported only for developement.
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 developement.
removeSuperfluousCases: List Record(val: List P, tower: TS) -> List Record(val: List P, tower: TS)
removeSuperfluousCases(llpwt) is an internal subroutine, exported only for developement.
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 developement.
stopTable!: () -> Void
stopTableGcd!() is an internal subroutine, exported only for developement.
subCase?: (Record(val: List P, tower: TS), Record(val: List P, tower: TS)) -> Boolean
subCase?(lpwt1, lpwt2) is an internal subroutine, exported only for developement.
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? returs 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.