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

sregset.spad line 32 [edit on github]

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 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 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?(\ ``ts`\ , us) <l5175617369436f6d706f6e656e745061636b616765-696e7465726e616c5375625175617369436f6d706f6e656e743f285c206060747360605c202c20757329>` 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. Ritt and Wu ordering.