LazardSetSolvingPackage(R, E, V, P, TS, ST)

nsregset.spad line 21 [edit on github]

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

A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros, and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover, the decompositions do not contain any redundant component. However, only zero-dimensional regular sets are normalized, since normalization may be time consumming in positive dimension. The decomposition process is that of [2].

normalizeIfCan : ST -> ST

normalizeIfCan(ts) returns ts in an normalized shape if ts is zero-dimensional.

zeroSetSplit : (List(P), Boolean) -> List(ST)

zeroSetSplit(lp, clos?) has the same specifications as zeroSetSplit(lp, clos?).