InternalRationalUnivariateRepresentationPackage(R, E, V, P, TS)¶

R: Join(PolynomialFactorizationExplicit, CharacteristicZero)
E: OrderedAbelianMonoidSup
V: OrderedSet
P: RecursivePolynomialCategory(R, E, V)
TS: SquareFreeRegularTriangularSetCategory(R, E, V, P)

An internal package for computing the rational univariate representation of a zero-dimensional algebraic variety given by a square-free triangular set. The main operation is rur. It is based on the generic algorithm description in [1]. References: [1] D. LAZARD “Solving Zero-dimensional Algebraic Systems” Journal of Symbolic Computation, 1992, 13, 117-131

checkRur: (TS, List TS) -> Boolean: checkRur(ts, lus) returns true if lus is a rational univariate representation of ts.

rur: (TS, Boolean) -> List TS: rur(ts, univ?) returns a rational univariate representation of ts. This assumes that the lowest polynomial in ts is a variable v which does not occur in the other polynomials of ts. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If univ? is true then these polynomials will have a constant initial.