# InternalRationalUnivariateRepresentationPackage(R, E, V, P, TS)ΒΆ

- R: Join(EuclideanDomain, 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.