zerodim.spad line 519 [edit on github]
A package for computing the rational univariate representation of a zero-dimensional algebraic variety given by a regular triangular set. This package is essentially an interface for the InternalRationalUnivariateRepresentationPackage constructor. It is used in the ZeroDimensionalSolvePackage for solving polynomial systems with finitely many solutions.
rur(lp) returns the same as rur(lp, true)
rur(lp, univ?) returns a rational univariate representation of lp. This assumes that lp defines a regular triangular ts whose associated variety is zero-dimensional over R. rur(lp, univ?) returns a list of items [u, lc] where u is an irreducible univariate polynomial and each c in lc involves two variables: one from ls, called the coordinate of c, and an extra variable which represents any root of u. Every root of u leads to a tuple of values for the coordinates of lc. Moreover, a point x belongs to the variety associated with lp iff there exists an item [u, lc] in rur(lp, univ?) and a root r of u such that x is given by the tuple of values for the coordinates of lc evaluated at r. If univ? is true then each polynomial c will have a constant leading coefficient w.r.t. its coordinate. See the example which illustrates the ZeroDimensionalSolvePackage package constructor.
rur(lp, univ?, check?) returns the same as rur(lp, true). Moreover, if check? is true then the result is checked.