Sample Points Sample points are either in primitive or extended representation. A sample point in primitive representation is a list (M,I,b) of length 3. M is the integral minimal polynomial of an algebraic number alpha and I is an isolating interval for alpha as a root of M. b is a list (b_1,...,b_k), k >= 1, where the b_i are the coordinates of the sample point, each integrally represented as elements of Q(alpha). If all coordinates of b are rational numbers then M and I are arbitrary but are usually taken to be x and [0] respectively. Elements of an algebraic number field Q(alpha) are, in various contexts, in either of two representations. Let beta be an element of Q(alpha), n the degree of alpha. If beta /= 0, the rational representation of beta is the unique rational polynomial (element of Q[x], B, of degree less than n such that B(alpha) = beta. The integral representation of beta is the unique pair (b,B^) such that b is a rational number, B^ is a positive primitive integral polynomial, and B = b * B^. If beta = 0 then its representation in either case is just the single-precision integer 0. A sample point in extended representation is a list (A,J,M,I,b) of length 5. M, I, and b are the same as in primitive representation above. A and J define an additional algebraic number b_{k+1} as the unique root of the algebraic polynomial A in the isolating interval J, A being a squarefree polynomial with coefficients in Q(alpha). The program CONVERT converts a sample point from extended to primitive representation by computing a primitive element gamma for Q(alpha,beta).