The MinimalPolynomial(r, n) function uses the lattice algorithm to find a polynomial of degree n (or less) with small integer coefficients which has the given approximation r of an algebraic number as one of its roots.

The root r may be real or complex.  It may be input as a floating-point approximation to a root or as an exact algebraic number.  In the latter case, it will first be evaluated in floating point at Digits precision. Note that this procedure is intended for approximate inputs, because if r is an exact algebraic number then the minimum polynomial can be found with the command evala(Norm(_X-r)), where r is in RootOf notation.

If a third argument is specified, then the value  is given the same weight as the coefficients in determining the polynomial. The default value for acc is 10^(Digits-2).

This function is part of the PolynomialTools package, and so it can be used in the form MinimalPolynomial(..) only after executing the command with(PolynomialTools). However, it can always be accessed through the long form of the command by using PolynomialTools[MinimalPolynomial](..).