Important: The polytools package has been deprecated. Use the superseding command PolynomialTools[MinimalPolynomial] instead.

The minpoly 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.

If a third argument is specified, then the value $\mathrm{acc}\left|f\left(r\right)\right|$ is given the same weight as the coefficients in determining the polynomial. The default value for acc is 10^(Digits-2).

$\mathrm{with}\left(\mathrm{polytools}\right)\:$

$r≔\mathrm{evalf}\left(1+\mathrm{sqrt}\left(2\right)\right)$

$r≔2.414213562$

$\mathrm{minpoly}\left(r\,2\right)$

${\mathrm{\_X}}^2-2\mathrm{\_X}-1$

$r≔1+\mathrm{sqrt}\left(2\right)$

$r≔1+\sqrt{2}$

$\mathrm{minpoly}\left(r\,2\right)$

${\mathrm{\_X}}^2-2\mathrm{\_X}-1$

$\mathrm{minpoly}\left(1.234\,3\right)$

$22{\mathrm{\_X}}^3-5{\mathrm{\_X}}^2+61\mathrm{\_X}-109$

$\mathrm{fsolve}\left(\,\mathrm{\_X}\right)$

$1.234000001$

$r≔\mathrm{evalf}\left(\mathrm{sqrt}\left(2\right)+\mathrm{sqrt}\left(-3\right)\right)$

$r≔1.414213562+1.732050808\mathrm{I}$

$\mathrm{minpoly}\left(r\,4\right)$

${\mathrm{\_X}}^4+2{\mathrm{\_X}}^2+25$