Find the minimal polynomial using lattice basis reduction

First try at double precision

> readlib(lattice):

> Digits := 16;

> e1 := cos(Pi/36);

> r1 := evalf(e1);

> p1 := minpoly(r1,12);

Now redo the computation at 60 digits precision to see the correct answer.

> Digits := 60;

> r1 := evalf(e1);

> p1 := minpoly(r1,12);

Check the above using higher precision and by using the procedure with the option.

> Digits := 2*Digits;

> almost_zero_1 := subs(_X=evalf(e1),p1);

> zero_1 := combine(subs(_X=e1,p1),trig);