1. The USES of LLL

> Digits:=20:readlib(lattice):

Let us discover Machin's formulafor

lin_dep([arctan(1),arctan(1/5),arctan(1/239)]);

And let's discover whether a floating pointnumber is algebraic:

> rtp(2^(1/3)+3^(1/2));

> Digits:=20: minpoly(2^(1/3)+3^(1/2));

> Digits:=40: minpoly(2^(1/3)+3^(1/2),degree=6);

> R:=sqrt((sqrt(5)+1)/2);evalf(%,10);minpoly(R,degree=4);solve(%);

>