% Test of algebraic number package.
defpoly sqrt2**2-2;
1/(sqrt2+1);
(x**2+2*sqrt2*x+2)/(x+sqrt2);
on gcd;
(x**3+(sqrt2-2)*x**2-(2*sqrt2+3)*x-3*sqrt2)/(x**2-2);
off gcd;
sqrt(x**2-2*sqrt2*x*y+2*y**2);
off arnum; %to start a new algebraic extension.
defpoly cbrt5**3-5;
on rationalize;
1/(x-cbrt5);
off rationalize;
off arnum; %to start a new algebraic extension.
%The following examples are taken from P.S. Wang Math. Comp. 30,
% 134,(1976),p.324.
on factor;
defpoly i**2+1=0;
w0 := x**2+1;
w1 := x**4-1;
w2 := x**4+(i+2)*x**3+(2*i+5)*x**2+(2*i+6)*x+6;
w3 := (2*i+3)*x**4+(3*i-2)*x**3-2*(i+1)*x**2+i*x-1;
off arnum;
defpoly a**2-5;
w4 := x**2+x-1;
off arnum;
defpoly a**2+a+2;
w5 := x**4+3*x**2+4;
off arnum;
defpoly a**3+2=0;
w6:=64*x**6-4;
off arnum;
defpoly a**4+a**3+a**2+a+1=0;
w7:=16*x**4+8*x**3+4*x**2+2*x+1;
off arnum, factor;
defpoly sqrt5**2-5,cbrt3**3-3;
cbrt3**3;
sqrt5**2;
cbrt3;
sqrt5;
sqrt(x**2+2*(sqrt5-cbrt3)*x+5-2*sqrt5*cbrt3+cbrt3**2);
on rationalize;
1/(x+sqrt5-cbrt3);
off arnum, rationalize;
split_field(x**3+2);
for each j in ws product (x-j);
split_field(x**3+4*x**2+x-1);
for each j in ws product (x-j);
split_field(x**3-3*x+7);
for each j in ws product (x-j);
split_field(x**3+4*x**2+x-1);
for each j in ws product (x-j);
split_field(x**3-x**2-x-1);
for each j in ws product (x-j);
% A longer example.
off arnum;
defpoly a**6+3*a**5+6*a**4+a**3-3*a**2+12*a+16;
factorize(x**3-3);
end;