read NormalBasis;

f :=y^8-y^7+x*y^7+2*x^3*y^5+3*x*y^5-x*y^4+5*x^2*y^4+2*y^3+x^4*y^3
 -3*x^5*y^2+5*x^2*y^2+5*x^4*y^2+y+x^3*y+3*x^2*y-x^7*y+x^8-x^7+1-2*x^5+x:

n := degree(f,y);

alpha := RootOf(f,y):

V := Candidates(f,x,y);

beta := select(has,V,y)[1];
beta :=  subs(y=alpha, beta):
m_beta := evala(Norm(y - beta));

# So far, what's implemented is reducing the degree in x.
# Reducing the coefficient size in Q is not yet implemented.
# This will be done here at hoc.

m_beta := primpart(subs(y=y/7,m_beta)):
m_beta := collect(m_beta, y):
m_beta := sort(m_beta, y);

# Note that since degree(m_beta, x) is 1, the above computation is
# essentially equivalent to computing:
#
#    with(algcurves);
#    parametrization(f,x,y, t);