

<p>We define the cyclotomic field of the 6th root of unity.</p>

{{{id=1|
K.<eta> = CyclotomicField(6);
///
}}}

<p>Just a test.</p>

{{{id=2|
eta^2-eta+1;
///
0
}}}

<p>The 3-dimensional affine space over K.</p>

{{{id=3|
A3.<zeta,nu,nub> = AffineSpace(K,3);A3;
///
Affine Space of dimension 3 over Cyclotomic Field of order 6 and degree 2
}}}

<p>The hypersurface W=\cal{W} (see Proposition 10.3).</p>

{{{id=4|
W = A3.subscheme(zeta^2-(nu*nub-2)*zeta+nu^3+nub^3-5*nu*nub+5);
///
}}}

<p>The locus where g is not defined.</p>

{{{id=6|
gsing = (A3.subscheme([zeta-1])).union(A3.subscheme([zeta-nu*nub+3]));
///
}}}

<p>The singular set Y of g: W -&gt; X.</p>

{{{id=5|
Y = W.intersection(gsing);
///
}}}

<p>The decomposition of Y into irreducible componenets.</p>

{{{id=7|
Y.irreducible_components();
///
[
Closed subscheme of Affine Space of dimension 3 over Cyclotomic Field of order 6 and degree 2 defined by:
  nu + nub + 2,
  zeta - 1,
Closed subscheme of Affine Space of dimension 3 over Cyclotomic Field of order 6 and degree 2 defined by:
  nu + (eta - 1)*nub + (-2*eta),
  zeta - 1,
Closed subscheme of Affine Space of dimension 3 over Cyclotomic Field of order 6 and degree 2 defined by:
  nu + (-eta)*nub + (2*eta - 2),
  zeta - 1,
Closed subscheme of Affine Space of dimension 3 over Cyclotomic Field of order 6 and degree 2 defined by:
  nu + nub + 2,
  nub^2 + zeta + 2*nub + 3,
Closed subscheme of Affine Space of dimension 3 over Cyclotomic Field of order 6 and degree 2 defined by:
  nu + (eta - 1)*nub + (-2*eta),
  nub^2 + (-eta)*zeta + (2*eta - 2)*nub + (-3*eta),
Closed subscheme of Affine Space of dimension 3 over Cyclotomic Field of order 6 and degree 2 defined by:
  nu + (-eta)*nub + (2*eta - 2),
  nub^2 + (eta - 1)*zeta + (-2*eta)*nub + (3*eta - 3)
]
}}}