Jean-Pierre Flori wrote:
> Hi all,
> 
> It seems we are left with only one failing doctest, which just looks
> like a different but potentially valid answer:
> https://trac.sagemath.org/ticket/17254#comment:364
> 
> Does any one knows enough about resolution of singularities to validate
> the new answer?

The failing doctest is

sage: set_verbose(-1)
sage: K.<a> = QuadraticField(3)
sage: A.<x,y> = AffineSpace(K, 2)
sage: C = A.curve(x^4 + 2*x^2 + a*y^3 + 1)
sage: C.resolution_of_singularities(extend=True)[0] # long time (2 seconds)
(Affine Plane Curve over Number Field in a0 with defining polynomial y^4
- 4*y^2 + 16 defined by
24*x^2*ss1^3 + 24*ss1^3 + (a0^3 - 8*a0),
 Affine Plane Curve over Number Field in a0 with defining polynomial y^4
- 4*y^2 + 16 defined by
 24*s1^2*ss0 + (a0^3 - 8*a0)*ss0^2 + (6*a0^3)*s1,
 Affine Plane Curve over Number Field in a0 with defining polynomial y^4
- 4*y^2 + 16 defined by
 8*y^2*s0^4 + (-4*a0^3)*y*s0^3 - 32*s0^2 + (a0^3 - 8*a0)*y)


The new answer has changed signs in two cases (cf. diff in the comment
JP links to above):

(Affine Plane Curve over Number Field in a0 with defining polynomial y^4
- 4*y^2 + 16 defined by
24*x^2*ss1^3 + 24*ss1^3 + (a0^3 - 8*a0),
 Affine Plane Curve over Number Field in a0 with defining polynomial y^4
- 4*y^2 + 16 defined by
 24*s1^2*ss0 + (a0^3 - 8*a0)*ss0^2 + (-6*a0^3)*s1,
---------------------------------------^
 Affine Plane Curve over Number Field in a0 with defining polynomial y^4
- 4*y^2 + 16 defined by
 8*y^2*s0^4 + (4*a0^3)*y*s0^3 - 32*s0^2 + (a0^3 - 8*a0)*y)
---------------^


-leif


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