Is there a mistake in PolynomialTraits_d::Sturm_habicht_sequence?

[stla]

Hello,

Either there's a mistake in PolynomialTraits_d::Sturm_habicht_sequence or I misunderstand something.

I have a polynomial x^3.y^4 + x^2.y^2 + 3*y - 6. I do PolynomialTraits_d::Sturm_habicht_sequence shs; and then shs(myPolynomial, out, 0). The 0 means that I want the Sturm-Habicht sequence with respect to the first variable, x. Here are the results:

[[1]]
-243*x^14 + 972*x^13 - 972*x^12 - 12*x^11 + 24*x^10 

[[2]]
-27*x^9 + 2*x^8.y + 54*x^8 

[[3]]
3*x^4.y^2 + 2*x^2.y 

[[4]]
x^4.y^3 + x^2.y^2 + 3*x - 6 

The last one should be my polynomial, but as you can see, the variables x and y have been swapped.

So there are two possibilities:

• I misunderstand something;
• CGAL permutes the variables in order to apply the algorithm with the outermost variable, but then it forgets to apply the inverse permutation to the results.

What do you think?