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Substitution error when computing fundamental groups.

#42206Openenriqueartal 创建于 2026-05-19
t: bug
E
enriqueartalcommented
### Steps To Reproduce If one computes the fundamental group of an arrangement of projective plane curves in some cases an error happens, e.g., when one of the curves passes through $[0:1:0]$ and there are tangent lines different from $z=0$. The error happens if the first two variables are $u, v$. ### Expected Behavior No error in the computation. ### Actual Behavior ``` sage: P.<u, v, w> = ProjectivePlaneCurveArrangements(QQ) sage: f = u * v - w^2 sage: P(f).fundamental_group() --------------------------------------------------------------------------- TypeError Traceback (most recent call last) Cell In[4], line 1 ----> 1 P(f).fundamental_group() File /usr/local/sage/src/sage/schemes/curves/plane_curve_arrangement.py:898, in ProjectivePlaneCurveArrangementElement.fundamental_group(self, simplified) 896 changes = any(g.degree(v) < g.degree() > 1 for g in affines) 897 while changes: --> 898 affines = [f.subs({u: u + v}) for f in affines] 899 changes = any(g.degree(v) < g.degree() > 1 for g in affines) 900 C_affine = affine(affines) File sage/rings/polynomial/multi_polynomial_libsingular.pyx:3687, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs() -> 3687 'Could not get source, probably due dynamically evaluated source code.' TypeError: keys do not match self's parent sage: Curve(f).fundamental_group() Finitely presented group < x0 | x0^2 > sage: P.<x, y, z> = ProjectivePlaneCurveArrangements(QQ) sage: g = x * y - z^2 sage: P(g).fundamental_group() Finitely presented group < x | x^2 > ``` ### Additional Information _No response_ ### Environment I follow a PR with a solution. ### Checklist - [x] I have searched the existing issues for a bug report that matches the one I want to file, without success. - [x] I have read the documentation and troubleshoot guide
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