Hey folks,
I'm pretty new to this, so please be patient.
During my developement of an implementation of characteristic classes of
the tangent bdl of manifolds, I've encountered a problem when wedging
unnamed differential forms on non-parallelizable manifolds. Let's have an
example:
sage: S2 = Manifold(2, name='S2', latex_name=r'S^2', start_index=1)
sage: U = S2.open_subset(name='U', latex_name=r'S^2 \setminus \{\text{South
pole}\}')
sage: V = S2.open_subset(name='V', latex_name=r'S^2 \setminus \{\text{North
pole}\}')
sage: S2.declare_union(U,V)
sage: c_xy.<t,z> = U.chart()
sage: c_uv.<u,v> = V.chart()
sage: xy_to_uv = c_xy.transition_map(c_uv, (x/(x^2+y^2), y/(x^2+y^2)),
intersection_name='W', restrictions1= x^2+y^2
!=0,
restrictions2= u^2+v^2!=0)
sage: uv_to_xy = xy_to_uv.inverse()
sage: e_tz = c_tz.frame()
sage: e_uv = c_uv.frame(); print(e_uv)
sage: omega = S2.diff_form(1, name='omega', latex_name=r'\omega')
sage: unnamed = S2.diff_form(1)
sage: omega[e_xy,:] = -x^2, y^2; show(omega.disp(e_tz))
sage: omega.add_comp_by_continuation(e_uv, V.intersection(U), c_uv)
sage: unnamed[e_xy,:] = -x^2, y^2; show(omega.disp(e_tz))
sage: unnamed.add_comp_by_continuation(e_uv, V.intersection(U), c_uv)
sage: unnamed.wedge(omega)
---------------------------------------------------------------------------UnboundLocalError
Traceback (most recent call
last)<ipython-input-40-a6a98dadea76> in <module>()----> 1 unnamed.wedge(omega)
/opt/sagemath-8.6/local/lib/python2.7/site-packages/sage/manifolds/differentiable/diff_form.pyc
in wedge(self, other) 520 vmodule =
dom_resu.vector_field_module(dest_map=dest_map_resu) 521 resu_degree
= self._tensor_rank + other._tensor_rank--> 522 resu =
vmodule.alternating_form(resu_degree, name=resu_name, 523
latex_name=resu_latex_name) 524 for dom in
self_r._restrictions:
UnboundLocalError: local variable 'resu_name' referenced before assignment
Unfortunately, I'm not a professional in python, but I guess the problem could
be solved by declaring resu_name and resu_latex_name in the wedge method of the
manifolds/differentiable/tensorfield.py file as "None" in the very beginning.
In fact, solving this is crucial for calculations with mixed differential forms
and its matrices in order to compute the characteristic classes.
What is the next step? Create a ticket?
Also, I like to discuss my developement so far. But that might be better for
another thread.
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