Displaying hyperbolic point should require maxima

[videlec]

The underlying problem is that elt.square_root() when elt belongs to a number field, relies on the symbolic ring.

from flatsurf import HyperbolicPlane
x = polygen(QQ)
K = NumberField(x^3 - 2, 'cbrt3', embedding=AA(2)**(1/3))
cbrt3 = K.gen()
H2 = HyperbolicPlane(K)
g0 = H2.geodesic(0, 1)
g1 = H2.geodesic(1/2 - cbrt3/5, 2)
p = g0.intersection(g1)
print(p)

gives

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
Cell In[29], line 1
----> 1 p.coordinates('half_plane')

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/flatsurf/geometry/hyperbolic.py:8767, in HyperbolicPoint.coordinates(self, model, ring)
   8765 square = 1 - x * x - y * y
   8766 try:
-> 8767     sqrt = square.sqrt()
   8768     if sqrt not in x.parent():
   8769         raise ValueError(f"square root of {square} not in {x.parent()}")

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/rings/number_field/number_field_element.pyx:2264, in sage.rings.number_field.number_field_element.NumberFieldElement.sqrt (build/cythonized/sage/rings/number_field/number_field_element.cpp:22045)()
   2262     from sage.misc.functional import sqrt
   2263     from sage.symbolic.ring import SR
-> 2264     root = sqrt(SR(self))
   2265     roots = [[root, 1], [-root, 1]]
   2266 except TypeError:

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9534)()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_ (build/cythonized/sage/structure/coerce_maps.c:6236)()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/rings/number_field/number_field_element.pyx:2965, in sage.rings.number_field.number_field_element.NumberFieldElement._symbolic_ (build/cythonized/sage/rings/number_field/number_field_element.cpp:27165)()
   2963 # Convert the embedding to an embedding into AA or QQbar
   2964 embedding = refine_embedding(embedding, infinity)
-> 2965 a = embedding(self).radical_expression()
   2966 if a.parent() == SR:
   2967     return a

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/rings/qqbar.py:4700, in AlgebraicNumber_base.radical_expression(self)
   4698 else:
   4699     interval_field = ComplexIntervalField(self._value.prec())
-> 4700 roots = poly.roots(SR, multiplicities=False)
   4701 if len(roots) != poly.degree():
   4702     return self

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/rings/polynomial/polynomial_element.pyx:8235, in sage.rings.polynomial.polynomial_element.Polynomial.roots (build/cythonized/sage/rings/polynomial/polynomial_element.c:66304)()
   8233 var = SR(vname)
   8234 expr = self(var)
-> 8235 rts = expr.solve(var,
   8236                  explicit_solutions=True,
   8237                  multiplicities=multiplicities)

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/symbolic/expression.pyx:12320, in sage.symbolic.expression.Expression.solve (build/cythonized/sage/symbolic/expression.cpp:91690)()
  12318 """
  12319 from sage.symbolic.relation import solve
> 12320 return solve(self, x, multiplicities=multiplicities,
  12321                       solution_dict=solution_dict,
  12322                       explicit_solutions=explicit_solutions,

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/symbolic/relation.py:1071, in solve(f, *args, **kwds)
   1066         raise TypeError("The first argument to solve() should be a "
   1067                         "symbolic expression or a list of symbolic "
   1068                         "expressions.")
   1070 if isinstance(f, Expression): # f is a single expression
-> 1071     return _solve_expression(f, x, explicit_solutions, multiplicities, to_poly_solve, solution_dict, algorithm, domain)
   1073 if not isinstance(f, (list, tuple)):
   1074     raise TypeError("The first argument must be a symbolic expression or a list of symbolic expressions.")

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/symbolic/relation.py:1330, in _solve_expression(f, x, explicit_solutions, multiplicities, to_poly_solve, solution_dict, algorithm, domain)
   1327     return _giac_solver(f, x, solution_dict)
   1329 # from here on, maxima is used for solution
-> 1330 m = ex._maxima_()
   1331 P = m.parent()
   1332 if explicit_solutions:

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/symbolic/expression.pyx:1236, in sage.symbolic.expression.Expression._maxima_ (build/cythonized/sage/symbolic/expression.cpp:36201)()
   1234     # Maybe not such a great idea because the "default" interface is another one
   1235     from sage.calculus.calculus import maxima
-> 1236     return super()._interface_(maxima)
   1237 else:
   1238     return super()._interface_(session)

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/structure/sage_object.pyx:686, in sage.structure.sage_object.SageObject._interface_ (build/cythonized/sage/structure/sage_object.c:5708)()
    684     except (KeyError, ValueError):
    685         pass
--> 686 nm = I.name()
    687 init_func = getattr(self, '_%s_init_' % nm, None)
    688 if init_func is not None:

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/misc/lazy_import.pyx:359, in sage.misc.lazy_import.LazyImport.__getattr__ (build/cythonized/sage/misc/lazy_import.c:4242)()
    357         True
    358     """
--> 359     return getattr(self.get_object(), attr)
    360 
    361 # We need to wrap all the slot methods, as they are not forwarded

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/misc/lazy_import.pyx:216, in sage.misc.lazy_import.LazyImport.get_object (build/cythonized/sage/misc/lazy_import.c:2674)()
    214     if likely(self._object is not None):
    215         return self._object
--> 216     return self._get_object()
    217 
    218 cpdef _get_object(self):

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/misc/lazy_import.pyx:252, in sage.misc.lazy_import.LazyImport._get_object (build/cythonized/sage/misc/lazy_import.c:2998)()
    250 
    251         try:
--> 252             self._object = getattr(__import__(self._module, {}, {}, [self._name]), self._name)
    253         except ImportError as e:
    254             if self._feature:

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/interfaces/maxima_lib.py:112
    110 ecl_eval("(setf *load-verbose* NIL)")
    111 if MAXIMA_FAS:
--> 112     ecl_eval("(require 'maxima \"{}\")".format(MAXIMA_FAS))
    113 else:
    114     ecl_eval("(require 'maxima)")

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/libs/ecl.pyx:1352, in sage.libs.ecl.ecl_eval (build/cythonized/sage/libs/ecl.c:10944)()
   1350 
   1351 #convenience routine to more easily evaluate strings
-> 1352 cpdef EclObject ecl_eval(str s):
   1353     r"""
   1354     Read and evaluate string in Lisp and return the result

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/libs/ecl.pyx:1375, in sage.libs.ecl.ecl_eval (build/cythonized/sage/libs/ecl.c:10877)()
   1373 """
   1374 cdef cl_object o
-> 1375 o=ecl_safe_eval(python_to_ecl(s, True))
   1376 return ecl_wrap(o)
   1377 

File ~/proj/eskin/flatsurf-0.5.2/lib/python3.9/site-packages/sage/libs/ecl.pyx:321, in sage.libs.ecl.ecl_safe_eval (build/cythonized/sage/libs/ecl.c:5659)()
    319         raise KeyboardInterrupt("ECL says: {}".format(message))
    320     else:
--> 321         raise RuntimeError("ECL says: {}".format(message))
    322 else:
    323     return ret

RuntimeError: ECL says: Filesystem error with pathname #P"/home/jule/proj/eskin/flatsurf-0.5.2/lib/ecl/maxima.fas".
Either
 1) the file does not exist, or
 2) we are not allowed to access the file, or
 3) the pathname points to a broken symbolic link.

[saraedum]

Fixed in #254.