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
commented
10 months ago
The underlying problem is that
elt.square_root()wheneltbelongs to a number field, relies on the symbolic ring.gives