With Sage 10.2 on MacOS, I tried to do
t=var('t')
integral(cos(1+i*t), (t,0,1))
But I get an error:
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call last)
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/interfaces/maxima_lib.py:807, in MaximaLib.sr_integral(self, *args)
806 try:
--> 807 return max_to_sr(maxima_eval(([max_integrate],[sr_to_max(SR(a)) for a in args])))
808 except RuntimeError as error:
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/libs/ecl.pyx:830, in sage.libs.ecl.EclObject.__call__ (build/cythonized/sage/libs/ecl.c:11677)()
829 lispargs = EclObject(list(args))
--> 830 return ecl_wrap(ecl_safe_apply(self.obj,(<EclObject>lispargs).obj))
831
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/libs/ecl.pyx:353, in sage.libs.ecl.ecl_safe_apply (build/cythonized/sage/libs/ecl.c:9184)()
352 else:
--> 353 raise RuntimeError("ECL says: {}".format(message))
354 else:
RuntimeError: ECL says: Maxima asks: Is floor((%i+1)/(2*%pi)) positive, negative or zero?
During handling of the above exception, another exception occurred:
ValueError Traceback (most recent call last)
Cell In [82], line 1
----> 1 integral(cos(Integer(1)+i*t), (t,Integer(0),Integer(1)))
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/misc/functional.py:791, in integral(x, *args, **kwds)
658 """
659 Return an indefinite or definite integral of an object ``x``.
660
(...)
788
789 """
790 if hasattr(x, 'integral'):
--> 791 return x.integral(*args, **kwds)
792 else:
793 from sage.symbolic.ring import SR
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/expression.pyx:13270, in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:119603)()
13268 R = SR
13269 return R(integral(f, v, a, b, **kwds))
> 13270 return integral(self, *args, **kwds)
13271
13272 integrate = integral
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/integration/integral.py:1066, in integrate(expression, v, a, b, algorithm, hold)
1064 return indefinite_integral(expression, v, hold=hold)
1065 else:
-> 1066 return definite_integral(expression, v, a, b, hold=hold)
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/function.pyx:1046, in sage.symbolic.function.BuiltinFunction.__call__ (build/cythonized/sage/symbolic/function.c:15112)()
1044 res = self._evalf_try_(*args)
1045 if res is None:
-> 1046 res = super().__call__(
1047 *args, coerce=coerce, hold=hold)
1048
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/function.pyx:555, in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.c:9795)()
553 raise TypeError("arguments must be symbolic expressions")
554
--> 555 return call_registered_function(self._serial, self._nargs, args, hold,
556 not symbolic_input, SR)
557
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/pynac_function_impl.pxi:1, in sage.symbolic.expression.call_registered_function (build/cythonized/sage/symbolic/expression.cpp:137568)()
----> 1 cpdef call_registered_function(unsigned serial,
2 int nargs,
3 list args,
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/pynac_function_impl.pxi:47, in sage.symbolic.expression.call_registered_function (build/cythonized/sage/symbolic/expression.cpp:137103)()
45 for i in range(len(args)):
46 vec.push_back((<Expression>args[i])._gobj)
---> 47 res = g_function_evalv(serial, vec, hold)
48 elif nargs == 1:
49 res = g_function_eval1(serial,
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/function.pyx:1136, in sage.symbolic.function.BuiltinFunction._evalf_or_eval_ (build/cythonized/sage/symbolic/function.c:16356)()
1134 res = self._evalf_try_(*args)
1135 if res is None:
-> 1136 return self._eval0_(*args)
1137 else:
1138 return res
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/integration/integral.py:254, in DefiniteIntegral._eval_(self, f, x, a, b)
252 for integrator in self.integrators:
253 try:
--> 254 A = integrator(*args)
255 except (NotImplementedError, TypeError,
256 AttributeError, RuntimeError):
257 pass
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/symbolic/integration/external.py:46, in maxima_integrator(expression, v, a, b)
44 result = maxima.sr_integral(expression, v)
45 else:
---> 46 result = maxima.sr_integral(expression, v, a, b)
47 return result._sage_()
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/interfaces/maxima_lib.py:815, in MaximaLib.sr_integral(self, *args)
813 raise ValueError("Integral is divergent.")
814 elif "Is" in s: # Maxima asked for a condition
--> 815 self._missing_assumption(s)
816 else:
817 raise
File /private/var/tmp/sage-10.2-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/interfaces/maxima_lib.py:1056, in MaximaLib._missing_assumption(self, errstr)
1053 outstr = "Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume("\
1054 + errstr[jj+1:k] + ">0)', see `assume?` for more details)\n" + errstr
1055 outstr = outstr.replace('_SAGE_VAR_','')
-> 1056 raise ValueError(outstr)
ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(floor((%i+1)/(2*%pi))>0)', see `assume?` for more details)
Is floor((%i+1)/(2*%pi)) positive, negative or zero?
I am not sure what I'm being asked to assume, or how, since there should be complete information here (no unknown variables).
Incidentally, the indefinite integral integral(cos(1+i*t), t) works fine and returns -I*sin(I*t + 1) as expected.
