I've been trying for a while to find why some integrals cause giac to crash. This is different from earlier question I asked.
This seem to be an interface issue between sagemath and giac.
Here is an integrand which causes giac to crash according to sagemath. Ok, may be due sagemath changing the form of the integrand. I do not know. (this takes about almost 10 minutes to crash, which I do not know why so long).
btw, is there a way to see what exactly sagemath sends to giac in the call if sagemath changes the form of the integrand? Is there a way to trace the call?
sage: var("x f e a b z")
sage: integrand = cot(f * x + e) * (a + b * sin(f * x + e) ^ 2) ^ (1 / 2)
sage: integrand
sqrt(b*sin(f*x + e)^2 + a)*cot(f*x + e)
sage: integrate(integrand, x, algorithm="giac")
Giac crashed -- automatically restarting.
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
File /usr/lib/python3.10/site-packages/sage/interfaces/interface.py:1216, in InterfaceElement.__getattr__(self, attrname)
1215 try:
-> 1216 P = self._check_valid()
1217 except ValueError:
File /usr/lib/python3.10/site-packages/sage/interfaces/expect.py:1500, in ExpectElement._check_valid(self)
1498 if P is None or P._session_number == BAD_SESSION or self._session_number == -1 or \
1499 P._session_number != self._session_number:
-> 1500 raise ValueError("The %s session in which this object was defined is no longer running."%P.name())
1501 except AttributeError:
ValueError: The giac session in which this object was defined is no longer running.
During handling of the above exception, another exception occurred:
AttributeError Traceback (most recent call last)
Input In [9], in <module>
----> 1 integrate(integrand, x, algorithm="giac")
File /usr/lib/python3.10/site-packages/sage/misc/functional.py:764, in integral(x, *args, **kwds)
639 """
640 Return an indefinite or definite integral of an object ``x``.
641
(...)
761
762 """
763 if hasattr(x, 'integral'):
--> 764 return x.integral(*args, **kwds)
765 else:
766 from sage.symbolic.ring import SR
File /usr/lib/python3.10/site-packages/sage/symbolic/expression.pyx:13138, in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:95254)()
13136 R = SR
13137 return R(integral(f, v, a, b, **kwds))
> 13138 return integral(self, *args, **kwds)
13139
13140 integrate = integral
File /usr/lib/python3.10/site-packages/sage/symbolic/integration/integral.py:1047, in integrate(expression, v, a, b, algorithm, hold)
1045 if not integrator:
1046 raise ValueError("Unknown algorithm: %s" % algorithm)
-> 1047 return integrator(expression, v, a, b)
1048 if a is None:
1049 return indefinite_integral(expression, v, hold=hold)
File /usr/lib/python3.10/site-packages/sage/symbolic/integration/external.py:258, in giac_integrator(expression, v, a, b)
256 return expression.integrate(v, a, b, hold=True)
257 else:
--> 258 return result._sage_()
File /usr/lib/python3.10/site-packages/sage/interfaces/giac.py:1135, in GiacElement._sage_(self, locals)
1131 from sage.calculus.calculus import symbolic_expression_from_string, SR_parser_giac
1133 result = repr(self) # string representation
-> 1135 if str(self.type()) not in ['DOM_LIST', 'vector', 'vecteur']:
1136
1137 # Merge the user-specified locals dictionary and the symbol_table
1138 # (locals takes priority)
1139 lsymbols = symbol_table['giac'].copy()
1140 lsymbols.update(locals)
File /usr/lib/python3.10/site-packages/sage/interfaces/interface.py:1218, in InterfaceElement.__getattr__(self, attrname)
1216 P = self._check_valid()
1217 except ValueError:
-> 1218 raise AttributeError(attrname)
1219 if attrname[:1] == "_":
1220 raise AttributeError
AttributeError: type
sage:
When I change e to say z the crash goes away! This answer returns immediately also.
sage: integrand = cot(f * x + z) * (a + b * sin(f * x + z) ^ 2) ^ (1 / 2)
sage: integrand
sqrt(b*sin(f*x + z)^2 + a)*cot(f*x + z)
sage: integrate(integrand, x, algorithm="giac")
(a*arctan(sqrt(b*sin(f*x + z)^2 + a)/sqrt(-a))/sqrt(-a) + sqrt(b*sin(f*x + z)^2 + a))/f
Note that the above used to work OK in 9.3. i.e. when using e, it used to work and return the same antiderivative shown above but with z replaced by e. I have report showing this worked before with giac. so something changed.
Notice that giac, e is the Euler constant. And I assume sagemath knows this ofcourse and it changes internally e to some made up VAR symbol before calling giac and in return reverse this back to e in sagemath space.
Here is the same thing inside giac, both complete immeadility.
2>> integrand:=sqrt(b*sin(f*x + e)^2 + a)*cot(f*x + e)
3>> integrate(integrand,x)
1/b/f*b*(sqrt(a+b*sin(f*x+exp(1))^2)+2*a/2/sqrt(-a)*atan(sqrt(a+b*sin(f*x+exp(1))^2)/sqrt(-a)))
4>> integrand:=sqrt(b*sin(f*x + z)^2 + a)*cot(f*x + z)
5>> integrate(integrand,x)
1/b/f*b*(sqrt(a+b*sin(f*x+z)^2)+2*a/2/sqrt(-a)*atan(sqrt(a+b*sin(f*x+z)^2)/sqrt(-a)))
No crash inside giac for same integrand using e or z
my question is: Why giac crashes when using e but not when using z? Surely the letter should not have made a difference? Is this a new interface problem? Why this same integral worked in 9.3 but not in 9.5? I am running the same test.
Is this new issue? Maybe I should make a ticket on it?
