Simple Integration Problem
Hi, these simple steps used to work in Sage 8.0. They now give an error in 8.9. I tried in CoCalc, same problem. Do I need to change anything? If this is a Sage regression, how can I work around it? Thanks.
Sage 8.0 behavior:
sage: var('x t')
(x, t)
sage: psi = function('psi')(x, t)
sage: integrate(conjugate(psi) * diff(psi, x), x)
integrate(conjugate(psi(x, t))*diff(psi(x, t), x), x)
In 8.9 it gives:
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.9, Release Date: 2019-09-29 │
│ Using Python 2.7.15. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: var('x t')
(x, t)
sage: psi = function('psi')(x, t)
sage: integrate(conjugate(psi) * diff(psi, x), x)
---------------------------------------------------------------------------
...
ValueError: No differentiation variable specified.
Posting the complete trace below:
sage: var('x t')
(x, t)
sage: psi = function('psi')(x, t)
sage: integrate(conjugate(psi) * diff(psi, x), x)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-3-13afb3c477cd> in <module>()
----> 1 integrate(conjugate(psi) * diff(psi, x), x)
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/misc/functional.pyc in integral
(x, *args, **kwds)
751 """
752 if hasattr(x, 'integral'):
--> 753 return x.integral(*args, **kwds)
754 else:
755 from sage.symbolic.ring import SR
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage
.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:64036
)()
12360 R = ring.SR
12361 return R(integral(f, v, a, b, **kwds))
> 12362 return integral(self, *args, **kwds)
12363
12364 integrate = integral
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.p
yc in integrate(expression, v, a, b, algorithm, hold)
912 return integrator(expression, v, a, b)
913 if a is None:
--> 914 return indefinite_integral(expression, v, hold=hold)
915 else:
916 return definite_integral(expression, v, a, b, hold=hold)
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/function.pyx in sage.s
ymbolic.function.BuiltinFunction.__call__ (build/cythonized/sage/symbolic/function.cpp:11847)
()
996 res = self._evalf_try_(*args)
997 if res is None:
--> 998 res = super(BuiltinFunction, self).__call__(
999 *args, coerce=coerce, hold=hold)
1000
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/function.pyx in sage.s
ymbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6927)()
490 (<Expression>args[0])._gobj, hold)
491 elif self._nargs == 2:
--> 492 res = g_function_eval2(self._serial, (<Expression>args[0])._gobj,
493 (<Expression>args[1])._gobj, hold)
494 elif self._nargs == 3:
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.p
yc in _eval_(self, f, x)
92 for integrator in self.integrators:
93 try:
---> 94 A = integrator(f, x)
95 except (NotImplementedError, TypeError):
96 pass
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/integration/external.p
yc in sympy_integrator(expression, v, a, b)
66 else:
67 result = sympy.integrate(ex, (v, a._sympy_(), b._sympy_()))
---> 68 return result._sage_()
69
70 def mma_free_integrator(expression, v, a=None, b=None):
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/interfaces/sympy.pyc in _sympys
age_integral(self)
307 """
308 from sage.misc.functional import integral
--> 309 f, limits = self.function._sage_(), list(self.limits)
310 for limit in limits:
311 if len(limit) == 1:
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/interfaces/sympy.pyc in _sympys
age_mul(self)
204 s = 1
205 for x in self.args:
--> 206 s *= x._sage_()
207 return s
208
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/interfaces/sympy.pyc in _sympys
age_derivative(self)
333 f = self.args[0]._sage_()
334 args = [[a._sage_() for a in arg] if isinstance(arg,tuple) else arg._sage_() for
arg in self.args[2:]]
--> 335 return derivative(f, *args)
336
337 def _sympysage_order(self):
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/calculus/functional.pyc in deri
vative(f, *args, **kwds)
129 """
130 try:
--> 131 return f.derivative(*args, **kwds)
132 except AttributeError:
133 pass
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage
.symbolic.expression.Expression.derivative (build/cythonized/sage/symbolic/expression.cpp:255
45)()
4172 ValueError: No differentiation variable specified.
4173 """
-> 4174 return multi_derivative(self, args)
4175
4176 diff = differentiate = derivative
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/misc/derivative.pyx in sage.mis
c.derivative.multi_derivative (build/cythonized/sage/misc/derivative.c:3016)()
217 if not args:
218 # fast version where no arguments supplied
--> 219 return F._derivative()
220
221 for arg in derivative_parse(args):
/home/bryanso/sage-8.9/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage
.symbolic.expression.Expression._derivative (build/cythonized/sage/symbolic/expression.cpp:25
887)()
4234 return self.gradient()
4235 else:
-> 4236 raise ValueError("No differentiation variable specified.")
4237 if not isinstance(deg, (int, long, sage.rings.integer.Integer)) \
4238 or deg < 1:
ValueError: No differentiation variable specified.
This:
Is highly suspicious...
That clearly looks like a bug.
But I am not sure if it is directly related to my problem, which has the same variable x for diff and integrate.
But thanks for pointing out this new situation.
Maybe this can help to pinpoint the bug:
returns
Similarly,
returns
Here are a couple of more to-the-point examples:
This shows the correct result:
diff(psi(x, t), x). However, that's where things go wrong:returns
This behavior can be reduced even to the following:
This returns
So maybe the bug is where this evaluation is defined or maybe somewhere in the definition of
function. However, I must point out thatreturns
so I'd check the evaluation part of the code.
Also, the following work:
Hi desjas, all of your test cases return the same way in Sage 8.0 My problem does not happen in 8.0. I actually tried a few versions up to 8.8. All good. It started in 8.9. So logically I tend to think your test cases may not help pinpoint the error I observed.
The follow also errors out. This test does not have conjugate.
var('x t') f = function('f')(x, t) g = function('g')(x, t) integrate(g * diff(f, x), x)