It looks like in the git master the integral works:
In [1]: var('a')
Out[1]: a
In [2]: integrate(abs(a)*exp(-abs(a)*x), (x, 0, oo))
Out[2]:
⎧ π
⎪ 1 for │periodic_argument(│a│, ∞)│ < ─
⎪ 2
⎪
⎪∞
⎨⌠
⎪⎮ -x⋅│a│
⎪⎮ ℯ ⋅│a│ dx otherwise
⎪⌡
⎪0
⎩
But the limit bug still exists (it's simply bypassed by the new
integration algorithm), so if you could still open an issue for that,
that would be great.
Aaron Meurer
On Mon, Jun 18, 2012 at 1:12 PM, Aaron Meurer <[email protected]> wrote:
> It's definitely a bug. integrate should catch NotImplementedError from
> limit() and return an unevaluated Integral.
>
> Also, not knowing the sign of abs is definitely a bug as well. Please open
> an issue for this at http://code.google.com/p/sympy/issues/list.
>
> Aaron Meurer
>
> On Jun 18, 2012, at 12:53 PM, Barak Yair Reif <[email protected]> wrote:
>
> I tried to look for this bug and haven't found it (maybe my lacking search
> skills), still I felt uncomfortable to open an issue.
>
> Here is the code:
>
> x=Symbol("x")
>
> f1=2*E**(-2*x)
> F1=integrate(f1,(x,0,oo))
> print F1 #Works great:
>
> a=Symbol("a")
> f2=abs(a)*E**(-abs(a)*x)
> F2=integrate(f2,(x,0,oo)) #fails
>
> and the output is:
>
> Traceback (most recent call last):
> File "C:/Users/Barak/Desktop/python/temp", line 18, in <module>
> F2=integrate(f2,(x,0,oo))
> File "C:\Python27\lib\site-packages\sympy\utilities\decorator.py", line
> 24, in threaded_func
> return func(expr, *args, **kwargs)
> File "C:\Python27\lib\site-packages\sympy\integrals\integrals.py", line
> 847, in integrate
> return integral.doit(deep = False)
> File "C:\Python27\lib\site-packages\sympy\integrals\integrals.py", line
> 393, in doit
> function = antideriv._eval_interval(x, a, b)
> File "C:\Python27\lib\site-packages\sympy\core\expr.py", line 229, in
> _eval_interval
> B = limit(self, x, b)
> File "C:\Python27\lib\site-packages\sympy\series\limits.py", line 116, in
> limit
> return i*limit(d, z, z0, dir)
> File "C:\Python27\lib\site-packages\sympy\series\limits.py", line 192, in
> limit
> r = gruntz(e, z, z0, dir)
> File "C:\Python27\lib\site-packages\sympy\series\gruntz.py", line 678, in
> gruntz
> r = limitinf(e, z)
> File "C:\Python27\lib\site-packages\sympy\core\cache.py", line 101, in
> wrapper
> func_cache_it_cache[k] = r = func(*args, **kw_args)
> File "C:\Python27\lib\site-packages\sympy\series\gruntz.py", line 480, in
> limitinf
> c0, e0 = mrv_leadterm(e, x)
> File "C:\Python27\lib\site-packages\sympy\core\cache.py", line 101, in
> wrapper
> func_cache_it_cache[k] = r = func(*args, **kw_args)
> File "C:\Python27\lib\site-packages\sympy\series\gruntz.py", line 562, in
> mrv_leadterm
> f, logw = rewrite(exps, Omega, x, w)
> File "C:\Python27\lib\site-packages\sympy\series\gruntz.py", line 627, in
> rewrite
> raise NotImplementedError('Result depends on the sign of %s' % sig)
> NotImplementedError: Result depends on the sign of -sign(Abs(a))
>
>
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