New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

integrate(1/(x**2 + a**2)**2, x) is wrong if a is real #5907

Closed
asmeurer opened this Issue Oct 30, 2011 · 3 comments

Comments

Projects
None yet
3 participants
@asmeurer
Copy link
Member

asmeurer commented Oct 30, 2011

In [4]: a = Symbol('a', positive=True)

In [5]: integrate(1/(x**2 + a**2)**2, x)
Out[5]: 
                     ⎛x⎞
                 atan⎜─⎟
      x              ⎝a⎠
────────────── + ───────
   4      2  2        3 
2⋅a  + 2⋅a ⋅x      2⋅a  

In [6]: a = Symbol('a', real=True)

In [7]: integrate(1/(x**2 + a**2)**2, x)
Out[7]: 
      x       
──────────────
   4      2  2
2⋅a  + 2⋅a ⋅x 

It's easy to check that the first result is correct and the second is not.

Original issue for #5907: http://code.google.com/p/sympy/issues/detail?id=2808
Original author: https://code.google.com/u/asmeurer@gmail.com/

@asmeurer

This comment has been minimized.

Copy link
Member

asmeurer commented Oct 30, 2011

Note that this used to work in SymPy 0.7.0:

In [1]: a = Symbol('a', real=True)

In [2]: integrate(1/(x**2 + a**2)**2, x)
Out[2]: 
                      ⎛     4    ⎞        ⎛   4    ⎞
                      ⎜  ⅈ⋅a     ⎟        ⎜ⅈ⋅a     ⎟
                 ⅈ⋅log⎜- ──── + x⎟   ⅈ⋅log⎜──── + x⎟
                      ⎜     3    ⎟        ⎜   3    ⎟
      x               ⎝  │a│     ⎠        ⎝│a│     ⎠
────────────── - ───────────────── + ───────────────
   4      2  2              3                  3    
2⋅a  + 2⋅a ⋅x          4⋅│a│              4⋅│a│    

Then in SymPy 0.7.1 it failed with UnificationFailed: can't unify DMF(([], [mpz(1)]), ZZ) with 0, which was fixed by

commit 04a53dc970eb8632745fe0382c9864d0976231fa
Author: Mateusz Paprocki <mattpap@gmail.com>
Date:   Thu Oct 6 16:05:46 2011 -0700

    Fixed integrate(a/(a**2 + b*a + b*c*x**2), x) (#2718)

    In [1]: var('a:c', positive=True)
    Out[1]: (a, b, c)

    In [2]: integrate(a/(a**2+b*a+b*c*x**2),x)
    Out[2]:
              ⎛              ⎛    ___      3/2  ⎞            ⎞
      ___     ⎜            x⋅⎝a⋅╲╱ b ⋅c + b   ⋅c⎠            ⎟
    ╲╱ a ⋅atan⎜──────────────────────────────────────────────⎟
              ⎜ 3/2   ___   _______     ___     ___   _______⎟
              ⎝a   ⋅╲╱ c ⋅╲╱ a + b  + ╲╱ a ⋅b⋅╲╱ c ⋅╲╱ a + b ⎠
    ──────────────────────────────────────────────────────────
                        ___   ___   _______
                      ╲╱ b ⋅╲╱ c ⋅╲╱ a + b

    In [3]: simplify(_)
    Out[3]:
              ⎛   ___   ___   ⎞
      ___     ⎜ ╲╱ b ⋅╲╱ c ⋅x ⎟
    ╲╱ a ⋅atan⎜───────────────⎟
              ⎜  ___   _______⎟
              ⎝╲╱ a ⋅╲╱ a + b ⎠
    ───────────────────────────
         ___   ___   _______
       ╲╱ b ⋅╲╱ c ⋅╲╱ a + b

and then started giving the wrong result above.

**Cc:** matt...@gmail.com  

Original comment: http://code.google.com/p/sympy/issues/detail?id=2808#c1
Original author: https://code.google.com/u/asmeurer@gmail.com/

@asmeurer

This comment has been minimized.

Copy link
Member

asmeurer commented Mar 20, 2012

@flacjacket flacjacket added Wrong Result and removed WrongResult labels Mar 7, 2014

skirpichev added a commit to skirpichev/diofant that referenced this issue Nov 2, 2016

Add regression tests & mention closed issues
    close sympy/sympy#3112 (MrvAsympt was added in diofant#6)
    close sympy/sympy#9173 (test was added in 5a510ac)
    close sympy/sympy#9808 (fixed in 09e539b)
    close sympy/sympy#9341 (fixed in af98a00)
    close sympy/sympy#9908 (fixed in cc3fa8d)
    close sympy/sympy#6171 (test added in d278031)
    close sympy/sympy#9276 (diagnose_imports.py removed in ab8c535)
    close sympy/sympy#10201 (fixed in 0d0fc5f)
    close sympy/sympy#9057 (test was added in 8290a0c)
    close sympy/sympy#11159 (test was added in ffb76cb)
    close sympy/sympy#2839 (new AST transformers are used, see diofant#278 and diofant#167)
    close sympy/sympy#11081 (see ed01e16 and bb92329)
    close sympy/sympy#10974 (see 73fc425)
    close sympy/sympy#10806 (test in 539929a)
    close sympy/sympy#10801 (test in 2fe3da5)
    close sympy/sympy#9549 (test in 88bdefa)
    close sympy/sympy#4231 (test was added in fb411d5)
    close sympy/sympy#8634 (see 2fcbb58)
    close sympy/sympy#8481 (see 1ef20d3)
    close sympy/sympy#9956 (fixed in a34735f)
    close sympy/sympy#9747 (see e117c60)
    close sympy/sympy#7853 (see 3e4fbed)
    close sympy/sympy#9634 (see 2be03f5)
    close sympy/sympy#8500 (fixed in diofant#104 and finally in diofant#316)
    close sympy/sympy#9192 (see 9bf622f)
    close sympy/sympy#7130 (see e068fa3)
    close sympy/sympy#8514 (see b2d543b)
    close sympy/sympy#9334 (see 90de625)
    close sympy/sympy#8229 (see 9755b89)
    close sympy/sympy#8061 (see 7054f06)
    close sympy/sympy#7872 (tested in diofant#6)
    close sympy/sympy#3496 (tested in test_log_symbolic)
    close sympy/sympy#2929 (see da7db7a)
    close sympy/sympy#8203 (oo is not a real, see diofant#36)
    close sympy/sympy#7649 (0 is imaginary since diofant#8)
    close sympy/sympy#7256 (fixed in c0a4549)
    close sympy/sympy#6783 (see cb28d63)
    close sympy/sympy#5662 (is_integer issue fixed in 6bfa9f8, there is no is_bounded anymore)
    close sympy/sympy#5295 (fixed with diofant#354)
    close sympy/sympy#4856 (we now have flake/pep tests)
    close sympy/sympy#4555 (flake8 enabled after diofant#214)
    close sympy/sympy#5773 (cmp_to_key removed after diofant#164 and c9acbf0)
    close sympy/sympy#5484 (see above)

    Added regression tests:
    from https://groups.google.com/forum/#!topic/sympy/LkTMQKC_BOw
    fixes sympy/sympy#8825 (probably via diofant#209)
    fixes sympy/sympy#8635
    fixes sympy/sympy#8157
    fixes sympy/sympy#7872
    fixes sympy/sympy#7599
    fixes sympy/sympy#6179
    fixes sympy/sympy#5415
    fixes sympy/sympy#2865
    fixes sympy/sympy#5907
    fixes sympy/sympy#11722

    Closes diofant#347

skirpichev added a commit to skirpichev/diofant that referenced this issue Nov 2, 2016

Add regression tests & mention closed issues
    close sympy/sympy#3112 (MrvAsympt was added in diofant#6)
    close sympy/sympy#9173 (test was added in 5a510ac)
    close sympy/sympy#9808 (fixed in 09e539b)
    close sympy/sympy#9341 (fixed in af98a00)
    close sympy/sympy#9908 (fixed in cc3fa8d)
    close sympy/sympy#6171 (test added in d278031)
    close sympy/sympy#9276 (diagnose_imports.py removed in ab8c535)
    close sympy/sympy#10201 (fixed in 0d0fc5f)
    close sympy/sympy#9057 (test was added in 8290a0c)
    close sympy/sympy#11159 (test was added in ffb76cb)
    close sympy/sympy#2839 (new AST transformers are used, see diofant#278 and diofant#167)
    close sympy/sympy#11081 (see ed01e16 and bb92329)
    close sympy/sympy#10974 (see 73fc425)
    close sympy/sympy#10806 (test in 539929a)
    close sympy/sympy#10801 (test in 2fe3da5)
    close sympy/sympy#9549 (test in 88bdefa)
    close sympy/sympy#4231 (test was added in fb411d5)
    close sympy/sympy#8634 (see 2fcbb58)
    close sympy/sympy#8481 (see 1ef20d3)
    close sympy/sympy#9956 (fixed in a34735f)
    close sympy/sympy#9747 (see e117c60)
    close sympy/sympy#7853 (see 3e4fbed)
    close sympy/sympy#9634 (see 2be03f5)
    close sympy/sympy#8500 (fixed in diofant#104 and finally in diofant#316)
    close sympy/sympy#9192 (see 9bf622f)
    close sympy/sympy#7130 (see e068fa3)
    close sympy/sympy#8514 (see b2d543b)
    close sympy/sympy#9334 (see 90de625)
    close sympy/sympy#8229 (see 9755b89)
    close sympy/sympy#8061 (see 7054f06)
    close sympy/sympy#7872 (tested in diofant#6)
    close sympy/sympy#3496 (tested in test_log_symbolic)
    close sympy/sympy#2929 (see da7db7a)
    close sympy/sympy#8203 (oo is not a real, see diofant#36)
    close sympy/sympy#7649 (0 is imaginary since diofant#8)
    close sympy/sympy#7256 (fixed in c0a4549)
    close sympy/sympy#6783 (see cb28d63)
    close sympy/sympy#5662 (is_integer issue fixed in 6bfa9f8, there is no is_bounded anymore)
    close sympy/sympy#5295 (fixed with diofant#354)
    close sympy/sympy#4856 (we now have flake/pep tests)
    close sympy/sympy#4555 (flake8 enabled after diofant#214)
    close sympy/sympy#5773 (cmp_to_key removed after diofant#164 and c9acbf0)
    close sympy/sympy#5484 (see above)

    Added regression tests:
    from https://groups.google.com/forum/#!topic/sympy/LkTMQKC_BOw
    fixes sympy/sympy#8825 (probably via diofant#209)
    fixes sympy/sympy#8635
    fixes sympy/sympy#8157
    fixes sympy/sympy#7872
    fixes sympy/sympy#7599
    fixes sympy/sympy#6179
    fixes sympy/sympy#5415
    fixes sympy/sympy#2865
    fixes sympy/sympy#5907
    fixes sympy/sympy#11722

    Closes diofant#347
@ghost

This comment has been minimized.

Copy link

ghost commented Feb 2, 2018

I think this has been fixed

>>> var('x a b c d')
>>> integrate(1/(x**2 + a**2)**2, x)
x/(2*a**4 + 2*a**2*x**2) + (-I*log(-I*a + x)/4 + I*log(I*a + x)/4)/a**3
>>> y = integrate(1/(x**2 + a**2)**2, x)
>>> z = diff(y,x)
>>> simplify(z)
1/(a**4 + 2*a**2*x**2 + x**4)

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment