Updates:
Labels: -NeedsReview NeedsBetterPatch mattpap
Comment #10 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
There is a bug:
In [11]: a = S("(1-5*x^2)/(x-2*x^3+x^5-1)")
In [12]: a
Out[12]:
⎛ 2⎞
-⎝1 - 5⋅x ⎠
─────────────────
3 5
1 - x + 2⋅x - x
In [13]: b = integrate(a, x)
In [14]: b
Out[14]:
⎛ 5 ⎛ ⎛ 2⎞⎞⎞
-RootSum⎝t - t - 1, Λ⎝t, t⋅log⎝x - t ⎠⎠⎠
In [15]: b.diff(x)
Out[15]:
5 - 12⋅s₆
─────────
4 - 6⋅s₆
Also, do you think something like this should still work?
In [1]: RootSum(x**5 - x + 1, sin)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/Users/aaronmeurer/Documents/Python/sympy/sympy/<ipython console> in
<module>()
/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/polys/rootoftools.py
in __new__(cls, expr, func, x)
545 func = Lambda(poly.gen, poly.gen)
546 elif not isinstance(func, Lambda) or func.nargs != 1:
--> 547 raise ValueError("expected a univariate Lambda,
got %s" % func)
548
549 (_, factors), terms = poly.factor_list(), []
ValueError: expected a univariate Lambda, got sin
And it isn't so slow for me:
In [38]: a = RootSum(x**5 - x + 1, Lambda(z, z*log(x - z)))
In [39]: %timeit a.diff(x)
10 loops, best of 3: 84.2 ms per loop
In [40]: %timeit a = RootSum(x**5 - x + 1, Lambda(z, z*log(x - z)))
100 loops, best of 3: 2.11 ms per loop
By the way, this fix should also help me fix some problems I have been
having in risch_integrate, namely with integrals that should return RootSum
(like risch_integrate(1/(exp(5*x) + exp(x) + 1), x)). Basically, the
integrator needs to be able to subtract the derivative of the RootSum in
order to get the remaining part of the integral, but until this fix, it
isn't possible.
--
You received this message because you are subscribed to the Google Groups
"sympy-issues" group.
To post to this group, send email to sympy-iss...@googlegroups.com.
To unsubscribe from this group, send email to
sympy-issues+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sympy-issues?hl=en.
