Updates:
Status: Fixed
Labels: -NeedsReview PassedReview
Comment #34 on issue 2132 by matt...@gmail.com: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
All this is in master now.
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Comment #27 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Now it can:
In [1]: f = 161*z**3 + 115*z**2 + 19*z + 1
In [2]: g = Lambda(z, z*log(-3381*z**4/4 - 3381*z**3/4 - 625*z**2/2 -
125*z/2 - 5 + exp(x)))
In [3]: RootSum(f, g)
Comment #28 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
It's pretty slow though (70% of time being spent in expand() (the most
annoying function in SymPy for me)).
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Comment #29 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
In 30c7fa78690828a0ac12b0e84c7ede31f4d4beff in polys12 I also fixed the
problem with subs() (actually I fixed RootOf(*RootOf(...).args)).
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Labels: -NeedsBetterPatch NeedsReview
Comment #30 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
(No comment was entered for this change.)
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Comment #31 on issue 2132 by Vinzent.Steinberg: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Do you use the general expand() or a specialized version, that does not try
to expand everything? I think there are many low-hanging fruits in
expand()...
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Comment #32 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
So implementing Frac() will make this faster by allowing it to do expand
entirely in Poly?
And I totally agree with you about expand(). Let's make it a priority to
make it
Comment #33 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
And by the way, my example now works (I forgot to throw in a term):
In [6]: cancel((a + x).diff(x))
Out[6]:
1
─
x5⋅x
1 + ℯ + ℯ
So this is exactly what
Comment #24 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
So, SymPy doesn't know that RootSum is commutative.
Now it knows. Also RootOf is now commutative.
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Comment #26 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
I think the problem, or at least part of the problem, is that it is trying
to expand the RootSum into a sum or RootOfs instead of simplifying the
rational function Lambda, which
Updates:
Labels: -NeedsBetterPatch NeedsReview
Comment #12 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
All problems from #10 and #11 were fixed:
In [1]: a = S((1-5*x^2)/(x-2*x^3+x^5-1))
In [2]: a
Out[2]:
⎛ 2⎞
-⎝1 -
Comment #13 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Good idea about just converting RootSum(..., sin) into RootSum(…, Lambda(i,
sin(i))).
It's good to see that you implemented an unevaluated form of RootSum; I was
going to
Comment #14 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
I used 'auto' keyword because RootSum with auto=False isn't unevaluated, it
just skips some of its simplification algorithms (this is different from
being unevaluated, like e.g.
Comment #15 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
I used 'auto' keyword because RootSum with auto=False isn't unevaluated
That is what I figured. This is fine then.
If it hangs on line 645, then this is performance issue.
Comment #17 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
polys12 is available from github.com/mattpap/sympy-polys
Known issues:
- possible bug in tests runner makes polystools.py fail on 2.4 (too many
tests ;)
- tests fail in ode
Comment #18 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Can you create a pull request and/or separate issue for polys12?
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Comment #19 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
PolynomialError: non-commutative expressions are not supported
Actually this is true:
In [1]: RootSum(x**2 + 1, Lambda(x, exp(x)))
Out[1]:
⎛ 2 ⎛x⎞⎞
RootSum⎝x +
Comment #21 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Unless this is trivial to fix, I would put this into a separate issue.
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Comment #22 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
It's issue 2134.
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Comment #23 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
And polys12 is issue 2133.
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Updates:
Owner: mattpap
Cc: -mattpap
Labels: Milestone-Release0.7.0
Comment #8 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
viete() function was added in 8f8e6a786b0d0e15a65b01a68367532a0cac55b7 to
polys11, e.g.:
Updates:
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Comment #9 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
In 74cd9297f0df1df6bbdeaf12616d62dd71141a0f support for auto-simplification
of rational functions was added to RootSum, e.g.:
In [1]: %time
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 ⎠
Comment #11 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
I just noticed, don't you have x and z backwards in that example (c.f. the
output from integrate in [29] in my OP)? It should be RootSum(z**5 - z**2
+ 1, Lambda(z, z*log(x -
Status: Accepted
Owner: asmeurer
CC: mattpap
Labels: Type-Defect Priority-Medium Integration Polynomial
New issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
diff does not work at all with RootSum. This makes it impossible to
reverse
Comment #1 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
There is also a bug with diff and Lambda:
In [31]: Lambda(z, z*log(x - z)).diff(x)
---
TypeError
Comment #2 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
In this particular case, this is an application of Viete formulas. Take an
expression:
In [6]: var('r1:6')
Out[6]: (r₁, r₂, r₃, r₄, r₅)
In [7]: R = _
In [8]: sum(r/(x - r) for r
Comment #3 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Excellent! Thanks for the information. So I guess what we need to do is:
1. Implement the Viete formulas in the polys somewhere.
2. Put in a check somewhere in RootSum to see it
Updates:
Status: Started
Comment #4 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
1. I started implementing this.
3. I'm aware of the fact that the lambda can be an arbitrary expression.
The example you gave can be done by
Comment #5 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
After a bit more research, I think it can be done. See
http://en.wikipedia.org/wiki/Newton_identities.
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Comment #7 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Ah, yes, I forgot about that function. Of course, it should be symmetric,
because to be symmetric just means that we can reorder the r_i any way we
like and still get the same
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