Updates:
Status: Fixed
Labels: -NeedsBetterPatch PassedReview
Comment #50 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
This was pushed in.
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Comment #46 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
This was also explained before, but let me explain again. diff can only
take derivatives with respect to objects that
Comment #47 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Yes, I know that the implementation uses ._diff_wrt, but the resulting
behaviour appears completely arbitrary
Comment #49 on issue 1816 by brad.froehle: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Because cos(2*x) can unambiguously be replaced in the original expression
with the simple rule of exact substitution
Comment #37 on issue 1816 by Vinzent.Steinberg: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I thing the most important thing is a clearly defined behavior. The
docstring should mention that it does this
Comment #38 on issue 1816 by brad.froehle: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I'm really uncomfortable with this, for example:
x = symbols('x')
diff(1-cos(x)**2,sin(x))
0
Comment #39 on issue 1816 by elliso...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
We have already established that derivatives wrt to function does *not*
commute with algebraic manipulations.
Comment #40 on issue 1816 by brad.froehle: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
So then these are derivatives with respect to formal variables with no
additional meaning like Frechet derivatives.
Comment #41 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Brad, Luke, Brian, Vinzent, Ronan, and others, what do you think of my
description in comment 35? If you are OK with
Comment #42 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Brian: The Hamiltonian is a constant for any specific trajectory of the
system, but it's not a constant over
Comment #43 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Aaron: it's a clear description of *some operation* (except that you didn't
explain what kind of objects are
Comment #44 on issue 1816 by hazelnu...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Aaron:
expr.subs(function, Dummy('x')).diff(Dummy('x')).subs(Dummy('x'),
function)
Makes perfect sense to
Comment #45 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
What users should enter is rather something like:
x, t = symbols('x, t')
xfunc = Function('x')
diff(2*x + 4,
Comment #24 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
If we're talking about elementary calculus, then deriving wrt a function
doesn't make sense. We already have
Comment #25 on issue 1816 by elliso...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I don't have any further time to put into arguing about the deep
mathematics of these derivatives. I feel like
Comment #26 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
OK, I think I get it now (after comment 23 it clicked for me).
So I think I am +1 to this now, even with the strange
Comment #27 on issue 1816 by Vinzent.Steinberg: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Can you cite an example of somewhere where this is computed as so with
the Lagrangian?
The simplest possible
Comment #28 on issue 1816 by elliso...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
The Falling Mass example here shows this, in that diff(L, x(t)) == mg,
which assumes that the derivative you
Comment #29 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
OK, that is evidence enough for me. And this would assumedly extend to
diff(f(x), x, n).diff(diff(f(x), x, m)) ==
Comment #30 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
There's absolutely no need here to compute diff(x', x) (whatever that
means). x and x' are separate,
Comment #31 on issue 1816 by Vinzent.Steinberg: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Sorry, I don't get your point. Why can't we consider diff(x'(t), x(t)) as
diff(x', x)? Let's say they are just
Comment #32 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
The problem is that in the conventional presentation of Lagrangian
mechanics, we use the same name for
Comment #34 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
In formal mathematics, Lagrangian mechanics is presented in terms of stuff
like differential manifolds and
Comment #35 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
From that Wikipedia page you reference: However, all that is meant by this
notation is the derivative of the function
Comment #20 on issue 1816 by renato.c...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I don't think what's being implemented is the Frechet derivative. For
example:
Comment #21 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I don't think you're interpreting WolframAlpha's output correctly. See
Comment #22 on issue 1816 by renato.c...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Yeah, maybe you are right, but then I have no idea what it is actually
computing.
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Comment #23 on issue 1816 by elliso...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
The issue topic looks more like a simple partial derivative, as is very
commonly used in mechanic
Yes,
Comment #19 on issue 1816 by Vinzent.Steinberg: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
In variational calculus, the first derivative of a functional is not that
complicated. Acutally, it's definition
Comment #10 on issue 1816 by Vinzent.Steinberg: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
As long as it does not introduce regressions I'm fine with merging it.
People who don't like derivative wrt a
Comment #11 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I don't understand what Derivative(f(g(x)), g(x)) or diff(f(g(x)), g(x))
are supposed to mean, mathematically.
Comment #12 on issue 1816 by elliso...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
The simplest way of thinking about derivatives wrt to function is that
functions like f(x) and g(x) are *no
Comment #13 on issue 1816 by elliso...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I should also note that the wikipedia page on the chain rule explains a bit
more about the notation, and also
Comment #14 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
My last concern was to add some raises() tests, which it seems has been
done, so I am +1 if the tests pass.
Brian's
Comment #15 on issue 1816 by ronan.l...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
@Brian: Could you please explain the intended meaning of diff(f(g(x)),
g(x)) and Derivative(f(g(x)), g(x)) in
Comment #16 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I think the best way to explain it is to just assert that diff(f(g(x)),
g(x)) is f'(g(x)). In other words, the derivative
Comment #17 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
WolframAlpha gives 0:
http://www.wolframalpha.com/input/?i=diff(diff(f(x),%20x),%20f(x))
Apparently it's a Fréchet
Comment #18 on issue 1816 by asmeurer: Adding partial derivatives and
taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
By the way, the distributional derivative exists for any integrable
function, even if it's continuous nowhere. I think
Comment #9 on issue 1816 by elliso...@gmail.com: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I checked and Mathematica returns *exactly* what my Funcderiv branch does.
Namely, it treats derivatives wrt
Comment #8 on issue 1816 by asmeurer: Adding partial derivatives and taking
derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I claim that the following is *now* correct even though this is different
from what wsa given after 1620 was fixed.
Hmm.
Updates:
Cc: asmeurer
Comment #4 on issue 1816 by elliso...@gmail.com: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I have implemented the _diff_wrt approach in my pull request. It appears
to
Updates:
Labels: -NeedsReview NeedsBetterPatch
Comment #5 on issue 1816 by asmeurer: Adding partial derivatives and taking
derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Tests and docs would be nice. So far, I get
In [2]: diff(f(x),
Comment #6 on issue 1816 by asmeurer: Adding partial derivatives and taking
derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
And this definitely needs to be fixed:
In [7]: f(g(x)).diff(x)
Out[7]:
dd
─(f(g(x)))⋅──(g(x))
dg(x)
Comment #7 on issue 1816 by elliso...@gmail.com: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
In my funcderiv branch the following now work:
In [2]: diff(f(x), x).diff(f(x))
Out[2]: 0
In [3]: (sin(f(x)) -
Status: New
Owner:
Labels: Type-Defect Priority-Medium
New issue 1816 by Yohumbus: Adding partial derivatives and taking
derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
What I have been trying to do is construct a lagrangian and perform the
Comment #1 on issue 1816 by asmeurer: Adding partial derivatives and taking
derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
This is probably related to issue 1660. The solution posted there is just
a quick fix though. I think we need
issue 1620
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