On Jun 19, 8:34 pm, Renato Coutinho <[email protected]> wrote:
> On Sun, Jun 19, 2011 at 9:30 PM, Chris Smith <[email protected]> wrote:
>
> > On Sun, Jun 19, 2011 at 7:05 PM, Renato Coutinho <[email protected]>
> > wrote:
>
> >> Hello,
>
> >> On Sun, Jun 19, 2011 at 3:51 PM, Mani Chandra <[email protected]> wrote:
> >> > Hi,
> >> > Is it possible to tell simplify that the partial derivatives with
> >> > respect to
> >> > two different variable commute so that it can simplify further? For ex:
> >> > d^2 f/dxdy + d^2 f/dydx
> >> > The above expression is left as it is by simplify(), but it would be
> >> > nice if
> >> > there were some way to tell it about the commutation so that it can
> >> > simplify
> >> > further.
>
> >> This is fixed in current development version, so that
>
> >> >>> f(x, y).diff(x, y) - f(x, y).diff(y, x)
> >> 0
>
> >> If you don't want this to happen, you have to use unevaluated
> >> derivatives (diff() always evaluates them):
>
> >> >>> Derivative(f(x, y), x, y) - Derivative(f(x, y), y, x)
> >> D(f(x, y), x, y) - D(f(x, y), y, x)
>
> > Notice that he used "+" not "-" -- does he want `2*D(f(x,y), x, y)` to be
> > returned?
>
> Yes, I think that's what he meant, and it works too, returning
> 2*D(f(x, y), x, y).
With current git I get the behavior
In [1]: x=Symbol('x')
In [2]: y=Symbol('y')
In [3]: f=Function('f')
In [4]: f(x,y).diff(x,y)-f(x,y).diff(y,x)
Out[4]: 0
In [5]: f(x,y).diff(x,y)+f(x,y).diff(y,x)
Out[5]:
2
d
2⋅─────(f(x, y))
dy dx
In [6]:
However, this is a new behavior compared to just a couple weeks ago (I
could not say when exactly was the last time I used git pull). The new
behavior assumes that the partial derivatives of the function f(x,y)
are continuous everywhere. See e.g.
http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives#Non-symmetry
Is this change intended?
Cheers,
Julien
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