On Sep 28, 3:09 pm, Tim Lahey <tim.la...@gmail.com> wrote:
> The D notation is used in Maple as an option, but almost always allows
> conversion to the standard notation.
OK, this thread should probably go to sage-devel or elsewhere, but I
don't know how to do that. Maple actually falls back on exactly the
same D notation (but the index more comfortably 1-based rather than 0-
based) in more complicated cases. Example in Maple:
> lprint(diff(f(g(u,v,w),y,z),u));
D[1](f)(g(u,v,w),y,z)*diff(g(u,v,w),u)
> lprint(diff(f(u+v,u-v),u));
D[1](f)(u+v,u-v)+D[2](f)(u+v,u-v)
> lprint(diff(f(x+6),x,x,x,x));
`@@`(D,4)(f)(x+6)
So maple seems to prefer "diff" if there is an obvious variable name
available, but doesn't go out of its way to invent auxiliary variable
names. Instead it uses D[1].
Comparing this to sage:
sage: var("x y z u v w")
sage: f=function('f')
sage: g=function('g')
sage: diff(f(g(u,v,w),y,z),u)
D[0](f)(g(u, v, w), y, z)*D[0](g)(u, v, w)
sage: diff(f(u+v,u-v),u)
D[0](f)(u + v, u - v) + D[1](f)(u + v, u - v)
sage: diff(f(x+6),x,x,x,x)
D[0, 0, 0, 0](f)(x + 6)
So it seems that sage only differs from maple in the most trivial case.
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