Hi Oscar,
In Sage 4.6 (currently 4.6alpha2) you will be able to do this using
differential forms:
sage: x, y, z = var('x, y, z')
sage: U = CoordinatePatch((x, y, z))
sage: F = DifferentialForms(U)
sage: f = F(x^2 + y + sin(z)); f
(x^2 + y + sin(z))
sage: g = f.diff(); g
cos(z)*dz + 2*x*dx + dy
sage: g.parent()
Algebra of differential forms in the variables x, y, z
It's only a small step from having d f to obtaining D f.
All the best,
J.
On 9 okt, 07:26, Oscar Lazo <estadisticame...@gmail.com> wrote:
> On Oct 8, 7:54 pm, Nils Bruin <nbr...@sfu.ca> wrote:
>
> > If you define x,y,z to be functions of m, it does what you want:
>
> > sage: var("m")
> > sage: x=function("x",m)
> > sage: y=function("y",m)
> > sage: z=function("z",m)
> > sage: diff(f,m)
> > cos(z(m))*D[0](z)(m) + 2*x(m)*D[0](x)(m) + D[0](y)(m)
>
> Yes, but the point of total differentiation is that the parameter m
> should be arbitrary. We should be able to handdle the differentials
> without the need to specify with respect to what we are
> differentiating, for instance:
>
> In[1]:= Dt[x y]
>
> Out[1]= y Dt[x] + x Dt[y]
>
> Before reading your reply I had though it would be easy to implement
> total differentiation in sage with the stuff we've already got, but on
> a second thought i don't think sage can express diffrentials by
> themselves right now...
>
> Oscar
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