I may have the answer: no, not directly.
Sage includes Pynac, which wraps GiNaC. GiNaC has indexed
expressions, which just might do exactly what I want. (I don't have
ginsh running to test differentiation.) But it looks like indexed
expressions are not hooked up for use in Sage. I am posting to sage-
devel to investigate further.
- Ryan
On Jun 30, 2:45 pm, Ryan Hinton <iob...@email.com> wrote:
> Thanks for the reply! That's a perfect example of what I am doing
> now. Can I go one level higher and define my generating function as a
> product of terms *while leaving the actual degrees, coefficients, and
> even the number of dimensions symbolic*. So instead of getting
> something like
>
> (5*x0*x1 + 1)*(3*x0*x1*x4 + 1)
>
> I want to get something like
>
> product(exponent_list, lambda c,d: 1 + c * pot(x, d))
>
> Maybe the second argument should be some kind of a paramaterizable
> expression. So what I'm looking for is a "first-class" product/
> summation construct, and an arbitrary number of generators for my
> formal power sum. Even a way to specify the generic construct
>
> vector_power(x, d)
>
> that will float around in my expressions until I take a derivative.
> For example, I want something notionally like the following.
>
> sage: vector_power(x,d).derivative(x[1])
> d[1] * vector_power(x,d) / x[1]
>
> So the ``vector_power`` construct would have to know how to use the
> power rule of differentiation.
>
> Does this make sense? Is it possible?
>
> Thanks!
>
> - Ryan
>
> On Jun 30, 11:37 am, pang <pablo.ang...@uam.es> wrote:
>
> > > Can I do this in Sage?
>
> > Sure. Here you have some tips:
>
> > {{{id=1|
> > #Create n variables with names x1, x2 ... xn
> > #and store them in a list vs
> > n = 5
> > vs = var(' '.join('x%d'%j for j in range(5)))
> > vs
> > ///
> > (x0, x1, x2, x3, x4)
>
> > }}}
>
> > {{{id=6|
> > def pot(vs,ds):
> > return prod(v^d for v,d in zip(vs,ds))
>
> > pot(vs,[1,2,3])
> > ///
> > x0*x1^2*x2^3
>
> > }}}
>
> > {{{id=2|
> > def generating_function(cs):
> > return prod(1 + c*pot(vs,ds) for ds,c in cs.items())
>
> > generating_function({(1,1,0,0,1):3, (1,1,0,0,0):5})
> > ///
> > (5*x0*x1 + 1)*(3*x0*x1*x4 + 1)
>
> > }}}
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