Hi Ondrej,
Thanks for the quick response. I took a look at the Sum class tests,
but there is still one part I'm not clear on.
In defining a summation, I would like to have the sum over an array of
symbols, indexed by an iterate.
For example, In the sum
\sum_{i=0}^4 tau_i,
I'd like each tau[i] to itself be a symbol, since I later want to
differentiate with respect to these symbols.
I'd like to do this:
In [17]: tau = []
In [18]: for i in range(10):
....: tau.append(Symbol('tau_%s' % i))
In [19]: Sum(tau[i]**2, (i, 0, 9))
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
or
In [20]: Sum(i**2, (i, tau))
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
Ideally, this would give some compact representation of
tau[0]**2 + tau[1]**2 + ... + tau[9]**2
Is there something I'm missing?
Thanks again,
Danny
On Dec 30, 7:26 am, "Ondrej Certik" <ond...@certik.cz> wrote:
> Hi Danny!
>
> On Mon, Dec 29, 2008 at 4:01 PM, Danny Tarlow <dannytar...@gmail.com> wrote:
>
> [...]
>
> >> Is this possible to do with Sympy? If I were interested in working on
> >> something like this, how hard would it be for a sympy newbie (but
> >> competent programmer) to implement? Any tips on where to start?
>
> Thanks for both your emails. You need to use the Sum class for that,
> and I think it will probably need a little enhancements so that
> everything runs smoothly. I think it should be pretty easy for you to
> get going with sympy, it's our aim to have the code hackable, so that
> people can take it and customize it for their needs and enhance it to
> get the job done. I suggest you learn git, just a few commands are
> enough, see our tutorial:
>
> http://docs.sympy.org/sympy-patches-tutorial.html
>
> feel free to ask any question if you don't understand something in the
> sources. You can also come to #sympy at freenode to chat in live.
>
> > For concreteness, here is an example of one of my attempts:
>
> [...]
>
> > The output is a mess:
> > mu := [tau_0/5 + tau_1/5 + tau_2/5 + tau_3/5 + tau_4/5]
> > sigma := [2*mu*tau_0 + 2*mu*tau_1 + 2*mu*tau_2 + 2*mu*tau_3 +
> > 2*mu*tau_4 - tau_0**2 - tau_1**2 - tau_2**2 - tau_3**2 - tau_4**2 -
> > 5*mu**2]
> > tau_0 := [mu]
>
> > Ideally, I'd like to get something more like this, where the sums are
> > left in tact:
> > mu := 1/5 * \sum_{i=0}^4 tau_i
> > sigma := 1/5 * \sum_{i=0}^4 (mu - tau_i) ** 2
> > tau_0 := [mu]
>
> I see. You need to keep things in the Sum class, unfortunately the
> docstring of it is not so much helpful (it can be your first patch if
> you want:), but read it's tests here:
>
> sympy/concrete/tests/test_sums_products.py
>
> to get dozens of examples of usage. E.g.:
>
> In [3]: Sum(1/k**k, (k, 1, oo))
> Out[3]: Sum(k**(-k), (k, 1, oo))
>
> In your case probably more something like this:
>
> In [4]: Sum(1/k**k, (k, 1, 5))
> Out[4]: Sum(k**(-k), (k, 1, 5))
>
> In [5]: Sum(1/k**k, (k, 1, 5)).doit()
> Out[5]:
> 27891287
> ────────
> 21600000
>
> E.g. you don't want to call the "doit()" function. Please report
> everything that isn't working with the Sum into our issues. If things
> are easy to fix, I'll fix it myself, if it takes more time, I'll help
> you fix it.
>
>
>
> > For extra credit, there would also be a way to substitute sufficient
> > statistics for the \sum_{i=0}^4 tau_i terms, for example, so that the
> > sample mean could be computed once, then used many times in the
> > updates.
>
> the .subs() method should do that.
>
>
>
> > Thanks in advance.
>
> Ondrej
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