On 04/02/2010 12:47 PM, Franco Saliola wrote:
I forgot to more the conversation below from sage-support to sage-devel.
---------- Forwarded message ----------
From: Franco Saliola<sali...@gmail.com>
Date: Fri, Apr 2, 2010 at 1:45 PM
Subject: Re: [sage-support] Is there an efficient method of producing
indexed variables?
To: sage-supp...@googlegroups.com
On Thu, Apr 1, 2010 at 10:50 PM, Minh Nguyen<nguyenmi...@gmail.com> wrote:
Hi,
On Fri, Apr 2, 2010 at 12:36 PM, scott.h<scott.he...@gmail.com> wrote:
<SNIP>
It seems like this should be simple but for the life of me I can't
figure out how to do it.
Here I'm taking a guess at what you really want to do. See the
following Sage session:
[mv...@sage ~]$ sage
----------------------------------------------------------------------
| Sage Version 4.3.5, Release Date: 2010-03-28 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: n = 3
sage: M = random_matrix(ZZ, nrows=n); M
[ 2 2 -2]
[ 4 2 -7]
[ 2 -1 1]
sage: # create a list of unknown constants; these are actually
symbolic variables
sage: C = [var("C_%s" % i) for i in range(n)]; C
[C_0, C_1, C_2]
sage: X = [randint(1, 10) for i in range(n)]; X
[2, 3, 2]
sage: F = [C[i] * exp(M[i,i] * x) for i in range(n)]; F
[C_0*e^(2*x), C_1*e^(2*x), C_2*e^x]
sage: [F[i].substitute(x=X[i]) for i in range(n)]
[C_0*e^4, C_1*e^6, C_2*e^2]
It might be useful to have a constructor to simplify this.
One would be able to do something like this:
sage: a = SymbolicVariables('a')
sage: sum(a[i]*x^i for i in range(3))
a2*x^2 + a1*x + a0
and Minh's session above would become:
sage: n = 3
sage: M = random_matrix(ZZ, nrows=n)
sage: c = SymbolicVariables('c')
sage: [c[i] * exp(M[i,i] * x) for i in range(n)]
[c0*e^(-x), c1*e^(-5*x), c2*e^(13*x)]
Here is a very simple implementation of SymbolicVariables.
class SymbolicVariables(SageObject):
def __init__(self, prefix='x'):
self._prefix = prefix
def __getitem__(self, i):
return var("%s%s"%(self._prefix, i))
Thoughts?
This has come up several times before on sage-devel, and I've always
liked it. For example, Nathann Cohen brought this up when he was first
integrating the linear programming stuff. I believe Robert Bradshaw
suggested this "indexing creates a variable" approach a while ago too.
When/if we wrap pynac vectors/matrices, though, or have "symbolic vector
variables", we might have to be careful about how we treat the
__getitem__ function. I think in your case, where you explicitly are
creating x with the understanding that indexing x creates new variables,
things would be fine, though.
Thanks,
Jason
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