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?
Franco
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