Well, can't you just do expr.subs(f, sin(x))? subs should work for anything
(assuming it makes sense).
Or maybe I still don't understand what you want to do.
Aaron Meurer
On Sep 7, 2010, at 10:45 AM, Rahul Siddharthan wrote:
> On Tue, Sep 7, 2010 at 9:21 PM, Aaron S. Meurer <asmeu...@gmail.com> wrote:
>> I don't think it's possible to substitute just theta without concern for x,
>> but this should work
>>
>> In [9]: f = Function('theta')(x)
>>
>> In [10]: f
>> Out[10]: θ(x)
>>
>> In [11]: expr = 6*f + x
>>
>> In [12]: expr
>> Out[12]: x + 6⋅θ(x)
>>
>> In [13]: g = Function('beta')(x)
>>
>> In [14]: g
>> Out[14]: β(x)
>>
>> In [15]: expr.subs(f, g)
>> Out[15]: x + 6⋅β(x)
>
> OK, but that just gets me from theta to beta... can I substitute an
> actual function, like sin?
>
> But it doesn't matter -- I just realised I don't actually need it
> (though it would be nice to have it).
>
> The situation is this: my implementation of SICM lets me calculate the
> Lagrangian, the Lagrange equations, and the "first-order" Lagrange
> equations for any Lagrangian. For example, for the harmonic
> oscillator I get the first order equations (functions to be equated to
> zero):
> -v(t) + D(x(t), t)
> (k*x(t) + m*D(v(t), t))/m
> (equating each to zero, the first just defines the velocity and the
> second is Newton's law.)
>
> Now it would be nice to use these equations (or rather, equations for
> less trivial systems) in an integrator, but that requires substituting
> values for x(t) and v(t). But I can actually get equivalent equations
> in terms of symbols x and v, rather than functions x(t) and v(t), via
> a rather clever procedure in SICM called Gamma_bar -- and that is
> preferable for the integrator, anyway.
>
> Thanks,
>
> Rahul
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