V wrote:
> On Mar 30, 6:07 pm, Jason Grout <[email protected]> wrote:
>> V wrote:
>>> Hi,
>>> I'm fairly new to sage with some background in maxima.
>>> My workbook is shared at
>>> http://www.sagenb.org/home/pub/410/
>>> the last three lines show the error I get.
>>> Basically, I derive an equilibrium condition that I would like to use
>>> in the previous stage of my game (solving by backwards induction), but
>>> maxima fails (line -2) with simplifying after the substitution is
>>> made, even though the substitution is successful (line -3).
>>> I expect to receive the line in the last "paragraph" as defined by
>>> D1p.
>>> Is this a bug or did I made a mistake?
>> In this line,
>>
>> solve([q1==q1.substitute(q2=sol2[0][1].right()).simplify_full()], q1)
>>
>> you are trying to solve for "q1", but q1 is not a variable, it's the
>> expression:
>>
>> f2^alpha*p1^(alpha - 1)*p2^(beta - alpha*beta)*q2^alpha*A^(1 - alpha)/f1
>>
>> Did you mean to solve for a variable in the solve statement above?
>>
>
> The expression in the solve line would be a demand function where q
> stands for quantity. But as it is derived from a later stage of the
> game, q is present on the "right hand side" as well, and I would like
> to express the demand function explicitly, that is I have q=f(q,x)
> where x are all the other parameters and q is defined implicitly, and
> I would like to have q=g(x).
>
> I thought solve would do this for me, even though I already understand
> why it doesn't, I still don't know how to do it. Could you give me a
> hint, please?
I see.
Disclaimer: I don't know the mathematics that you are doing, so forgive
me if I mess things up below...
When you do q1==q1.subs(...), what the computer sees is:
f2^alpha*p1^(alpha - 1)*p2^(beta - alpha*beta)*q2^alpha*A^(1 - alpha)/f1
== f1^(alpha^2 - 1)*p1^((alpha - alpha^2)*beta + alpha - 1)*p2^((1 -
alpha)*beta + alpha^2 - alpha)*q1^alpha^2*A^(1 - alpha^2)
This doesn't seem like what you want; you want the left side to be a
single variable, and the right side to have q1 be that same single
variable. So maybe you can do something like:
sage: var('q')
sage: q==q1.substitute(q2=sol2[0][1].right()).simplify_full().subs(q1=q)
q == f1^(alpha^2 - 1)*p1^((alpha - alpha^2)*beta + alpha - 1)*p2^((1 -
alpha)*beta + alpha^2 - alpha)*q^alpha^2*A^(1 - alpha^2)
sage:
solve(q==q1.substitute(q2=sol2[0][1].right()).simplify_full().subs(q1=q), q)
[q == f1^(alpha^2 - 1)*p1^((alpha - alpha^2)*beta + alpha - 1)*p2^((1 -
alpha)*beta + alpha^2 - alpha)*q^alpha^2*A^(1 - alpha^2)]
So it doesn't look like maxima is able to handle this.
Jason
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