[sage-support] Re: substitution problem
This is exactly what I wanted. Thanks for your help! :)
I'll look up the maxima manuals to see if I can force it to think
harder. Thanks anyway!
Have a nice day!
V
On Mar 31, 3:35 pm, Jason Grout wrote:
> V wrote:
> > On Mar 30, 6:07 pm, Jason Grout 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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[sage-support] Re: substitution problem
V wrote:
> On Mar 30, 6:07 pm, Jason Grout 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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[sage-support] Re: substitution problem
On Mar 30, 6:07 pm, Jason Grout 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? Thanks, V --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: substitution problem
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? Jason --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
