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Problems with Solve?

asked 2013-04-09 08:08:39 -0500

russ_hensel gravatar image

` running in the notebook ( Sage 5.1 )

 --- this input ---

 var( "Z", "A" )
 equ   = 1.*Z/A^(1/3) + 2.*(A - 2*Z)/A == 0
 print equ
 sol = solve( equ, A )
 print sol

 --- gives ---
 Z/A^(1/3) - 2*(-A + 2.00000000000000*Z)/A == 0
 [
 A == -2*(A^(4/3) - 2*A^(1/3)*Z)/Z
 ]

--- my problem ---

if I have solved for A, why is A still on the RHS, I expected only Z as a variable. This problems is similar to the real one I am having with a much more complicated formula. `

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Comments

Well, if it can't be solved by Maxima, then this is what it will return. And indeed there are some equations (not necessarily this one) that can't be solved at all in "formula" form, see e.g. http://samjshah.com/2009/12/27/insolvability-of-the-quintic/ for a nice example of someone using Sage to point this out to students.

kcrisman gravatar imagekcrisman ( 2013-04-09 08:32:21 -0500 )edit

(Of course, that doesn't mean that yours is unsolvable (by radicals), just that Maxima couldn't figure out how to do it. Maybe try `expand()` or `equ.simplify_full()` or something to get another form it might be able to do.)

kcrisman gravatar imagekcrisman ( 2013-04-09 08:33:09 -0500 )edit

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answered 2013-04-10 23:33:39 -0500

Hi,

You can solve this one with maxima. First you define a = A^(1/3) in your equation and multiply the LHS by a. Then

sage: var('a','z')
sage: EQ = z * a^2 + 2*(a^3 - 2*z) == 0
sage: EQ.solve(a)
...
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Asked: 2013-04-09 08:08:39 -0500

Seen: 91 times

Last updated: Apr 10 '13