# Problems with Solve?

 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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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.

( 2013-04-09 15:32:21 +0200 )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.)

( 2013-04-09 15:33:09 +0200 )edit

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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)
...

more