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RE: Interactive simplifying

• To: mathgroup at smc.vnet.net
• Subject: [mg31927] RE: [mg31913] Interactive simplifying
• From: "David Park" <djmp at earthlink.net>
• Date: Wed, 12 Dec 2001 04:14:12 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Steve,

You are correct that cutting and pasting is not a great way to manipulate an
equation. I think you can better do what you wish by mapping pure functions
onto both sides of the equation. Here is a solution of a simpler version of
your equation using this technique. I'll leave the more complicated case to
you.

Sqrt[a*z + b] + Sqrt[c*z + d] == g
(#1^2 & ) /@ % //ExpandAll
(#1 - g^2 - 2*Sqrt[b + a*z]*Sqrt[d + c*z] & ) /@ %
(#1^2 & ) /@ % //ExpandAll
%[[1]] - %[[2]] == 0
(Collect[#1, z] & ) /@ %
Solve[%, z]

I guess I shouldn't say that there was no copying and pasting. I did copy
and paste the expressions to be shifted from one side of the equation to the
other into the third line.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

> From: Steve Gray [mailto:stevebg at adelphia.net]
To: mathgroup at smc.vnet.net
>
>     I am trying to do something like this:
> Solve[Sqrt[a*z+b] + Sqrt[c*z+d] + Sqrt[e*z+f] == g, z] ,
> which on first try gives an answer with about 10,000 terms. In
> addition, the
> output is all messed up. Totally useless.
>     Thinking to help it along, I used the common trick of putting
> one of the
> Sqrt's on the right side, squaring the whole thing, collecting
> the Sqrt's on
> one side, squaring, and doing it again until no sqrts are left.
> This gives a
> complicated but not impossible 4th degree polynomial in z (with about 400
> terms of a,...,g to various low powers), which with good substitutions of
> new simplifying parameters is manageable.
>     I did this with Mathematica's help but in a very awkward way: I got a
> partial answer, saw what the best next step would be, cut and
> pasted part of
> the expression onto a new line, added parentheses and squarings here and
> there, manually transposed with proper sign changes, etc. This worked and
> was not too painful but is very prone to error.
>     I thought that M. would have Transpose and other operators to help, or
> even select-and-drag with automatic sign change and other "corrections."
>     There oughta be a better way. Anyone? Thanks in advance for any help.
>
>