Complex equation in maxima

Question

After issuing the command with "solve" function:

%i2 solve((a-b-sqrt(-c^2+2*c*y-y^2+r^2))^2+(d-y)^2=2*r^2*(1-cos(e)),y);

The output is: enter image description here

Why there is unknown quantity "y" on the right side?

P.S.

There's no "Maxima" tag, what a pity! However, I was redirected here by a stackoverflow moderator, so I assume it is not offtopic.

Maxima is a computer algebra system based on a 1982 version of Macsyma. It is written in Common Lisp and runs on all POSIX platforms such as Mac OS X, Unix, BSD, and GNU/Linux as well as under Microsoft Windows. It is free software released under the terms of the GNU General Public License.
source: http://en.wikipedia.org/wiki/Maxima_%28software%29

Clearly, Maxima was not entirely successful at isolating the variable you want... — J. M. ain't a mathematician, Jul 23 '12 at 00:42
W|A spits out a pretty lengthy result that doesn't seem to have $y=$ (something with $y$ in it)... — The Chaz 2.0, Jul 23 '12 at 00:50
@TheChaz there are two "y" under the square root. Or this "W|A" shortcut which I don't understand (google also doesn't know anything about "W|A maxima") is significant. — 0x6B6F77616C74, Jul 23 '12 at 01:05
@kowalt, that I cannot say; I do not have the thing installed on my computer to evaluate this properly. — J. M. ain't a mathematician, Jul 23 '12 at 01:17

score 5 · Accepted Answer · answered Jul 23 '12 at 02:05

5

The general solve command in Macsyma has limited capabilities for dealing with algebraic functions. You can work around this by using the rational function package as in the code below. There I define w to be the sqrt, then solve for w, square, then solve for y.

(algebraic:true, tellrat( w^2 = -c^2+2*c*y-y^2+r^2 ));

solve(rat(solve(rat((a-b-w)^2+(d-y)^2 = 2*r^2*(1-cos(e))),w)^2),y)

answered Jul 23 '12 at 02:05

Bill Dubuque

282,220

This is useful. – copper.hat Jul 23 '12 at 03:01
The result is five lines long, like in the wolframalpha.com. – 0x6B6F77616C74 Jul 23 '12 at 14:53
Thanks, this helped a lot. Could you explain a little more what rat() and tellrat() are doing here and why these steps are used. I was able to solve an equation with this method but I'm bother that I don't really understand why it works. – jcoffland Nov 17 '15 at 22:03

Complex equation in maxima

1 Answers1

Linked