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## #2592 solve gives very different (wrong) answer than %solve

None
open
nobody
5
2013-07-02
2013-06-13
kcrisman
No

First noticed here and reported at Sage ticket 14628. Appended is how to get x7: the relevant part is that we get different answers from solve and %solve, and the first is quite wrong. I'm really sorry we don't have a smaller example!

```(%i1) display2d:false;

(%o1) false
(%i2) declare(phi,real);

(%o2) done
(%i15) solve(x7,phi);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
(%o15) [phi = 0,phi = %pi-acos(sqrt(5)/2-1/2),phi = acos(sqrt(5)/2+1/2)]

(%i16) %solve(x7,phi);

(%o16) %union([phi = 2*%pi*%z21+%pi/2])
```

and these are definitely very different solutions.

```x1:    - sqrt(2)*sin(-phi)*sin(phi)/((sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)*(cos(-phi)^2 + 2*sin(-phi)*sin(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + sin(-phi)^2 - 2*cos(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) - 2*sin(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 - 4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2));
x2: x1 + sqrt(2)*cos(-phi)*cos(phi)/((sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)*(cos(-phi)^2 + 2*sin(-phi)*sin(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + sin(-phi)^2 - 2*cos(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) - 2*sin(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 - 4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2));
x3: x2 - sqrt(2)*cos(-phi)/((sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)*(cos(-phi)^2 + 2*sin(-phi)*sin(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + sin(-phi)^2 - 2*cos(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) - 2*sin(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 - 4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2));
x4: x3 - sqrt(2)*sin(phi)^2/((sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2*(cos(-phi)^2 + 2*sin(-phi)*sin(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + sin(-phi)^2 - 2*cos(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) - 2*sin(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 - 4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2));
x5: x4 - sqrt(2)*cos(phi)^2/((sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2*(cos(-phi)^2 + 2*sin(-phi)*sin(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + sin(-phi)^2 - 2*cos(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) - 2*sin(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 - 4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2));
x6: x5 + 2*sqrt(2)*cos(phi)/((sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2*(cos(-phi)^2 + 2*sin(-phi)*sin(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + sin(-phi)^2 - 2*cos(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) - 2*sin(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 - 4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2));
x7: x6 - sqrt(2)/((sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2*(cos(-phi)^2 + 2*sin(-phi)*sin(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + sin(-phi)^2 - 2*cos(-phi)*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) - 2*sin(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*cos(-phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1) + 2*sin(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 - 4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2));
```