Comment #160 on issue 1694 by smichr: solve has many issues with fractions
http://code.google.com/p/sympy/issues/detail?id=1694
The branch is 1694.
Thanks for the problem, Aaron. This flushed up some more errors. Now, all
four solution sets have the same first solution that is equivalent to what
you recalled:
eq = f - (2*x + 2*y + sqrt(x**2 + y**2))
a = x*y
Solving eq for x
x1, x2 = solve(eq, x)
solve(a.subs(x, x1).diff(y), y)
[2*f/7 - f*2**(1/2)/14, f/3 - I*f*2**(1/2)/6, f/3 + I*f*2**(1/2)/6]
solve(a.subs(x, x2).diff(y), y)
[2*f/7 - f*2**(1/2)/14, 2*f/7 + f*2**(1/2)/14, f/3 - I*f*2**(1/2)/6, f/3 +
I*f*2**(1/2)/6]
Now in terms of y
y1, y2 = solve(eq, y)
solve(a.subs(y, y1).diff(x), x)
[2*f/7 - f*2**(1/2)/14, f/3 - I*f*2**(1/2)/6, f/3 + I*f*2**(1/2)/6]
solve(a.subs(y, y2).diff(x), x)
[2*f/7 - f*2**(1/2)/14, 2*f/7 + f*2**(1/2)/14, f/3 - I*f*2**(1/2)/6, f/3 +
I*f*2**(1/2)/6]
As this shows there are potentially more errors lurking we can either try
close off this issue and start a new issue for additional solving
enhancement (namely, tsolve and solvable non-linear systems) or try to put
this in all together. The only thing I would like to add at this point is
the enhanced Lambert solver, but that can wait.
Does anyone have a preference?
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