Understanding the 'solve()' result with braces and brackets ("([{x:z},{x:y}],[1,1])")
Having following code
var('x,y,z')
P=-x^2*y + x*y^2 + x^2*z - y^2*z - x*z^2 + y*z^2 == 0
solve(P,x,y,z)
Sage gives me a result of
([{x:z},{x:y}],[1,1])
which I am not really able to interpret, also the help(solve) did not get me any further - is there anyone who can help me out with that?
(btw. as -(x-y)*(x-z)*(y-z)==0
is an alternate form for writing the polynomial my expected answer would be something like x=y or x=z or y=z
but in other cases where I'd get a similar answer I would have no idea, so I'd be happy to get this format explained.)