I think this is indeed a bug, so thanks for reporting it. My impression
from a quick look at the code is that sagemath expands the expression into
a polynomial (a linear combination of monomials) before trying to factor
it. If the expansion has only a single term (a constant times a monomial),
I meant to say that f.expand() gives the correct answer.
To see why, factor out the common factors (x-y)(y-z)(z-x).
Once you did so, the rest is ( (x-y) + (y-z) + (z-x) )
and so I expect f.factor() returns 0.
The statement "the given expression cannot be factorized further"
seems weird to me.
--
sage: var("x, y, z")
(x, y, z)
sage: Ex = (x-y)^2*(y-z)*(z-x) + (y-z)^2*(z-x)*(x-y) + (z-x)^2*(x-y)*(y-z)
sage: Ex
-(x - y)^2*(x - z)*(y - z) + (x - y)*(x - z)^2*(y - z) - (x - y)*(x - z)*(y -
z)^2
sage: Ex.expand()
0
sage: Ex.factor()
-(x - y)^2*(x - z)*(y - z) + (x - y)*(x - z)^2*(y - z) - (x
I checked this on my SageMath v9.6.beta5 on Ubuntu 20.04 LTS, and it checks
out
[image: Screenshot from 2022-04-03 14-58-46.png]
On Sunday, April 3, 2022 at 2:57:35 PM UTC+5:30 Adarsh Kishore wrote:
> By the way, f.expand() is not wrong. The expression is identically equal
> to 0 for all value
Which version of Sage are you using? And on which platform?
On Sunday, April 3, 2022 at 10:44:59 AM UTC+5:30 a.simpl...@gmail.com wrote:
> The following code
>
> > var("z y z")
> > f = (x-y)^2*(y-z)*(z-x) + (y-z)^2*(z-x)*(x-y) + (z-x)^2*(x-y)*(y-z)
> > f.expand()
>
> outputs 0.
> But
> > f.factor
