Indeed, the factor function of Sage is terribly buggy at the moment, see
https://trac.sagemath.org/ticket/27304
The issue you report seems to have been triggered by
https://trac.sagemath.org/ticket/23835 (merged in Sage 8.4.beta3) as well,
since we have a correct result in Sage 8.3:
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.3, Release Date: 2018-08-03 │
│ Type "notebook()" for the browser-based notebook interface. │
│ Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: var('t u')
(t, u)
sage: L = (u + t)/(u - t)
sage: factor( L.substitute(t=sqrt(u)))
(u + sqrt(u))/(u - sqrt(u))
but not in Sage 8.4 and later.
Eric.
Le lundi 6 mai 2019 16:29:37 UTC+2, Roberto Avanzi a écrit :
>
> Hello
>
> I haven't been able to find this very same bug in the trac or in the
> sage-level group, even though some related ones have been reported
>
> L = (u + t)/(u - t)
> factor( L.substitute(t=sqrt(u)))
>
> yields
>
> (u + 1)/(u - 1)
>
> which is wrong (the example is small enough to be verifiable by hand).
> Mathematica, OTOH
>
> l[t_] := (u + t)/(u - t);
> Factor[l[Sqrt[u]]]
>
> returns the correct result
>
> (1 + Sqrt[u])/(-1 + Sqrt[u])
>
> If this is a previously unknown bug, I would like to submit it (or if
> anybody wants to submit it and inform me, they're welcome!)
>
> best
> Roberto
>
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