Let's end this thread.  

To sum up, there is no evidence of a problem with sage (or its interface 
with fricas), because the report was based on the false assumption that 
typing "dilog(-x + 1)" in fricas means the same thing as typing it in 
sage.  However, in reality, telling dilog(-x + 1) to fricas is the same as 
telling dilog(x) to sage. Thus, the integral done in fricas translates to 
the following in sage:

sage: integrand=(dilog(x)^2 - log(-x + 1)*polylog(3, x))/x
sage: integrate(integrand,x,algorithm="fricas")
dilog(x)*polylog(3, x)

After converting back to fricas, this is the same answer that was obtained 
by using fricas directly.  

On Tuesday, January 14, 2025 at 11:06:10 AM UTC-7 axio...@yahoo.de wrote:

> Nope. From what you say follows that Sage’s dilog(x) and Fricas’ 
> dilog(1-x) are the *same mathematical object*. Therefore, the Fricas 
> translation of Sage’s dilog(<something>) should be dilog(1-<something>). 
> And *vice-versa* : the Sage’s translation of Fricas’ dilog(<something>) 
> should be Sage’s dilog(1-<something>).
>
> That's precisely what the FriCAS-SageMath interface currently does.
>
> Martin
>

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