That is definitely a bug.  Doing it step by step works:

sage: fd=f.denominator(); gd=g.denominator()
sage: fn=f.numerator(); gn=g.numerator()
sage: fn*gd+fd*gn
2*t^18 + t^11 + t^10 + 2*t^2
sage: hn = fn*gd+fd*gn
sage: hd = fd*gd
sage: hn.gcd(hd)
t^3 + 2*t^2
sage: hn/hd
(2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + t^7 +
t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^17 + t^9 + t)

sage 3.4.alpha0 gives the same thing.

John Cremona

2009/3/7 Alex Lara <lrodr...@gmail.com>:
>
> Hi guys,
>
> I recently upgrade sage from 3.2.3 to 3.3. I'm also have sage 3.1.1
> The thing is that the following commands give different results:
>
> F.<theta>=FiniteField(9)
> A.<t> = PolynomialRing(F)
> K.<t> = FractionField(A)
> f= 2/(t^2+2*t); g =t^9/(t^18 + t^10 + t^2);f+g
>
> In 3.1.1 gives the right answer (I guess) but in 3.2.3 give an error:
>
> ZeroDivisionError                         Traceback (most recent call
> last)
> ...
> ZeroDivisionError: division by zero in finite field.
>
> I don't know how those commands work in 3.2.3.
>
> I had a problem with sage 3.2.3, but Craig Citro helped me. Sage 3.2.3
> couldn't open objects created in sage 3.1.1. This objects contain
> polynomials p(T) in F_q(t)[T]. Perhaps these problems are related.
>
> Any idea of how to fix that?
>
> >
>

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