Try Maxima:

taylor(1/(x+x^2),x,0,3)
gives
1/x-1+x-x^2+x^3 ....

which may be what you want.  But I'm not sure because the
text you quote looks like gobbledygook.
RJF


On Monday, July 9, 2012 1:27:30 AM UTC-7, John Cremona wrote:
>
> A colleague reported this, which looks like a bug to me.  This is in 
> Sage-5.1.rc0.  Note that g.prec() is only 19 though f.prec() is 
> Infinity. 
>
> John 
>
>   I'm not sure who to bother about this, so I thought I could ask you. 
>  Here is a version of a Sage behaviour (feature? bug?) that bit me 
> recently. 
>
> sage: R, x = PowerSeriesRing(ZZ, 'x', default_prec = 80).objgen() 
> sage: f = x + x^2 
> sage: f.parent() 
> Power Series Ring in x over Integer Ring 
> sage: f.parent().default_prec() 
> 80 
> sage: g = 1/f 
> sage: g.parent() 
> Laurent Series Ring in x over Integer Ring 
> sage: g.parent().default_prec() 
> 20     (??????) 
> sage: h = 1/2 * f 
> sage: h.parent() 
> Power Series Ring in x over Rational Field 
> sage: h.parent().default_prec() 
> 80 
>
> That was a big surprise to me!  Sometimes the precision is carried 
> over to the new ring, and sometimes it isn't?  Now that I've found 
> this, I can catch it my code, but it does seem strange...  It seems 
> more reasonable for the precision to always be carried over? 
>
> Am I confused here? 
>
> best, 
>
> saul 
>

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