On Jul 14, 2009, at 9:18 AM, Doug wrote:

> Hi all; I'm brand new to sage and am finding it really fun and
> useful.

Thanks.

> Of course, I don't know anyone else who uses it and thus need
> to rely on the general community when reading documentation and
> scratching my head leave me with open questions.

Note that Sage's calculus stuff, while still very useful, isn't as  
well developed as some of the other parts of Sage. We use maxima a s  
a backend, but it doesn't always do what we want, and is sometimes  
incompletely wrapped. (This is an area of active development.)

> Here's my first:
>
> sage: foo = (x-1)^2/(x+2)^2 + 2*(x-1)/(x+2)
> sage: bar = foo*(x+2)
> sage: bar
> (x + 2)*((x - 1)^2/(x + 2)^2 + 2*(x - 1)/(x + 2))
>
> How come (x+2) isn't canceling in each of the parts?

Probably because x might be -2. Also, you have to explicitly simplify  
to do any non-trivial transformations (because it may be expensive to  
do so).

sage: bar.simplify_full()
3*(x^2 - 1)/(x + 2)

- Robert


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