You missed the point of the article. It's not what version of Python he's using or what libraries already exist. It's about creating an understanding of simple methods for numerically solving equations.
> Isn't Python 2.7 the version usually used
Yes. But because the 2.x series is backward compatible, you will be able to run 2.6 code on 2.7. Honestly, if he was writing on 2.7 the code probably would look identical. For that matter, it would probably look identical on Python 3, except for print statements.
> using the R language
I'm not familiar with R, I always thought it was more for statistics like curve fitting or ANOVA. (I actually am not really sure what ANOVA is, but stats people seem to like that word, so I'll toss it out there.) Sage [1] would be the tool I'd turn to for symbolic equation solving.
[1] http://sagemath.org