Today's blog post is really from Jason Grout. It's why he likes Sage. This is from an email he sent out today, which I liked reading:
"It depends on the area, so you'll have to give me an area to get a more specific answer. In general, Sage has somewhat weaker general symbolic capabilities (i.e., integrals, etc.) than mathematica or maple (though usually this does not seem to be a problem in undergraduate-level problems). It has *much* stronger number theory functionality. Things are object-oriented in Sage and Sage understands mathematical structures and how they relate (using category theory). For example, Sage knows what a vector space is, what a finite field is, etc. You can actually create a finite field or an extension of the rationals and ask questions about it. You can create a polynomial ring over a field and then just work with it.
Sage is also generally faster than either Mathematica or Maple, in my experience.
The web interface to Sage is a huge plus to Sage over mathematica and maple. Of course, being free and open-source is something that is unmatched in either Mathematica or Maple; that is a very important point that is sometimes overlooked. You can literally see what is going on inside of Sage, where you have to guess what is happening in Mathematica or Maple.
One reason that Sage was chosen for an AIM workshop on helping undergraduate research was that the participants didn't have a common computational system (i.e., some had access to Mathematica, some had access to Maple, some had access to neither). They could use Sage because it was free, whereas it would have been problematic to insist that every person somehow acquire access to a specific piece of commercial software. Related to this, I had a student complain on my course evaluations about me using Mathematica in class because it is hard for our students here to have access to Mathematica, and they would have to pay in order to use it at home, etc.
If you are teaching future secondary ed teachers, then they most likely will not have access to Maple or Mathematica when they are teaching high school because of the cost. However, they *will* have access to Sage, so using Sage directly benefits their future students because whatever they learn can be used in their high school classes.
Another huge plus to Sage, in my eyes, is that it is based on one of the most prevalent and easiest-to-use computer languages around, Python. Students that learn to use Mathematica and Maple learn a language that they, in most likelyhood, will never use once they graduate. However, Python is used in many, many industries, so their python knowledge from using Sage is directly applicable later on.
Those are a few things that came to my mind right away. After some time thinking about it, I probably will have other things that make Sage more effective for me than other commercial software.