Although Sage is based on Python (so in particular any Python syntax will work), you really don't need to know Python to get started using Sage-I didn't when I started.
I used the online notebook for around 6 months before I installed a copy on my own computer, and this was because I became interested in developing Sage. (I just googled "sage notebook screenshot.") It's been designed to look and work like the Mathematica notebook system, and it's surprisingly slick and easy to use. Here's a screenshot of what the notebook looks like. This is a very popular option-I believe that in the last 9 months around 30,000 people have created accounts! It's perfectly suited for high school students and undergraduates, since no installation is necessary, and hence it can be used straight away in any computer lab with internet access. I think this is really nice-it feels like it's your "gmail" but for maths, so you can just log in from anywhere and "check your maths" if you want :-D
SPEEDCRUNCH BUTTONS FOR FREE
This is true, the binary download comes in at around 1 gig, however you can use it for free online, without having to install a thing! Head on over to The Sage Notebook, and sign up for a free account, which will allow you to create and save your own worksheets. Firstly someone mentioned that Sage is quite large to install.
A few people have mentioned Sage, but I think deserves a bit more of a plug.
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