I am considering purchasing a premium account for Wolfram Alpha, but before I do, I thought I should explore other options.
Is there any free software with capabilities that rival that of Wolfram Alpha's premium version?
I use a lot of different software for mathematics, such as Desmos, but nothing else that even rivals the power of Wolfram Alpha's free version. Is there anything amazing out there that I am not aware of?
On
Paid Option
Wolfram Alpha is built upon Wolfram's Mathematica engine (and some extras). If you like it full capabilities and intend to spend some cash I would recommend buying Mathematica. The student or teacher edition prices are very good value.
Free Option
Before you spend money I recommend trying out Wolfram's Programming Lab. It is a free web based slim version of Mathematica. As far as I can tell it has the full functionality of Mathematica but is time limited (reasonably generously). (The time limit appears to be IP based so if you don't have a fixed IP you would be able to use it even more.)
You may try SAGE for an experiment. It has inbuilt platforms for R, Singular, Maxima(which is very similar to Mathematica), Octave(which is similar to MATLAB), Python, GAP, GP and HTML. It has interactive tutorials included through which you can incorporate any extra functions not included.