1 | initial version |

Here is my personal point of view:

(1) Sage is a rapidly growing project. The first version was released in 2005. Thus one could expect there's a lot of space to improve. Indeed the community looks very active.

(2) In terms of powerful and speed, I would think Mathematica is still better so far. I mainly use Sage or Mathematica to do symbolic calculation. I found Mathematica can do more symbolic integrations than Sage could. The ODE solver is also more convenient. Also, Sage calls Maxima to do simplifications, which is more slowly than Mathematica.

(3) In terms of stability, I have met several bugs in Sage and I would not mark it as very stable. But the good thing is the bugs breaks the calculation explicitly (by saying something is wrong), instead of give you a wrong result. Also for every bug I met, I could eventually find a workaround, with the help of very kind community.

(4) Despite (2) and (3), I am still moving my previous Mathematica work to Sage. Why? Most importantly, it is because Sage is based on Python, and Mathematica has its own language. The Python-Sage resolution has much better support on class, name-space, etc. Thus when we have a lot of codes, it is much easier to reuse them in Python than in Mathematica (including the .m package).

(5) It's also a matter of Windows / Linux. Sage is more native on Linux, while Mathematica behaves better on Windows. (I have never used Mac thus I don't have comment on that.) The Linux support (especially notebook interface) of Mathematica is very slow, and occasionally unstable.

Considering the above differences, currently, if you want to use a CAS to do a number of small calculations (say, calculate a integration in your work and insert the result back to your hand-writing notes), I would recommend Mathematica (despite the price issue...). On the other hand, if you write a lot of code and want to reuse them, Sage is a sage option.

Finally, I am looking forward to seeing sage become better and better. The active development group give us users a lot of hope.

2 | No.2 Revision |

Here is my personal point of view:

(1) Sage is a rapidly growing project. The first version was released in 2005. Thus one could expect there's a lot of space to improve. Indeed the community ~~looks ~~is very active.

(2) In terms of powerful and speed, I would think Mathematica is still better so far. I mainly use Sage or Mathematica to do symbolic calculation. I found Mathematica can do more symbolic integrations than Sage could. The ODE solver is also more convenient. Also, Sage calls Maxima to do simplifications, which is more slowly than Mathematica.

(3) In terms of stability, I have met several bugs in Sage and I would not mark it as very stable. But the good thing is the bugs breaks the calculation explicitly (by saying something is wrong), instead of give you a wrong result. Also for every bug I met, I could eventually find a workaround, with the help of very kind community.

(4) Despite (2) and (3), I am still moving my previous Mathematica work to Sage. Why? Most importantly, it is because Sage is based on Python, and Mathematica has its own language. The Python-Sage resolution has much better support on class, name-space, etc. Thus when we have a lot of codes, it is much easier to reuse them in Python than in Mathematica (including the .m package).

(5) It's also a matter of Windows / Linux. Sage is more native on Linux, while Mathematica behaves better on Windows. (I have never used Mac thus I don't have comment on that.) The Linux support (especially notebook interface) of Mathematica is very slow, and occasionally unstable.

(6) There are also a number of other differences. For example, in Sage one has to define a variable before use (although don't need to declare). Mathematica doesn't need that. The former is safer but the latter is convenient. Also, one can view source code of a function in sage by typing, e.g. expand?? . This improves my programming technique because then I easily learn how more professional people write code.

Considering the above differences, currently, if you want to use a CAS to do a number of small calculations (say, calculate a integration in your work and insert the result back to your hand-writing notes), I would recommend Mathematica (despite the price issue...). On the other hand, if you write a lot of code and want to reuse them, Sage is a sage option.

Finally, I am looking forward to seeing sage become better and better. The active development group give us end users a lot of hope.

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