I'm basing this on my experience a few years back.
It's not that you can't do it with other software, Mathematica just has all of it included by default, with very comprehensive documentation. And a slick UI.
Sure you can probably do most of it in python, but you'll find yourself chasing some obscure modules to get some things working. Even just to get arbitrary precision calculations for just about everything, for example. And don't forget the importance of a documentation that explains every option with examples (barring some obscure stuff, which can be quite annoying if you encounter it).
Since it's all integrated Mathematica allows you to go from calculating Sin[2] to arbitrary precision, to calculating the derivative of Sin[2x], to showing the first 10 terms of its Taylor series. All using the same sine function.
This does have some downsides. For one it's a pretty heavy program to run. And because they want to include everything they need to be quite opinionated about certain things. There are multiple ways to define fractional derivatives for instance, since they include a function for it they must have picked one of them. And then there are the name clashes, I once had to laugh quite loudly when I tried "Rotate[{0,1}, 45deg]" and got back an image of {0,1} at a 45 degree angle.
It is an impressive piece of engineering. Which could have had much more of an impact if it was a bit more open, but oh well...
You should give it a spin. It’s an incredibly comprehensive Computer Algebra System with all the batteries included…. No, with a small nuclear reactor in the box.
I’m just sad that I don’t have access anymore after college, being too cheap to pay for a license.
- Far better language design, actually designed from ground up to write Mathematics in, rather than hacked in later.
- Specially, the language supports symbolic computation natively. In a lot of software, you have to declare symbols as symbolic variables before using them. In Mathematica, you don't have to deal with this nonsense.
- A library of both symbolic and numerical algorithms that is far far far better than any other library out there. Especially its outstanding how much symbolic computation algorithms are built in. Fairly fast numerical algorithms as well. Best of all, Mathematica guesses the best algorithm to use in a particular situation with frightening accuracy.
- A lot of Maths is just built in. Example: A number of common Groups are just there for you to immediately start playing with.
It's not that you can't do it with other software, Mathematica just has all of it included by default, with very comprehensive documentation. And a slick UI.
Sure you can probably do most of it in python, but you'll find yourself chasing some obscure modules to get some things working. Even just to get arbitrary precision calculations for just about everything, for example. And don't forget the importance of a documentation that explains every option with examples (barring some obscure stuff, which can be quite annoying if you encounter it).
Since it's all integrated Mathematica allows you to go from calculating Sin[2] to arbitrary precision, to calculating the derivative of Sin[2x], to showing the first 10 terms of its Taylor series. All using the same sine function.
This does have some downsides. For one it's a pretty heavy program to run. And because they want to include everything they need to be quite opinionated about certain things. There are multiple ways to define fractional derivatives for instance, since they include a function for it they must have picked one of them. And then there are the name clashes, I once had to laugh quite loudly when I tried "Rotate[{0,1}, 45deg]" and got back an image of {0,1} at a 45 degree angle.
It is an impressive piece of engineering. Which could have had much more of an impact if it was a bit more open, but oh well...