Mathematica Learning mathematica for algebra

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Hi All,

I'm thinking about buying mathematica as the student edition is pretty cheap. I would mainly need it for stuff like calculating with polynomial rings, finding generators for ideals, solving systems of polynomial equations etc. over finite fields i.e. I'm doing algebraic geometry mostly. I was wondering if there are any good packages for mathematica that would help with this stuff that I should know of?

There's also a bunch of free packages available like PARI/GP, Macaulay2 and so forth. I have zero experience with any of these computer programs even though I also majored in CS as an undergrad and have extensive programming experience since my early teens.

I was also wondering which book about mathematica I should buy? I'll much rather have something fairly advanced, since I don't need to be taught how to program from scratch and mainly just want the general syntax covered and the best practices of using mathematica's built-in properties efficiently. If it covers any of the functionality involving the kind of math I do, even better.

Thanks.

 

[Dale]

I like the online help quite a bit. I actually have not needed a separate reference book and I have been using Mathematica for ~13 years now. They have both "tutorials" that include a good introduction to a particular topic and an overview of the most important commands and they also have a more typical function-by-function description which is very thorough.