CAS for algebraic geometry, which one?

Question

I use Maple to compute Groebner bases and find it very efficient/fast for my current needs. However, several introductory textbooks on algebraic geometry refer to Singular, which I never used before. I could not find a comparison of the two computer algebra systems.

1. What are the main differences between Maple and Singular?
2. For large polynomial systems, how does their performance differ?

Answer 1

Singular implements some specialized algorithms that Maple does not, such as the Shimoyama-Yokoyama algorithm for primary decomposition. And some of its implementations are better, e.g. the Groebner walk algorithm. Maple has its strengths as well, such as polynomial factoring and gcd.

Answer 2

Differences: Singular is free; Maple is not. Singular is open source; Maple is only partially open source (the parts written in Maple itself are viewable). Singular is for polynomial computations; Maple is much broader then that. Singular does not have a GUI; Maple has several.