On Jan 22, 2008 11:48 PM, Paul Zimmermann <[EMAIL PROTECTED]> wrote: > thank you for your explanations. > > > The 'int' (and its bignum counterpart, 'long') are native Python > > types. As far as I know, we don't modify Python at all; removing > > 'int' would be major surgery, and we're not going to do it. > > > > 'Integer' is a Sage type. This means it has lots of useful > > mathematical convenience methods (like .is_square()), it participates > > in the coercion model, etc. Also, 'Integer' is implemented with GMP, > > and 'long' is not, so 'Integer' is much faster for large numbers. > > Would it be possible to extend long by new methods like is_square, and get > rid of Integer?
No, not without changing Python. The semantics of the two types are almost totally different. As Carl Witty explained, having these two distinct long integer types is part of the "price" we pay by using an unmodified Python interpreter for Sage. The benefit is that we immediately are working with a language that has *millions* of users, and huge standard library, and very powerful packages available such as numpy, scipy, twisted etc. I think the pros more than outweigh the cons, though it won't be surprising of people disagree with me -- after all every other popular computer algebra system besides Sage reinvents its own language. > I guess 'long' is based on GMP too, does it make sense to have two concurrent > interfaces to GMP integers? > Paul Zimmermann long is _not_ based on GMP. long is implemented from scratch in C by the Python developers. It is completely independent from GMP, and has much different performance characteristics, storage formats, etc. On Jan 23, 2008 5:18 AM, pgdoyle <[EMAIL PROTECTED]> wrote: > Why does Python not use the GMP routines for long integers, if they > are so much faster? Despite it's huge standard library, Python is relative easy to build from source on a huge range of architectures -- e.g., a full Python interpreter is installed on my iphone; there was one on my plam treo before. GMP is far more difficult to build. I think that's the core reason why Python does not use GMP, and it's a really good one. Also, keep in mind that very fast arbitrary precision integer arithmetic is hardly relevant for 99.9999% of Python applications (text processing, networking, quick and dirty GUI's), and Python longs aren't that bad when the integer size isn't too big. -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
