On Monday 30 October 2006 22:38, David Harvey wrote: > I want to start applying our arithmetic architecture to _mul_. The fast > pathway for __mul__ needs to be able to quickly identify the case of > multiplying an element of a base ring of an algebra by an element of > the algebra (or commutative algebra as the case may be). The sanest way > to do this really fast is for base_ring to be a cdef attribute of > Algebra and CommutativeAlgebra. > > Unfortunately this is going to run us into multiple inheritance > problems with matrices (and possibly other things). Currently in > William's development code, the MatrixSpace_generic class inherits from > Generators. This has a bunch of cdef'd attributes. So it won't be > possible to simultaneously inherit from Algebra too, if Algebra has a > cdef'd base_ring.
I've got an evil idea: What if Generators had a base_ring cdef'd? I know that this makes no sense for general Generators but it would only be one single pointer which isn't even visible to Python (i.e. not confusing the higher levels). A big fat warning in a comment where it is defined would clarify everything for library developers. It's a hack and probably to reject but I guess it should be on the table before being rejected. > I suppose another possibility is for the *elements* of an algebra to > carry around a cdef pointer to the base ring, much like they already > carry around a pointer to the parent. That will be ever-so-slightly > faster, but it will increase the memory consumption of every element. > This is probably not a big deal, as most algebra elements will already > take up a lot of space anyway, and it's just one extra pointer. The > algebras themselves can also keep a base_ring, but as a python > attribute, and they won't have as fast access to it. > On the other hand.... maybe this test doesn't need to be so fast after > all. We can still test first for matching RingElement parents very > quickly. If it's true that algebra elements are generally quite > complicated objects, then probably a python attribute lookup is not > such a big deal. Maybe I'm over-optimising. About the quite complicated objects: I guess the simplest/smallest algebra element I can think of is a dense matrix over GF(2), i.e. a bitstring. That's something SAGE should have in a very fast way. Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _icq: 177334829 _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
