Plain old coercions are cached on the codomain. Since our generic, global objects like ZZ and QQ tend to coerce universally *into* other rings, this tends to mean that the morphisms, which hold strong references to domain and codomain, are hanging off the more temporary objects, i.e., ZZ and QQ are not holding references TO them. That's good because it gives a chance to recycle rings that aren't in use anymore.
However, for binary op discovery, the two operands are often essentially symmetric, so there is no preferred one to store info on. In fact, it seems the coercion framework ships this off into some global table elsewhere. Great care is taken to not hold strong references in the keys of the dictionaries, but the coercion morphisms themselves are held with strong references (that's the point!). However, those morphisms themselves hold strong references to domain and codomain! Example: sage: import gc sage: T=type(GF(2)) sage: gc.collect() 0 sage: len(list(o for o in gc.get_objects() if type(o) is T)) 1 sage: sage: for p in prime_range(2,300): ....: k=GF(p) ....: _=ZZ(1)+k(1) ....: sage: del k, _ sage: gc.collect() 0 sage: len(list(o for o in gc.get_objects() if type(o) is T)) 62 We see that after garbage collection the finite fields still remain in memory, even though the user does not hold any reference to them. To illustrate that the coercion model indeed has references to these: sage: cm = sage.structure.element.get_coercion_model() sage: maps, actions = cm.get_cache() sage: L = maps.values() #as far as I can tell, these are strong refs sage: V=[l[0].codomain() for l in L if l is not None and l[0] is not None] sage: len(list(v for v in V if type(v) is T)) 62 I don't see how we can avoid this. In principle the coercion maps don't need to hold references to their domain and codomain, because these are part of the key by which they are looked up. So in principle one could have a kind of "coercion map stub" stored that gets reequiped with domain and codomain upon lookup in the relevant dictionary. However, doing something like that might be hard to do without significant speed penalty. Plus forbidding people to refer to domain and codomain in a map is a rather severe restriction (think morphism CRT morphism Z/3Z x Z/5Z -> Z/15Z for instance) A heuristic/hacky way to do it is by storing the morphism on one of the concerned rings (chosen by a heuristic to likely be the most short- lived one) and change the global dictionary to be weakly keyed and only hold a redirection "look on first" or "look on second" to tell the system where to look for the actual morphism. Comments? (Especially Robert Bradshaw's insights would be very valuable here). -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
