People discussing the merits of languages based on statistical popularity should note how many newspapers publish astrology columns. The language shootouts are not entirely relevant, since the question here has to do with suitability of a language for implementation of a computer algebra framework, and for detailed implementation of some routines. We seem to agree that Python is not suitable, and that is why Cython is used instead. But Python can be used for some things, and isn't it nice that we can do everything in one language, except the things that we can't do in that language.
Regarding using GMP or MPIR as the bignum library in Lisp 1. The occurrence of 11 mpz_adds in the core of ECL is presumably the only occurrences EVER, and you could add any amount of additional code in Lisp and never see another one. So it is an absolute limit, not one "relative to the size of the program". Sage, seems to sprinkle them around. And so readably. 2. The built-in arithmetic standard for lisp requires non-destructive arithmetic in general; it is possible to use destructive (mutating) operations within the evaluation of expressions only when the "destruction" cannot be viewed outside the context of that expression. For example, compiling (+ a b c d e f) could be done with only one temporary to do (+e f) (+ d (+ e f)) , .... Or a naive compiler might use 5 temporaries, as (+ a(+ b (+ c (+ d (+ e f))))). The generic arithmetic package I wrote is somewhat akin to a compiler in that it takes an expression like that given above, figures out how to allocate temporaries and call mpz_ programs. It is probably cleverer than the default ECL code generation using mpz_ code in a purely functional framework. This is sometimes an important distinction to make, that a functional form for communicating computations does not necessarily require a data flow that is purely functional. I think I've tried to make this point a few times in this thread. 3. The allegation of painfully slow operations on huge numbers may seem like a particularly telling point, but this is probably done in the absence of any profiling, which is to say: how much does one use huge huge numbers? Thus arithmetic on integers of 31, 63, or 127 bits may be faster NOT using GMP, and may be umpteen times more common. Of course to run a profiler, one has to have a set of important applications which should be considered as a benchmark. Finding Mersenne primes might be important to some people, whereas to others they are just wastes of electricity. The smaller ones are known and it would probably be pointless to re-examine them. 4. Bill seems to think that it might even be possible for Maxima to just do single precision arithmetic. That doesn't work for the kind of computer algebra system that most people want. Any conforming Common Lisp must provide bignums, and that's what Maxima uses for integers. 5. When I said that Lisp could use Python libraries, I was referring to the useful libraries written in whatever language, which are called by Python. Those libraries can be loaded and invoked by Lisp, and I've used this once in the past (coincidentally, my first try to find a GMP library got me gmpy, and I loaded that into Lisp.) But calling python from lisp generally is not hard; see http://common-lisp.net/project/python-on-lisp/ There is also CLPython, which I think is a Python syntax language that is implemented in CL. 6. There is a fundamental difference of opinion in language design between William Stein and the view I hold (and share with many others) that the best way to write a very large system is to simultaneously work "top down" on the high level objectives, and "build up" from the lower language -- to define a new, more suitable, language to achieve those high-level objectives. That is, in Lisp, where building languages upon languages is relatively easy, it seems obvious that one should cover up, at the earliest opportunity, the ugliness of the APIs of the utility functions, and wrap them in functionality suitable for whatever ... mathematics. plotting. parallel execution ... So William Stein takes it as a point of pride that people use python syntax and directly access APIs for GMP. I take it as a weakness which leads to error-prone verbose programming. 7. I have no problem with summer-of-code high school or college or ... students writing programs. Relying on this code as part of the core of a system is however not such a great plan. RJF --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
