Am 29.03.2014 05:16, schrieb Richard Fateman:
On Monday, March 24, 2014 3:42:01 AM UTC-7, Joachim Durchholz wrote:
Am 24.03.2014 01:58, schrieb Richard Fateman:
Now we must address what is meant by integer. In common lisp, integer
meansarbitrary precision integer.
> Consequently, every rational number IS an integer/integer.
[...]
> It seems to me the meanings of words in sympy should correspond to
> their meanings in mathematics not some hack mockery of the word that
> appears in one or even several programming languages.
Your position seems inconsistent - you derive your idea about the nature
of rational numbers from Common Lisp, yet you denounce exactly that kind
of reasoning as "some hack mockery of the word that appears in [...]
programming languages".
No, I derive my idea about the nature of rational numbers from standard
mathematical
definitions. It turns out that Common Lisp implements this.
You derive your idea that a number is just its representation from CL.
Which is not what math says. In math, a number is a model (not even a
representation) plus a set of axioms; by that definition, floats in any
programming language (including CL) aren't even numbers because they
don't satisfy the number axioms. (The purpose of floats is outside the
domain of symbolic math. That's why we're discussing it here.)
> Though I suppose
there is a finiteness argument that there are integers whose binary
representation
is so long that they cannot be stored in your computer's memory.
There is, but it's a special case of what we need to do anyway - that
SymPy will either deliver a correct result or report an error.
> There are also
integers whose
binary representation is so long that even using all the electrons in the
known universe,
one cannot write the number out, so it is perhaps just a matter of how you
feel about
such inherent limits of finiteness of computational devices.
That's a more fundamental problem with floats actually.
A float runs out of precision long before the computer runs out of
memory, so SymPy could be forced to report failure long before memory is
exhausted.
Worse, float implementations do not reliably report precision loss. Not
for all C implementations (which Python takes its float implementation
from), and not even for all hardware chips that do the actual bit munging.
I have started to wonder whether we shouldn't throw Float support out.
We'd not doing numerics anyway. Not the kind that uses floats.
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