On Monday, March 31, 2014 9:28:23 AM UTC-7, Sergey Kirpichev wrote:
>
> On Sat, Mar 29, 2014 at 01:28:54PM -0700, Richard Fateman wrote:
> > Common Lisp uses floating-point arithmetic for floats, exact
> arithmetic
> > for the data type used for rationals.
>
> Good news. Python does same.
>
> > If you stick with integers and ratios of integers, Common
> > Lisp does mathematically valid arithmetic.
>
> Excelent! Python too.
>
> The problem is: float arithmetic is not a "valid arithmetic" by
> design. And the question is: should we use float "numbers" in SymPy
> at all.
>
I think the answer from a practical perspective is that you can't exclude
floats.
>
> > But I admit, we shouldn't allow
> > using of Float's (or builtin float type) in symbolic mathematics.
> >
> > I disagree, from experience. People want to introduce floats. For
> > example, some people
> > write squareroot(x) as x^0.5
> > Saves typing, and they believe it is the same thing.
>
> But that's not necessary floats! It's just a different
> notation for rational 1/2 (as "they believe").
>
So are you taking the view, now, that 0.5 is rational?
>
> In [1]: Rational('0.123')
> Out[1]:
> 123
> ────
> 1000
> In [2]: Float('0.123')
> Out[2]: 0.123000000000000
> In [3]: type(_)
> Out[3]: sympy.core.numbers.Float
> In [4]: sympify('0.123')
> Out[4]: 0.123000000000000
> In [5]: type(_)
> Out[5]: sympy.core.numbers.Float
>
> The little problem here is that float(0.3) != 3/10 internally, for
> example (despite people think so). See this:
> https://docs.python.org/2/tutorial/floatingpoint.html
>
> In [16]: Decimal(0.3)
> Out[16]:
> Decimal('0.299999999999999988897769753748434595763683319091796875')
> In [17]: Rational(0.3)
> Out[17]:
> 5404319552844595
> ─────────────────
> 18014398509481984
> In [18]: Rational(str(0.3))
> Out[18]: 3/10
>
> End of story. It seems, people want to introduce not floats but a fancy
> notation for rationals.
You can't predict the future.
> If this is only the reason why we keep Float
> object - we should drop Float's and fix sympify to map python's floats
> to Rational's instead (for example: sympify(0.2) -> Rational(str(0.2))).
>
Sometimes floats can be very handy. Finding approximations to roots
of a polynomial. Compared to rational arithmetic, where different, usually
much slower methods, might be used.
>
> Is there a real need for floats in symbolic mathematics package?
>
Just because you might not need them now, doesn't really answer the
question.
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