Lossless Number Conversion

[Chris Spencer]

Is there any library for Python that implements a kind of universal
number object. Something that, if you divide two integers, generates a
ratio instead of a float, or if you take the square root of a negative,
generates a complex number instead of raising an exception? Lisp has
something like this, and it makes number crunching much more convenient.

Chris

[mensanator]

Chris Spencer wrote:

Is there any library for Python that implements a kind of universal
number object. Something that, if you divide two integers, generates a
ratio instead of a float, or if you take the square root of a negative,
generates a complex number instead of raising an exception? Lisp has
something like this, and it makes number crunching much more convenient.

Chris

The GMPY module has unlimited precision rationals:

from gmpy import * r = mpq(1,1) # create the rational 1/1
for i in range(2,50): r = r + mpq(1,i) # add the rational 1/i to the running sum
print r
3/2
11/6
25/12
137/60
49/20
363/140
761/280
7129/2520
7381/2520
83711/27720
86021/27720
1145993/360360
1171733/360360
1195757/360360
2436559/720720
42142223/12252240
14274301/4084080
275295799/77597520
55835135/15519504
18858053/5173168
19093197/5173168
444316699/118982864
1347822955/356948592
34052522467/8923714800
34395742267/8923714800
312536252003/80313433200
315404588903/80313433200
9227046511387/2329089562800
9304682830147/2329089562800
290774257297357/72201776446800
586061125622639/144403552893600

So you can keep absolute precision all the way to the end
of the calculation. And you can always convert it to a float
by dividing the numerator by the denominator:
print mpf(r.numer())/mpf(r.denom())

4.47920533832942505756047179296

[Andreas Kostyrka]

Am Sonntag, den 28.08.2005, 21:36 +0000 schrieb Chris Spencer:

Is there any library for Python that implements a kind of universal
number object. Something that, if you divide two integers, generates a
ratio instead of a float, or if you take the square root of a negative,
generates a complex number instead of raising an exception? Lisp has
something like this, and it makes number crunching much more convenient.

Yes and no. There isn't general solution. But for example you want to
allow complex number, just use cmath.

Andreas

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[Raymond L. Buvel]

Chris Spencer wrote:

Is there any library for Python that implements a kind of universal
number object. Something that, if you divide two integers, generates a
ratio instead of a float, or if you take the square root of a negative,
generates a complex number instead of raising an exception? Lisp has
something like this, and it makes number crunching much more convenient.

Chris

If you are on any Unix-like platform, you might want to check out clnum.
It works like the gmpy package but has complex versions of rationals
and arbitrary precision floats.

http://calcrpnpy.sourceforge.net/clnum.html