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Python's numeric tower

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  Python's numeric tower Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-06-15 02:51 +0000
    Re: Python's numeric tower Ian Kelly <ian.g.kelly@gmail.com> - 2014-06-15 01:22 -0600
      Re: Python's numeric tower Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-06-15 15:33 +0000
        Re: Python's numeric tower Roy Smith <roy@panix.com> - 2014-06-15 13:28 -0400
          Re: Python's numeric tower Ian Kelly <ian.g.kelly@gmail.com> - 2014-06-15 11:45 -0600
          Re: Python's numeric tower Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-06-16 00:38 +0000
            Re: Python's numeric tower Chris Angelico <rosuav@gmail.com> - 2014-06-16 11:02 +1000
              Re: Python's numeric tower Roy Smith <roy@panix.com> - 2014-06-15 21:57 -0400
                Re: Python's numeric tower Chris Angelico <rosuav@gmail.com> - 2014-06-16 12:04 +1000
                  Re: Python's numeric tower Roy Smith <roy@panix.com> - 2014-06-15 22:17 -0400
                    Re: Python's numeric tower Dan Sommers <dan@tombstonezero.net> - 2014-06-16 03:38 +0000
                      Re: Python's numeric tower Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-06-16 09:29 +0100
                    Re: Python's numeric tower Roy Smith <roy@panix.com> - 2014-06-15 23:48 -0400

#73283 — Python's numeric tower

Does anyone know any examples of values or types from the standard 
library or well-known third-party libraries which satisfies 
isinstance(a, numbers.Number) but not isinstance(a, numbers.Complex)?


-- 
Steven D'Aprano
http://import-that.dreamwidth.org/

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#73286

On Sat, Jun 14, 2014 at 8:51 PM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> Does anyone know any examples of values or types from the standard
> library or well-known third-party libraries which satisfies
> isinstance(a, numbers.Number) but not isinstance(a, numbers.Complex)?

>>> issubclass(decimal.Decimal, numbers.Number)
True
>>> issubclass(decimal.Decimal, numbers.Complex)
False

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#73293

On Sun, 15 Jun 2014 01:22:50 -0600, Ian Kelly wrote:

> On Sat, Jun 14, 2014 at 8:51 PM, Steven D'Aprano
> <steve+comp.lang.python@pearwood.info> wrote:
>> Does anyone know any examples of values or types from the standard
>> library or well-known third-party libraries which satisfies
>> isinstance(a, numbers.Number) but not isinstance(a, numbers.Complex)?
> 
>>>> issubclass(decimal.Decimal, numbers.Number)
> True
>>>> issubclass(decimal.Decimal, numbers.Complex)
> False

Well, that surprises and disappoints me, but thank you for the answer.


-- 
Steven

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#73294

In article <539dbcbe$0$29988$c3e8da3$5496439d@news.astraweb.com>,
 Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote:

> On Sun, 15 Jun 2014 01:22:50 -0600, Ian Kelly wrote:
> 
> > On Sat, Jun 14, 2014 at 8:51 PM, Steven D'Aprano
> > <steve+comp.lang.python@pearwood.info> wrote:
> >> Does anyone know any examples of values or types from the standard
> >> library or well-known third-party libraries which satisfies
> >> isinstance(a, numbers.Number) but not isinstance(a, numbers.Complex)?
> > 
> >>>> issubclass(decimal.Decimal, numbers.Number)
> > True
> >>>> issubclass(decimal.Decimal, numbers.Complex)
> > False
> 
> Well, that surprises and disappoints me, but thank you for the answer.

Why would you expect Decimal to be a subclass of Complex?

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#73295

On Sun, Jun 15, 2014 at 11:28 AM, Roy Smith <roy@panix.com> wrote:
> In article <539dbcbe$0$29988$c3e8da3$5496439d@news.astraweb.com>,
>  Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote:
>
>> On Sun, 15 Jun 2014 01:22:50 -0600, Ian Kelly wrote:
>>
>> > On Sat, Jun 14, 2014 at 8:51 PM, Steven D'Aprano
>> > <steve+comp.lang.python@pearwood.info> wrote:
>> >> Does anyone know any examples of values or types from the standard
>> >> library or well-known third-party libraries which satisfies
>> >> isinstance(a, numbers.Number) but not isinstance(a, numbers.Complex)?
>> >
>> >>>> issubclass(decimal.Decimal, numbers.Number)
>> > True
>> >>>> issubclass(decimal.Decimal, numbers.Complex)
>> > False
>>
>> Well, that surprises and disappoints me, but thank you for the answer.
>
> Why would you expect Decimal to be a subclass of Complex?

One might expect it for the same reason that float is a subclass of
Complex.  Decimal was intentionally excluded from the numeric tower
(as noted in PEP 3141), but apparently it still subclasses Number.  As
I understand it the reason Decimal was excluded was because it doesn't
fully implement the methods of Complex; for example, given two Complex
instances, one expects to be able to add them, but that doesn't always
hold for Decimal depending on the type of the other operand:

>>> Decimal("2.0") + 2.0
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unsupported operand type(s) for +: 'decimal.Decimal' and 'float'

The Number ast doesn't specify any particular behavior and is there to
"to make it easy for people to be fuzzy about what kind of number they
expect", so I guess the developers so no harm in letting Decimal
subclass it.

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#73298

On Sun, 15 Jun 2014 13:28:44 -0400, Roy Smith wrote:

> In article <539dbcbe$0$29988$c3e8da3$5496439d@news.astraweb.com>,
>  Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote:
> 
>> On Sun, 15 Jun 2014 01:22:50 -0600, Ian Kelly wrote:
>> 
>> > On Sat, Jun 14, 2014 at 8:51 PM, Steven D'Aprano
>> > <steve+comp.lang.python@pearwood.info> wrote:
>> >> Does anyone know any examples of values or types from the standard
>> >> library or well-known third-party libraries which satisfies
>> >> isinstance(a, numbers.Number) but not isinstance(a,
>> >> numbers.Complex)?
>> > 
>> >>>> issubclass(decimal.Decimal, numbers.Number)
>> > True
>> >>>> issubclass(decimal.Decimal, numbers.Complex)
>> > False
>> 
>> Well, that surprises and disappoints me, but thank you for the answer.
> 
> Why would you expect Decimal to be a subclass of Complex?


py> from decimal import Decimal
py> Decimal("1.5").imag
Decimal('0')


Mathematically, ℂ (complex) is a superset of ℝ (real), and Decimals are a 
kind of real(ish) number, like float:

py> from numbers import Complex
py> isinstance(1.5, Complex)
True


But then I suppose it is understandable that Decimal doesn't support the 
full range of complex arithmetic.


-- 
Steven

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#73300

On Mon, Jun 16, 2014 at 10:38 AM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> Mathematically, ℂ (complex) is a superset of ℝ (real), and Decimals are a
> kind of real(ish) number, like float:

The Python complex type represents a subset of ℂ. The Python Decimal
and float types implement a subset of ℝ, which as you say is a subset
of ℂ. The Python int type implements a subset of ℤ. (Although if you
have infinite storage, you could theoretically represent all of ℤ with
int, and possibly all of ℝ with Decimal. But I don't know of any
Python implementation that can utilize infinite RAM.)

The question isn't really about the mathematical number sets, but
about what operations you can do. The numbers.Complex type specifies
(3.4.0):

class Complex(Number)
 |  Complex defines the operations that work on the builtin complex type.
 |
 |  In short, those are: a conversion to complex, .real, .imag, +, -,
 |  *, /, abs(), .conjugate, ==, and !=.

>From what I can see, all of those operations are defined for Decimal,
*as long as you work exclusively with Decimal*. You can check their
.real and .imag (.imag will be Decimal('0'), and .real is self), you
can conjugate them (returns self), and you can do arithmetic with
them. But you can't mix complex and decimal, any more than you can mix
float and decimal:

>>> Decimal('2')+3.0
Traceback (most recent call last):
  File "<pyshell#30>", line 1, in <module>
    Decimal('2')+3.0
TypeError: unsupported operand type(s) for +: 'decimal.Decimal' and 'float'
>>> Decimal('2')+complex(3.0)
Traceback (most recent call last):
  File "<pyshell#31>", line 1, in <module>
    Decimal('2')+complex(3.0)
TypeError: unsupported operand type(s) for +: 'decimal.Decimal' and 'complex'

Ergo, currently, you can't say that decimal.Decimal can be treated as
a complex. (Although you can call complex(d) and get back a meaningful
value, within the limits of precision - again, same as with float(d).)

To contrast, numbers.Number places very few requirements on its
subclasses. And decimal.Decimal isn't a subclass of any of the rest of
the tower:

>>> for cls in numbers.__all__:
    print(cls,"-",isinstance(d,getattr(numbers,cls)))
Number - True
Complex - False
Real - False
Rational - False
Integral - False

As I understand it, isinstance(x,numbers.Complex) should be True for
anything that you can treat like a complex() - that is, that you can
add it to a complex(), do operations on it, etc, etc, etc. I'm not
sure what isinstance(x,numbers.Number) promises in terms of usability;
I guess if you have a list of Numbers that are all the same type, you
can probably sum them, but you can sum non-Numbers too. The docstring
is a bit vague - sure, it's a number, but what can you do with it?

ChrisA

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#73301

In article <mailman.11074.1402880950.18130.python-list@python.org>,
 Chris Angelico <rosuav@gmail.com> wrote:

> I guess if you have a list of Numbers that are all the same type, you
> can probably sum them, but you can sum non-Numbers too. The docstring
> is a bit vague - sure, it's a number, but what can you do with it?

You can use it to count to three!

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#73302

On Mon, Jun 16, 2014 at 11:57 AM, Roy Smith <roy@panix.com> wrote:
> In article <mailman.11074.1402880950.18130.python-list@python.org>,
>  Chris Angelico <rosuav@gmail.com> wrote:
>
>> I guess if you have a list of Numbers that are all the same type, you
>> can probably sum them, but you can sum non-Numbers too. The docstring
>> is a bit vague - sure, it's a number, but what can you do with it?
>
> You can use it to count to three!

Since "increment" is not a provided method, and the + and += operators
are not guaranteed to be defined for any definition of 1 on the other
side, I'm not sure that's actually true... but if you hold a hand
grenade and want to know whether to count to Decimal('3') or 3+0j or
Fraction(3, 1), I'm just going to tell you to throw the thing already!

ChrisA

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#73303

In article <mailman.11075.1402884256.18130.python-list@python.org>,
 Chris Angelico <rosuav@gmail.com> wrote:

> On Mon, Jun 16, 2014 at 11:57 AM, Roy Smith <roy@panix.com> wrote:
> > In article <mailman.11074.1402880950.18130.python-list@python.org>,
> >  Chris Angelico <rosuav@gmail.com> wrote:
> >
> >> I guess if you have a list of Numbers that are all the same type, you
> >> can probably sum them, but you can sum non-Numbers too. The docstring
> >> is a bit vague - sure, it's a number, but what can you do with it?
> >
> > You can use it to count to three!
> 
> Since "increment" is not a provided method, and the + and += operators
> are not guaranteed to be defined for any definition of 1 on the other
> side, I'm not sure that's actually true... but if you hold a hand
> grenade and want to know whether to count to Decimal('3') or 3+0j or
> Fraction(3, 1), I'm just going to tell you to throw the thing already!
> 
> ChrisA

I don't believe HandGrenade implements throw().  It does, however, 
implement lobbeth().

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#73304

On Sun, 15 Jun 2014 22:17:57 -0400, Roy Smith wrote:

> I don't believe HandGrenade implements throw().  It does, however,
> implement lobbeth().

And therein lies the problem with Object Oriented Programming:
instances of HandGrenade neither throw nor lobbeth.

One, Two, Five'ly yours,
Dan

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#73306

On 16/06/2014 04:38, Dan Sommers wrote:
> On Sun, 15 Jun 2014 22:17:57 -0400, Roy Smith wrote:
>
>> I don't believe HandGrenade implements throw().  It does, however,
>> implement lobbeth().
>
> And therein lies the problem with Object Oriented Programming:
> instances of HandGrenade neither throw nor lobbeth.
>
> One, Two, Five'ly yours,
> Dan
>

The above looks like a bug that should have been picked up, why hasn't 
OverflowError been raised?

-- 
My fellow Pythonistas, ask not what our language can do for you, ask 
what you can do for our language.

Mark Lawrence

---
This email is free from viruses and malware because avast! Antivirus protection is active.
http://www.avast.com

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#73305

In article <roy-ED231F.22175715062014@news.panix.com>,
 Roy Smith <roy@panix.com> wrote:

> In article <mailman.11075.1402884256.18130.python-list@python.org>,
>  Chris Angelico <rosuav@gmail.com> wrote:
> 
> > On Mon, Jun 16, 2014 at 11:57 AM, Roy Smith <roy@panix.com> wrote:
> > > In article <mailman.11074.1402880950.18130.python-list@python.org>,
> > >  Chris Angelico <rosuav@gmail.com> wrote:
> > >
> > >> I guess if you have a list of Numbers that are all the same type, you
> > >> can probably sum them, but you can sum non-Numbers too. The docstring
> > >> is a bit vague - sure, it's a number, but what can you do with it?
> > >
> > > You can use it to count to three!
> > 
> > Since "increment" is not a provided method, and the + and += operators
> > are not guaranteed to be defined for any definition of 1 on the other
> > side, I'm not sure that's actually true... but if you hold a hand
> > grenade and want to know whether to count to Decimal('3') or 3+0j or
> > Fraction(3, 1), I'm just going to tell you to throw the thing already!
> > 
> > ChrisA
> 
> I don't believe HandGrenade implements throw().  It does, however, 
> implement lobbeth().

On second thought, it probably implements lob().  You can, however 
derive lobbeth() by calling conjugate().

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