Why 1/3 == S(1)/3 is True ?

[Christophe Bal]

Hello.

For me the fact that  1/3 == S(1)/3  has value  True  sounds like a bug because  1/3  is a float, and  S(1)/3  a rational.

Christophe BAL

=== PYTHON ===

from sympy import *

a = 1/3

b = S(1)/3

print(a)

print(b)

print(a == b)

print(type(a))

print(type(b))

--- OUTPUT ---

0.3333333333333333

1/3

True

<class 'float'>

<class 'sympy.core.numbers.Rational'>

[Mateusz Paprocki]

Hi,

On 2 October 2014 15:02, Christophe Bal <proj...@gmail.com> wrote:
> Hello.
>
> For me the fact that 1/3 == S(1)/3 has value True sounds like a bug
> because 1/3 is a float, and S(1)/3 a rational.>

Because 1/3 == S(1)/3 is equivalent to Float(1/3) == S(1)/3 and
apparently __eq__ prefers Float comparison instead of Rational, so you
get True. I think there are some reasons why this works this way, but
indeed it seems wrong.

Mateusz

> Christophe BAL
>
> === PYTHON ===
>
> from sympy import *
>
> a = 1/3
> b = S(1)/3
>
> print(a)
> print(b)
>
> print(a == b)
> print(type(a))
> print(type(b))
>
> --- OUTPUT ---
>
> 0.3333333333333333
> 1/3
> True
> <class 'float'>
> <class 'sympy.core.numbers.Rational'>
>

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[Richard Fateman]

Lisp has a variety of equality testing predicates.

EQ  for  " same memory location"

=   for "numeric equality"

There's also EQL, EQUAL, CHAR=, STRING=. ...  

One of the benefits of NOT having infix syntax for relations like "="  is that

it puts these others on a more equal footing, language-wise.

I suppose you might argue that "types" solve this problem, but you

would be wrong.  It is perfectly possible to want to know if two strings

that are string=   are also eq -- that is, in the same memory location.

RJF

[Christophe Bal]

And what about the following code ?

The user of Sympy must know that types are different and so that the variable are not the same things. A float is not a rational.

Just try the following code using a classical sequence showing a weakness of the floats.

=== PYTHON ===

from sympy import *

a = 1/3

b = S(1)/3

print(a == b)

print(type(a))

print(type(b))

for i in range(31):

    print(a, ";", b)

    a = 4*a - 1

    b = 4*b - 1

== OUTPUT ===

True

<class 'float'>

<class 'sympy.core.numbers.Rational'>

0.3333333333333333 ; 1/3

0.33333333333333326 ; 1/3

0.33333333333333304 ; 1/3

0.33333333333333215 ; 1/3

0.3333333333333286 ; 1/3

0.3333333333333144 ; 1/3

0.33333333333325754 ; 1/3

0.33333333333303017 ; 1/3

0.3333333333321207 ; 1/3

0.3333333333284827 ; 1/3

0.3333333333139308 ; 1/3

0.3333333332557231 ; 1/3

0.3333333330228925 ; 1/3

0.3333333320915699 ; 1/3

0.3333333283662796 ; 1/3

0.3333333134651184 ; 1/3

0.33333325386047363 ; 1/3

0.33333301544189453 ; 1/3

0.3333320617675781 ; 1/3

0.3333282470703125 ; 1/3

0.33331298828125 ; 1/3

0.333251953125 ; 1/3

0.3330078125 ; 1/3

0.33203125 ; 1/3

0.328125 ; 1/3

0.3125 ; 1/3

0.25 ; 1/3

0.0 ; 1/3

-1.0 ; 1/3

-5.0 ; 1/3

-21.0 ; 1/3

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[Richard Fateman]

On Thursday, October 2, 2014 11:11:14 AM UTC-7, Christophe Bal wrote:

And what about the following code ?

The user of Sympy must know that types are different and so that the variable are not the same things. A float is not a rational.

A float "type"  is a different "type"   from some other numbers, but  in fact every binary float

represents a particular rational number,  of the form  integer X 2^integer.    Just happens that

1/3 as a rational number, is not a one of those binary floats.

[Christophe Bal]

Yes but the set of floats is not even a sub ring of the set of rational numbers.

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[Sergey Kirpichev]

On Thursday, October 2, 2014 5:02:10 PM UTC+4, Christophe Bal wrote:

For me the fact that  1/3 == S(1)/3  has value  True  sounds like a bug because  1/3  is a float, and  S(1)/3  a rational.

Looks as a bug, please report one on https://github.com/sympy/sympy/issues (through please search first for similar issues).

[Christophe Bal]

Just done.

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[Richard Fateman]

On Friday, October 3, 2014 11:23:27 AM UTC-7, Christophe Bal wrote:

Yes but the set of floats is not even a sub ring of the set of rational numbers.

Nevertheless, floating point computations are widely used.

I suspect that most users do not know what a a sub ring is.

If you wish to incorporate floats into a symbolic computation, you can do so

by talking about them as a subset of the rationals.  Arbitrary precision floats

allow you to approximate arbitrarily closely any rational by a nearby "binary rational".

You can then rework most (maybe all) of the (usual) numerical routines by  adding

a tolerance parameter.   e.g.  instead of  cos(x)  for x a float,  you have

cos(x,err)   for x a binary-rational-arbitrary-precision-"float"   and  err -- a similar

quantity that says how large an error is acceptable in the cosine computation.

Is there a finitely representable computational structure in sympy that is closed under  cosine()?