Re: Mathematics in Python are not correct

[Luis Zarrabeitia]

On Thursday 08 May 2008 06:54:42 pm wxPythoner@gmai l.com wrote:

The problem is that Python parses -123**0 as -(123**0), not as
(-123)**0.

Actually, I've always written it as (-123)**0. At least where I'm from,
exponentiation takes precedence even over unary "-". (to get a power of -123,
you must write $(-123)^0$ [latex])

Though not an authoritative source, wikipedia also uses the (-x)^y notation:

http://en.wikipedia.org/wiki/Exponentiation#Powers_of_minus_one

Btw, there seems to be a math problem in python with exponentiation. ..

>>0**0

1

That 0^0 should be a nan or exception, I guess, but not 1.

[just found out while trying the poster's example]

--
Luis Zarrabeitia (aka Kyrie)
Fac. de Matemática y Computación, UH.

http://profesores.matcom.uh.cu/~kyrie

[Dan Bishop]

Re: Mathematics in Python are not correct

On May 8, 6:14 pm, Luis Zarrabeitia <ky...@uh.cuwro te:

On Thursday 08 May 2008 06:54:42 pm wxPytho...@gmai l.com wrote:
>

The problem is that Python parses -123**0 as -(123**0), not as
(-123)**0.

>
Actually, I've always written it as (-123)**0. At least where I'm from,
exponentiation takes precedence even over unary "-". (to get a power of -123,
you must write $(-123)^0$ [latex])

FWIW, my TI-89 evaluates it as -1.

Though not an authoritative source, wikipedia also uses the (-x)^y notation:http://en.wikipedia.org/wiki/Exponen...s_of_minus_one
>
Btw, there seems to be a math problem in python with exponentiation. ..
>

>0**0

>
1
>
That 0^0 should be a nan or exception, I guess, but not 1.
>
[just found out while trying the poster's example]

Technically correct, but 0**0 == 1 is actually pretty useful. For one
thing, it lets you create a Vandermonde matrix without making 0 a
special case.

[Arnaud Delobelle]

Re: Mathematics in Python are not correct

Dan Bishop <danb_83@yahoo. comwrites:

On May 8, 6:14 pm, Luis Zarrabeitia <ky...@uh.cuwro te:

>On Thursday 08 May 2008 06:54:42 pm wxPytho...@gmai l.com wrote:
>>

The problem is that Python parses -123**0 as -(123**0), not as
(-123)**0.

>>
>Actually, I've always written it as (-123)**0. At least where I'm from,
>exponentiati on takes precedence even over unary "-". (to get a power of -123,
>you must write $(-123)^0$ [latex])

>
FWIW, my TI-89 evaluates it as -1.
>

>Though not an authoritative source, wikipedia also uses the (-x)^y
>notation:http://en.wikipedia.org/wiki/Exponen...s_of_minus_one
>>
>Btw, there seems to be a math problem in python with exponentiation. ..
>>

>>0**0

>>
>1
>>
>That 0^0 should be a nan or exception, I guess, but not 1.
>>
>[just found out while trying the poster's example]

>
Technically correct, but 0**0 == 1 is actually pretty useful. For one
thing, it lets you create a Vandermonde matrix without making 0 a
special case.

If we want Binomial expansion to work sanely, we need 0^0 = 1, e.g:

(x+0)^2 = 1*x^2*0^0 + 2*x*0 + 1*x^0*0^2
= x^2

Therefore 0^0 = 1

Also, x^y (for x, y natural numbers) can be defined as the number of
functions from Y to X where |X|=x and |Y|=y. As there is exactly one
function from the empty set to the empty set, 0^0 = 1.

The arguments for making 0^0 = 0 are weak, it is a bit more convincing
to want it to be undefined (as (0,0) is a point of discontinuity of
(x,y) -x^y).
--
Arnaud