sign of permutations

[John Cremona]

If pi is a permutation, e.g. defined by pi=permutations(4)[3], then
pi.signature() returns what I have always called the "sign" of pi, and
none of pi.sign(), pi.sgn(), sign(pi), sgn(pi) work.

Is there a good reason for not having, at least, the alias pi.sign =
pi.signature?

I cannot remember often having heard people talk of a permutations's
signature (let alone its parity, pace wikipedia) but I am prepared to
be over-ruled by an expert in combinatorics. However I still think
that the abbreviation "sign" would be reasonable to have too.

Perhaps number-theorists are just lazy:

sage: a = QuadraticField(101).gen()
sage: a.minimal_polynomial() # fails
sage: a.minimum_polynomial() # fails
sage: a.minpoly()
x^2 - 101

John

[Volker Braun]

http://www.googlefight.com/index.php?lang=en_GB&word1=permutation+signature&word2=permutation+sign

Sign wins over signature ;-)

[Simon King]

On 2012-09-04, Volker Braun <vbrau...@gmail.com> wrote:
> ------=_Part_113_29781094.1346766769517
> Content-Type: text/plain; charset=ISO-8859-1

>
> http://www.googlefight.com/index.php?lang=en_GB&word1=permutation+signature&word2=permutation+sign
>
> Sign wins over signature ;-)

Outch:
http://googlefight.com/index.php?lang=en_GB&word1=sage+maths&word2=sage+accountance

But I guess that's for sage-marketing.

[Rob Beezer]

On Tuesday, September 4, 2012 6:21:11 AM UTC-7, John Cremona wrote:

If pi is a permutation, e.g. defined by pi=permutations(4)[3], then
pi.signature() returns what I have always called the "sign" of pi, and
none of pi.sign(), pi.sgn(), sign(pi), sgn(pi) work.

But:

sage: G = SymmetricGroup(2)
sage: a = G("(1,2)")
sage: a.sign()
-1

So I'd say +1 to greater coordination between group element permutations and purely combinatorial permutations overall, and in particular having  .sign()  as John suggests for the "other" permutations.

Rob
 

[Kwankyu Lee]

Signature means to me a hand-written name.

So ++1 to .sign()

[Nicolas M. Thiery]

Hi Rob!

(CC to sage-combinat; this is thread [1] on sage-devel)

+1! This miscoordination has been an itch for us for quite a while.
In general, Permutations need some heavy refactoring which will be
best done all at once; but a simple change like this can be done right
away.

Cheers,
Nicolas

PS: https://groups.google.com/forum/?hl=fr&fromgroups=#!topic/sage-devel/DYVbTWWOMtE)
--
Nicolas M. Thi�ry "Isil" <nth...@users.sf.net>
http://Nicolas.Thiery.name/

[John Cremona]

Thanks for all the replies.  There is now a palindromic ticket for this at #13431.

John

Nicolas M. Thi�ry "Isil" <nth...@users.sf.net>
http://Nicolas.Thiery.name/

[Julien Puydt]

Le 05/09/2012 04:10, Kwankyu Lee a �crit :

> Signature means to me a hand-written name.

There's the signature of a quadratic form though.

Snark on #sagemath

[Keshav Kini]

Kwankyu Lee <ekwa...@gmail.com> writes:
> Signature means to me a hand-written name.

Well, there are other valid mathematical or CS meanings to "signature".
I agree that this one should be "sign", though.

-Keshav

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