character table of a finite field

finite-fields

asked 2016-09-22 23:32:34 +0100

xhimi
25 ●6

updated 2019-08-29 18:24:57 +0100

FrédéricC

5251 ●3 ●44 ●116

I am trying to calculate the character table of a finite field. The following is my code:

def character_table(q,n):
    k=GF(q^n)
    tr(x)=sum(x^(q^i) for i in [0..n-1])
    ksi = e^(2*pi*I/n)
    chi(x)=ksi^(tr(x))
    for a in k:
        L_a = [chi(a*x) for x in k]
        print L_a

And the TypeError is "free variable 'x' referenced before assignment in enclosing scope". Can somebody help me how to fix the code?

Thanks

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Comments

Beyond the error that you are getting, here are some comments.

The function definition's body (everything below the first line) should be indented four spaces.
You define L but never use it.
Are k and K supposed to be the same?

slelievre ( 2016-09-23 09:12:11 +0100 )edit

You are aware that Sage has finite group character tables via GAP as well, correct?

kcrisman ( 2016-09-23 14:11:36 +0100 )edit

@slelievre I fixed all your suggestions. Now I get "free variable 'x' referenced before assignment in enclosing scope". @kcrisman I tried that but I couldn't get the right syntax. Could you please help? It seems that character_table() does not have an attribute for abelian groups. Also, since I am new in sage, I thought it was worth it to try and define a function from scratch. I also having difficulties on using only the additive group of a finite field.

xhimi ( 2016-09-23 17:39:15 +0100 )edit

Ah, then see my answer (which is just a link).

kcrisman ( 2016-09-24 22:53:02 +0100 )edit

@slelievre Please see the edited question.

xhimi ( 2016-09-26 18:17:01 +0100 )edit

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answered 2016-09-23 09:05:08 +0100

slelievre
17704 ●22 ●160 ●350 http://carva.org/samue...

updated 2016-09-26 19:12:33 +0100

Some tips:

Instead of sum[...] you want sum(...).
Instead of tr(x) = ..., use def tr(x): return ...

This might be what you were trying to write:

def character_table(q, n):
    k = GF(q^n)
    def tr(x):
        return sum(x^(q^i) for i in [0..n-1])
    ksi = e^(2*pi*I/n)
    def chi(x):
        return ksi^(tr(x))
    for a in k:
        L_a = [chi(a*x) for x in k]
        print L_a

Calling this function prints something:

sage: character_table(3, 2)
[1, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, -1, -1, 1, 1, 1, 1, -1]
[1, -1, -1, 1, 1, 1, 1, -1, 1]
[1, -1, 1, 1, 1, 1, -1, 1, -1]
[1, 1, 1, 1, 1, -1, 1, -1, -1]
[1, 1, 1, 1, -1, 1, -1, -1, 1]
[1, 1, 1, -1, 1, -1, -1, 1, 1]
[1, 1, -1, 1, -1, -1, 1, 1, 1]
[1, -1, 1, -1, -1, 1, 1, 1, 1]