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how to get frobenius_element() in numberfield?

asked 2013-12-10 19:45:58 -0500

cjsh gravatar image

updated 2013-12-11 04:15:31 -0500

William Stein gravatar image
CLO7.<u> = CyclotomicField(7)

CLO7().***frobenius_element***() 

Traceback (click to the left of this block for traceback)
...
AttributeError:
'sage.rings.number_field.number_field_element.NumberFieldElement_abs\
olute' object has no attribute 'frobenius_element'
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answered 2013-12-11 03:28:40 -0500

John Cremona gravatar image

updated 2013-12-11 04:37:02 -0500

Here is way to do it.

sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):                                                                                       
    return F.hom([z^p])
....: 
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> z^2
sage: Frob(3)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> z^3
sage: Frob(5)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> z^5
sage: Frob(97)    
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1
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thank you very much!

cjsh gravatar imagecjsh ( 2013-12-11 19:35:21 -0500 )edit

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Asked: 2013-12-10 19:45:58 -0500

Seen: 107 times

Last updated: Dec 11 '13