Opened 7 years ago

Closed 7 years ago

#15053 closed defect (fixed)

Number fields think they can embed into finite fields

Reported by: robharron Owned by:
Priority: major Milestone: sage-5.12
Component: number fields Keywords: NumberField, embeddings
Cc: Merged in: sage-5.12.beta4
Authors: Robert Harron Reviewers: John Cremona
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

The embeddings function for number fields just checks for roots in the argument. For example: 

sage: K = NumberField(x^3-2, 'a')
sage: K.embeddings(GF(3))                                                                                                                                  
[                                                                                                                                                          
Ring morphism:                                                                                                                                             
  From: Number Field in a with defining polynomial x^3 - 2                                                                                                 
  To:   Finite Field of size 3                                                                                                                             
  Defn: a |--> 2                                                                                                                                           
]

Attachments (1)

trac_15053_embeddings_of_number_fields_into_fields_of_non-zero_characteristic.patch​ (1.1 KB) - added by robharron 7 years ago.

Download all attachments as: .zip

Change History (6)

Changed 7 years ago by robharron

comment:1 Changed 7 years ago by robharron

  • Status changed from new to needs_review

comment:2 Changed 7 years ago by cremona

  • Reviewers set to John Cremona
  • Status changed from needs_review to positive_review

This looks good to me. I suppose the underlying problem is that Sage is happy to coerce K.defining_polynomial() into the polynomial ring over the finite field.

Applies fine to 5.12.beta1 and tests pass.

comment:3 Changed 7 years ago by robharron

Yeah, that coercion bothered me a bit, but I'll settle for this ticket for now.

comment:4 Changed 7 years ago by jdemeyer

  • Authors set to Robert Harron

comment:5 Changed 7 years ago by jdemeyer

  • Merged in set to sage-5.12.beta4
  • Resolution set to fixed
  • Status changed from positive_review to closed
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