Opened 11 years ago

Closed 10 years ago

## #12143 closed defect (duplicate)

# PariError when creating a relative number field

Reported by: | culler | Owned by: | davidloeffler |
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Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |

Component: | number fields | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | Marco Streng | |

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

Please close as duplicate of #252

sage: t = QQ['t'].gen() sage: K.<a> = QQ.extension(t^6 - 1/4*t^3 - 1/64) sage: s = K['s'].gen() sage: g = s^4 + 2*a^2*s^2 + a^4 + a sage: L.<b> = K.extension(g)

fails with PariError?: inconsistent data (12)

The failure occurs in: rings.number_field.number_field_rel.pari_relative_polynomial().polisirreducible()

If, instead, one tries:

sage: L.<b> = K.extension(g, check=False)

it fails with PariError?: (5)

This time it fails in: pari_absolute_base_polynomial().rnfequation(self.pari_relative_polynomial(), 1)

### Change History (7)

### comment:1 follow-up: 2 Changed 11 years ago by

### comment:2 follow-up: 3 Changed 11 years ago by

Replying to culler:

Unfortunately I don't see any way to work around it in my project.

I think the following works:

sage: PQ.<t> = QQ[] sage: f = t^6 - 1/4*t^3 - 1/64 sage: f = PQ(pari(f).polredabs()) sage: K.<a> = QQ.extension(f) sage: s = K['s'].gen() sage: g = s^4 + 2*a^2*s^2 + a^4 + a sage: L.<b> = K.extension(g) sage: L Number Field in b with defining polynomial s^4 + 2*a^2*s^2 + a^4 + a over its base field sage: K Number Field in a with defining polynomial t^6 - 2*t^3 - 1

I think this technique could be used to sort out #252. But there are many details to be got right.

### comment:3 Changed 11 years ago by

Replying to fwclarke:

Thanks! That is very helpful. It is not the whole story, I'm afraid, since I am working in a tower of extensions and the call pari(f) seems to fail if f does not have rational coefficients. Still, it gets things off the ground and gives me a hint about where to look for the rest of the answer.

### comment:4 Changed 10 years ago by

Description: | modified (diff) |
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Status: | new → needs_review |

### comment:5 Changed 10 years ago by

Status: | needs_review → positive_review |
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### comment:6 Changed 10 years ago by

Milestone: | sage-5.10 → sage-duplicate/invalid/wontfix |
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### comment:7 Changed 10 years ago by

Resolution: | → duplicate |
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Reviewers: | → Marco Streng |

Status: | positive_review → closed |

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I see now that this is just another example of NumberField? not working with polynomials that are not monic or not integral, which goes back 5 years to #252. So feel free to close the ticket. Unfortunately I don't see any way to work around it in my project. Too bad.