#11319 closed defect (fixed)
Cannot create homomorphism from prime residue field to finite field
Reported by: | johanbosman | Owned by: | robertwb |
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Priority: | major | Milestone: | sage-4.8 |
Component: | coercion | Keywords: | residue fields, finite fields, hom, sd35 |
Cc: | Merged in: | sage-4.8.alpha6 | |
Authors: | Johan Bosman | Reviewers: | Kiran Kedlaya, Michiel Kosters |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Consider K = QQ(sqrt(337)). The prime 5 is inert in K and the prime 13 splits. We'll start with 13 to see what goes wrong:
sage: K.<w> = QuadraticField(337) sage: pp = K.ideal(13).factor()[0][0] sage: RF13 = K.residue_field(pp) sage: RF13.gens() (1,) sage: RF13.hom([GF(13)(1)]) ... TypeError: images do not define a valid homomorphism
However, for residue fields that aren't prime fields it does work:
sage: RF5 = K.residue_field(5) sage: F25 = GF(25, names='a', modulus=RF5.polynomial()) sage: RF5.hom([F25.0]) Ring morphism: From: Residue field in wbar of Fractional ideal (5) To: Finite Field in a of size 5^2 Defn: wbar |--> a
Btw, this is in sage 4.6.2. on Mac OS 10.6.7.
Attachments (2)
Change History (12)
comment:1 Changed 10 years ago by
- Description modified (diff)
Changed 10 years ago by
comment:2 Changed 10 years ago by
- Status changed from new to needs_review
comment:3 Changed 10 years ago by
- Status changed from needs_review to needs_work
comment:4 Changed 10 years ago by
- Status changed from needs_work to needs_review
In your example, you're trying to send the generator of k to the element 1 of F, which does indeed not define a field homomorphism. This does work:
sage: root = k.polynomial().roots(F)[0][0] sage: k.hom([root]) Ring morphism: From: Residue field in abar of Fractional ideal (7) To: Finite Field in b of size 7^3 Defn: abar |--> 4*b^2 + 4*b + 2
comment:5 Changed 10 years ago by
- Reviewers set to Kiran Kedlaya
- Status changed from needs_review to positive_review
Looks fine, applies against 4.7, no long doctest failures.
comment:6 Changed 10 years ago by
- Status changed from positive_review to needs_work
- Work issues set to examples
I think the new patch is a bit low on examples. For example, the ticket mentions number fields, so why not add a number field example?
comment:7 Changed 10 years ago by
- Status changed from needs_work to needs_review
- Work issues examples deleted
Example added. ;)
comment:8 Changed 10 years ago by
- Reviewers changed from Kiran Kedlaya to Kiran Kedlaya, Michiel Kosters
- Status changed from needs_review to positive_review
comment:9 Changed 9 years ago by
- Merged in set to sage-4.8.alpha6
- Resolution set to fixed
- Status changed from positive_review to closed
comment:10 Changed 9 years ago by
- Keywords sd35 added
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I was trying out the patch, and the following example didn't work out like I expected:
Should this patch fix this as well?