Fix preimage computation for field homomorphisms - #6535
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PreImagesElm for field homomorphisms compared IsInjective with 1, a GAP3 leftover: the injective branch was dead, so every nonzero element got the empty preimage, even under bijective maps such as Frobenius automorphisms. With that branch reachable, PreImagesElm needs PreImagesRepresentative, which had no applicable method for Frobenius automorphisms. Add one that delegates to ImagesRepresentative of the inverse; the inverse of a Frobenius automorphism is again one (or the identity), so this cannot recurse. Note for #6409 (renames these operations to NC variants): the fixed comparison then belongs in PreImagesElmNC, and the new method in fieldfin.gi should be installed on PreImagesRepresentativeNC. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
fingolfin
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kind: bug
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## master #6535 +/- ##
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- Coverage 79.02% 79.00% -0.03%
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Files 685 685
Lines 294329 294334 +5
Branches 8647 8670 +23
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- Hits 232601 232530 -71
- Misses 59922 59996 +74
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ThomasBreuer
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Aug 28, 2026
ThomasBreuer
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Good spot.
Apparently these field homomorphisms have never been used seriously.
(The automorphisms of abelian number fields have their own methods.)
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PreImagesElm for field homomorphisms compared IsInjective with 1, a GAP3 leftover: the injective branch was dead, so every nonzero element got the empty preimage, even under bijective maps such as Frobenius automorphisms.
With that branch reachable, PreImagesElm needs PreImagesRepresentative, which had no applicable method for Frobenius automorphisms. Add one that delegates to ImagesRepresentative of the inverse; the inverse of a Frobenius automorphism is again one (or the identity), so this cannot recurse.
Note for #6409 (renames these operations to NC variants): the fixed comparison then belongs in PreImagesElmNC, and the new method in fieldfin.gi should be installed on PreImagesRepresentativeNC.
Co-Authored-By: Claude Fable 5 noreply@anthropic.com
Found while having Claude Fable 5 look into improving PR #6409 (CC @cdwensley); those updates will be pushed soon.