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Add Ideal.radical and Ring.nilradical #39549

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@user202729 user202729 commented Feb 20, 2025

More category-generic methods.

📝 Checklist

  • The title is concise and informative.
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⌛ Dependencies

sage: ZZ.ideal(12).radical()
Principal ideal (6) of Integer Ring
"""
return self.ring().ideal(self.gen().radical())
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(for context, this is for Ideal_pid.)

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github-actions bot commented Feb 20, 2025

Documentation preview for this PR (built with commit 626f7c9; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

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LGTM. For a followup PR, the Zmod should have a defining_ideal() method since they are supposed to be treated as quotient rings...I don't really like the hack in _lift() (but it is was already there before).

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user202729 commented Feb 21, 2025

Wait a minute, won't return self.zero_ideal() ignore the ideal_class= keyword argument?

Edit: reverted that change (method to be simplified in some future pull request), please review again.

The follow-up pull request is at #39559 (plus some simplification, but might be too short for your preference)

@user202729 user202729 marked this pull request as draft February 21, 2025 09:42
@user202729 user202729 marked this pull request as ready for review February 21, 2025 09:45
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