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Renamed vector subspace complement to othrogonal_complement and changed the complement function #39659

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Fixes #31487. Added the change suggested by @DaveWitteMorris found in the comments of #31487. Changes the behavior of the complement function of vector subspaces. Instead of returning the orthogonal complement (which was the original behavior) it instead returns a subspace such that the direct sum of the two subspaces is the vector space itself. I haven't fully changes the behavior however. It still gives a deprecation message and returns the orthogonal complement unless orthogonal=False. If orthogonal=True then it does not print the deprecation message. I've also moved the original code for the orthogonal complement to it's own function named orthogonal_complement.

Things that may still be needed: More/Better examples in the complement function. In orthogonal_complement I replaced everywhere it said "complement" with "orthogonal complement". In the last example that change might not be appropriate but I am unsure. A post in the sage forums to debate if this change should be made and if the function name orthogonal_complement makes sense.

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  • The title is concise and informative.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
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Noel-Roemmele commented Mar 10, 2025

I also have yet to change tests that rely on the complement function to not include the deprecation message. That seems to be why some of the tests are failing.

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Documentation preview for this PR (built with commit 28d70e3; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

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Vector space complement over GF(2) gives incorrect result
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