implement new .torsion_basis
method based on random sampling
#40035
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
This implements a new algorithm for computing
E.torsion_basis
whenE
is an elliptic curve. The method is very simple: sample points, check order, then check they're linearly independent by pairing.From my testing, the algorithm is always faster than the previous "abelian_group" algorithm, so I set the default to "random_sampling" instead.
By factoring out the algorithm code, we can add algorithms more easily in the future.
We should probably have a method/flag to return also generators of$E[n]$ even when it's not isomorphic to $(Z / nZ)^2$ ,