Opened 11 years ago

Closed 9 years ago

## #11276 closed defect (duplicate)

# bug in documentation for non_surjective for Galois representations attached to elliptic curves

Reported by: | David Pathakjee | Owned by: | John Cremona |
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Priority: | minor | Milestone: | sage-duplicate/invalid/wontfix |

Component: | elliptic curves | Keywords: | galois representation, elliptic curves, non_surjective, documentation |

Cc: | William Stein | Merged in: | |

Authors: | Reviewers: | Chris Wuthrich | |

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

non_surjective() docstring incorrectly states that it's inconclusive and often wrong for p=2. The function it calls, is_surjective, is correct for p=2.

The docstring states that "[the] list of primes p such that the mod-p representation *might* not be surjective... usually contains 2, because of shortcomings of the algorithm..." However, non_surjective calls is_surjective, which should always be correct for p=2,3 because it computes the Galois group of the 2-division polynomial. (More precisely, its helper, _is_surjective, does this.) I suspect this caveat may have been written before the special cases for p=2,3 in _is_surjective had been written.

All that really needs to be done is to remove the phrase "(this list usually contains 2, because of shortcomings of the algorithm)" from the docstring.

### Change History (5)

### comment:1 Changed 9 years ago by

Description: | modified (diff) |
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### comment:2 Changed 9 years ago by

Milestone: | sage-5.11 → sage-5.12 |
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### comment:3 Changed 9 years ago by

Milestone: | sage-6.1 → sage-duplicate/invalid/wontfix |
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Status: | new → needs_review |

### comment:4 Changed 9 years ago by

Reviewers: | → Chris Wuthrich |
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Status: | needs_review → positive_review |

### comment:5 Changed 9 years ago by

Resolution: | → duplicate |
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Status: | positive_review → closed |

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This is a duplicate (well, striclty speaking a sub-ticket) of #11271. This should be closed.