Allow .maximal_order() of quaternion_algebra.py to extend a given order
#37675
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... and small refactoring of code
tscrim
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Apr 6, 2024
Caused by switched order of input arguments Amend: This time for real
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Credit to @tscrim for the help on how to do this!
tscrim
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Apr 18, 2024
- Corrected order of additional arguments - Fixed spacing for PEP8
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Apr 20, 2024
sagemathgh-37675: Allow `.maximal_order()` of `quaternion_algebra.py` to extend a given order 1. Added an optional argument `order_basis` to `.maximal_order()` to allow for extension of orders: If `order_basis` defines an order of the given quaternion algebra, then the method now returns a maximal order that contains the order specified by the given basis. ~~2. Added comparison functions `__le__`, `__ge__`, `__lt__` and `__gt__` for quaternion orders.~~ ~~3. Small edits of the comparison functions `__eq__` and `__ne__` for quaternion orders.~~ 2. Added a general comparison function `__richcmp__` for quaternion orders and removed the explicit implementation of `__eq__` and `__ne__`. More details on 1.: The algorithm used in `.maximal_order()` currently uses the standard basis `(1,i,j,k)` as a starting basis, but it extends to any starting basis whose first entry is equal to `1`. Using the helper method `basis_for_quaternion_lattice`, we transform any quaternion order basis input by the user to a basis of this form. Depends on sagemath#37644: Naturally, the extended algorithm can only work correctly if the base algorithm works correctly in the first place. URL: sagemath#37675 Reported by: Sebastian A. Spindler Reviewer(s): Sebastian A. Spindler, Travis Scrimshaw
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Feb 21, 2025
- Added missing tests for possible errors - Integrated `.ramified_places()` to check that new construction works correctly - Modified input checks to properly reject bad inputs - Added author entry for prior work on sagemath#37173, sagemath#37644 and sagemath#37675
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order_basisto.maximal_order()to allow for extension of orders: Iforder_basisdefines an order of the given quaternion algebra, then the method now returns a maximal order that contains the order specified by the given basis.2. Added comparison functions__le__,__ge__,__lt__and__gt__for quaternion orders.3. Small edits of the comparison functions__eq__and__ne__for quaternion orders.__richcmp__for quaternion orders and removed the explicit implementation of__eq__and__ne__.More details on 1.:
The algorithm used in
.maximal_order()currently uses the standard basis(1,i,j,k)as a starting basis, but it extends to any starting basis whose first entry is equal to1. Using the helper methodbasis_for_quaternion_lattice, we transform any quaternion order basis input by the user to a basis of this form.Depends on #37644: Naturally, the extended algorithm can only work correctly if the base algorithm works correctly in the first place.