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mention category in documentation
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yyyyx4 committed Feb 14, 2022
1 parent a8a2ba2 commit a001b6d
Showing 1 changed file with 10 additions and 3 deletions.
13 changes: 10 additions & 3 deletions src/sage/modules/free_module.py
Original file line number Diff line number Diff line change
Expand Up @@ -80,6 +80,12 @@
(2, 0, 0), (-2, 0, 0), (0, 2, 0), (0, -2, 0), (0, 0, 2), (0, 0, -2),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1), (1, 1, -1), ...]
For other infinite enumerated base rings (i.e., rings which
are objects of the category :class:`InfiniteEnumeratedSets`),
a free module of rank `r` is enumerated by applying
:meth:`FreeModule_ambient.linear_combination_of_basis`
to all vectors in `\ZZ^r`, enumerated in the way shown above.
TESTS:
We intersect a zero-dimensional vector space with a
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sage: [x for x in W]
[(0, 0), (a, a), (a + 1, a + 1), (1, 1)]
Free modules over (some) infinite rings iterate over module elements
ordered by (primarily) the 1-norm and (secondarily) the `\infty`-norm
of their coordinate vectors::
Free modules over enumerated infinite rings (i.e., those in the
category :class:`InfiniteEnumeratedSets`) iterate over module
elements ordered by (primarily) the 1-norm and (secondarily) the
`\infty`-norm of their coordinate vectors::
sage: it = iter(ZZ^3)
sage: vs = [next(it) for _ in range(1000)]
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