id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
23207,Exterior powers of free modules of finite rank,egourgoulhon,,"This ticket implements the exterior power /\^''p''^(''M'') for a free module of finite rank ''M'' (''p'' being a positive integer), i.e. the set of alternating contravariant tensors of type (''p'',0) on ''M''. Previously only the exterior power of the ''dual'' of ''M'', i.e. /\^''p''^(''M*''), was implemented, as the parent of alternating forms of degree ''p''. More specifically, the ticket introduces two new classes:
- the parent class `ExtPowerFreeModule` for /\^''p''^(''M'')
- the element class `AlternatingContrTensor` for elements of /\^''p''^(''M'')
Note that the pre-existing class for /\^''p''^(''M*''), which was called `ExtPowerFreeModule`, has been renamed `ExtPowerDualFreeModule`, since it regards the exterior power of the dual of ''M''.
The class for the elements of ''M'', `FiniteRankFreeModuleElement` , inherits from the new class `AlternatingContrTensor`, reflecting the fact that /\^1^(''M'') = ''M''. In particular, this allows one to consider module elements in operations like the exterior product or the interior product. For instance, for ''a'' and ''b'' in ''M'', `a.wedge(b)` returns now the element ''a''/\''b'' of /\^2^(''M'').
In addition, the ticket implements the interior products
- /\^''p''^(''M'') x /\^''q''^(''M*'') --> /\^''q-p''^(''M*'')
- /\^''p''^(''M*'') x /\^''q''^(''M'') --> /\^''q-p''^(''M'')
for ''p''<=''q'' via the method `interior_product` in classes `AlternatingContrTensor` and `FreeModuleAltForm`.
Besides, some slight updates in all source files in `src/sage/tensor/modules` have been performed:
- for the migration to Python3, a few `range(...)` have been changed to `list(range(...))` in places where a list is expected instead of an iterator
- bibliographic references have been reformated to provide links to the master bibliography file `src/doc/en/reference/references/index.rst`.",enhancement,closed,major,sage-8.1,linear algebra,fixed,free module exterior power,tscrim bpym,,Eric Gourgoulhon,Travis Scrimshaw,N/A,,b7970097c1aeb7f2960ff30ccec9e70627e50bb2,b7970097c1aeb7f2960ff30ccec9e70627e50bb2,,