#7522: Implement orthogonal complement in vector spaces
-------------------------------------------------+--------------------------
Reporter: kcrisman | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: linear algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: Karl-Dieter
Crisman
Authors: Jason Grout, Travis Scrimshaw | Merged in:
Dependencies: | Stopgaps:
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Changes (by tscrim):
* status: needs_work => needs_review
Comment:
First, if the ring is not a PID, there are many attributes that are not
there anymore (ex. `span()`), so getting the attribute error is consistent
with the rest of free modules.
As for them being inner product spaces, we have this in sage:
{{{
sage: F = FreeModule(Integers(8), 3)
sage: v = F([1, 2, 3])
sage: v*v
6
sage: F.inner_product_matrix()
[1 0 0]
[0 1 0]
[0 0 1]
}}}
so I think sage always assumes it has an inner product (although not
necessarily a nice inner product).
For the
{{{
Vector space of degree 3 and dimension 2 over Integer Ring
}}}
that was a doctest error coming from me thinking I know what the output
should be >_<.
Anyways, new version of the patch with the method now called
`complement()` and only for vector spaces.
For patchbot:
Apply: trac_7522-perp-ts.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7522#comment:14>
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