#19112: Add a function "isometry" to the quadratic forms package.
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Reporter: tgaona | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-7.1
Component: quadratic forms | Resolution:
Keywords: isometry | Merged in:
Authors: Tyler Gaona | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/tgaona/ticket/19112 | 642df1071e10e3a771abd7d02ceff017c0a3ef30
Dependencies: | Stopgaps:
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Comment (by annahaensch):
I understand the algorithm, I don't think it's so complicated. It just
looks for a vector w in W of length corresponding to, V[0][0], the upper
left most entry in V. Then it simply extends the basis of W to contain w,
preforms Gram Schmidt (fixing w), and then picks off <Q(w)> as an
orthogonal component of W and <V[0][0]> as an orthogonal component of V.
I feel satisfied the the algorithm does what it claims to do, and that it
is mathematically correct.
A few notes on the documentation:
1. In your documentation for {{{_diagonal_isometry()}}} you call the
function {{{isometry()}}} (of course it works out to be the same thing
here, since the forms are diagonal to begin with.
2. Your documentation for {{{_gram_schmidt()}}} is a bit misleading, since
it looks like you are treating the columns of a Gram matrix as a set of
vectors to be orthogonalized, rather, do the process on some sort of
(preferably basis) matrix.
In response to comment 45, I'm also not sure why v=parilist[i] got added.
Is there a reason you're touching {{{short_vector_list_up_to_length()}}}?
I think something may have happened on the merge.
--
Ticket URL: <http://trac.sagemath.org/ticket/19112#comment:47>
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