#19112: Add a function "isometry" to the quadratic forms package.
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Reporter: tgaona | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.10
Component: quadratic forms | Resolution:
Keywords: isometry | Merged in:
Authors: Tyler Gaona | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/tgaona/ticket/19112 | 582ae4500eb3652446c6f829310298953f8dbd02
Dependencies: | Stopgaps:
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Comment (by jdemeyer):
Replying to [comment:31 tgaona]:
> This block finds a pair of vectors `v` and `w` such that `Q(v) == F(v)`.
These vectors will represent a linear combination of the vectors in the
basis for each quadratic form. It's necessary that modifying the bases to
include these vectors not produce a basis whose matrix is singular. So
essentially this loop just looks for a pair of vectors satsifying these
properties. It starts with `v = [1, 0, 0]` (for a 3-dimensional form) and
finds `w` by calling `F.solve(Q(v))`. If this pair doesn't work, it finds
a new `v` and starts over. I get new `v`'s by incrementing each term in
the vector so the first few vectors that are generated are: `[1, 0, 0],
[1, 1, 0], [1, 1, 1], [2, 1, 1]...`
Sorry, I still don't understand the algorithm. You really need more
comments ''in the code''.
My feeling is that the current algorithm is too complicated (I don't think
you need to loop for `v`), but I cannot really say how to improve it since
I don't understand it.
--
Ticket URL: <http://trac.sagemath.org/ticket/19112#comment:34>
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