#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-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 | 9e211fecd4b525ad30276d37d442a68ce9bec8f0
Dependencies: #18669 | Stopgaps:
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Comment (by jdemeyer):
About solving quadratic forms:
Suppose you want to solve `Q(x) = c`. Consider the quadratic form `Q(x) -
c*z^2 = 0`, where `z` is an extra variable. Find a solution `(x,z)` to
this quadratic form using `qfsolve()`.
'''Case 1''': If `z != 0`, then `Q(x/z) = c`.
'''Case 2''': We found a solution `Q(x) = 0`. Let `e` be any vector such
that `B(x,e) != 0`, where `B` is the bilinear form corresponding to `Q`.
To find `e`, just try all unit vectors `(0,..0,1,0...0)`. Let `a = (c -
Q(e))/B(x,e)` and let `y = e + a*x`. Then `Q(y) = c`.
It would be great if you could implement this on a separate ticket.
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Ticket URL: <http://trac.sagemath.org/ticket/19112#comment:12>
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