#19112: Add a function "isometry" to the quadratic forms package.
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Reporter: tgaona | Owner:
Type: enhancement | Status: needs_info
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: | Stopgaps:
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Comment (by tgaona):
Hi Jeroen,
Sorry for the slow response. This method should be able to return
isometries for forms over fields, where I believe
is_globally_equivalent_to just works over the ring of integers. For
example:
{{{
sage: Q = DiagonalQuadraticForm(QQ, [1, 5])
sage: F = QuadraticForm(QQ, 2, [1, 12, 81])
sage: Q.is_globally_equivalent_to(F)
False
sage: Q.is_rationally_isometric(F)
True
sage: T = Q.isometry(F)
sage: T
[ 1 -2]
[ 0 1/3]
sage: Q.Gram_matrix() == T.transpose() * F.Gram_matrix() * T
True
}}}
So Q is equivalent to F over the rationals, but is_globally_equivalent_to
doesn't recognize this. This method was intended to complement the
is_rationally_isometric method, so perhaps it should be refactored to work
in a similar manner as is_globally_equivalent_to, i.e, adding an optional
flag to is_rationally_isometric to return the transition matrix for the
isometry.
--
Ticket URL: <http://trac.sagemath.org/ticket/19112#comment:4>
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