#15392: Implement minimal model algorithm
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Reporter: bhutz | Owner: bhutz
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: algebraic geometry | Resolution:
Keywords: sage-days55 | Merged in:
Authors: bhutz | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Looks good to me. Some very small points:
The fact that
{{{
sage: phi.minimal_model().resultant()
}}}
doesn't work seems a little strange. Shouldn't it be
`return_conjugation=False` by default? Also wouldn't
`return_transformation` be a better name? Certainly in the doctest:
{{{
sage: f.minimal_model(False)
}}}
should refer to the keyword argument by keyword. A "positional" false is
rather unclear here, even though it works.
Finally (and this is for another ticket): If we're "minimizing" rational
transformations, shouldn't we also be "reducing" them, i.e., compute an
SL(2,Z) transformation that makes the coefficients small? The most simple
approach would be to "reduce" the binary form describing the fixed points
or (if that's too degenerate) the points of period n for some small n.
See [Stoll, Michael; Cremona, John E., On the reduction theory of binary
forms. J. Reine Angew. Math. 565 (2003), 79–99.], which is fairly easy to
implement and which would be useful to have in sage anyway.
--
Ticket URL: <http://trac.sagemath.org/ticket/15392#comment:14>
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