#13189: fan isomorphism check
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.2
Component: algebraic geometry | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Volker Braun
Merged in: | Dependencies:
Stopgaps: |
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This patch implements testing for isomorphism (equivalence up to
`GL(n,ZZ)` rotation) of fans
{{{
sage: m1 = matrix([(1, 0), (0, -5), (-3, 4)])
sage: m2 = matrix([(3, 0), (1, 0), (-2, 1)])
sage: m1.elementary_divisors() == m2.elementary_divisors() == [1,1,0]
True
sage: fan1 = Fan([Cone([m1*vector([23, 14]), m1*vector([ 3,100])]),
... Cone([m1*vector([-1,-14]), m1*vector([-100, -5])])])
sage: fan2 = Fan([Cone([m2*vector([23, 14]), m2*vector([ 3,100])]),
... Cone([m2*vector([-1,-14]), m2*vector([-100, -5])])])
sage: fan1.is_isomorphic(fan2)
True
sage: fan1.isomorphism(fan2)
Fan morphism defined by the matrix
[18 1 -5]
[ 4 0 -1]
[ 5 0 -1]
Domain fan: Rational polyhedral fan in 3-d lattice N
Codomain fan: Rational polyhedral fan in 3-d lattice N
}}}
This is implemented by first computing the isomorphisms of auxiliary
labelled graphs, and then trying to lift those to actual fan morphisms.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13189>
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