#19595: Implement a check that a hyperplane arrangement is free
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.1
Component: geometry | Resolution:
Keywords: free, hyperplane | Merged in:
arrangement | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | dda0ab3d40972798cf18394d91eabf56418f36e5
public/hyperplanes/check_free-19595| Stopgaps:
Dependencies: |
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Comment (by mmarco):
There is a singular command called mstd, that produces a minimal set of
generators of an ideal of module. Try something like:
{{{
sage: H.<x,y,z> = HyperplaneArrangements(QQ)
sage: A = H( x-z, y-z, x+y, x+z, y+z, x, y, z)
sage: f = A.defining_polynomial()
sage: I = f + f.jacobian_ideal()
sage: IS = I._singular_()
sage: ISS = IS.syz()
sage: MSTD = ISS.mstd()
sage: M = MSTD[2]._sage_().transpose().submatrix(0,1)
sage: M
[ x y
z]
[ 0 x^2*y - y^3
x^2*z - z^3]
[ 0 x*y^3 + y^4 - x*y*z^2 - y^2*z^2
0]
sage: M.determinant()/f
-1
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/19595#comment:24>
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