#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):
I'm just parking some test code here for my own use:
{{{
import urllib
Qx.<x>=QQ[]
def interpolate(c,n):
M=matrix([[c[i]^k for k in range(n+1)]+[-c[i+1]*c[i]^k for k in
range(n+1)] for i in range(len(c)-1)])
v=list(M.right_kernel().basis()[0])
return Qx(v[:n+1])/Qx(v[n+1:])
V=[eval(c) for c in
urllib.urlopen("http://www.cecm.sfu.ca/~nbruin/intorbits/deg2.txt";)]
P1.<X,Y>=ProjectiveSpace(QQ,1)
def proj_map(f):
phi=f(X/Y)
return End(P1)([phi.numerator(),phi.denominator()])
[proj_map(interpolate(c,2)((x+1)/(x-1))).is_minimal_model() for c in
V[:50]]
}}}
I'm noticing it's awfully slow! I think I tried a similar thing with the
magma version and that was quite quick. Initial impression is that this is
just a sage problem:
{{{
ncalls tottime percall cumtime percall filename:lineno(function)
110 0.033 0.000 0.073 0.001 minimal_model.py:41(bCheck)
1847/1843 0.026 0.000 0.031 0.000
polynomial_ring.py:299(_element_constructor_)
26/22 0.022 0.001 0.062 0.003 minimal_model.py:122(blift)
264 0.015 0.000 0.020 0.000 {method 'subs' of
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'
objects}
2097 0.011 0.000 0.015 0.000 {method 'sub' of
'_sre.SRE_Pattern' objects}
943 0.010 0.000 0.033 0.000
polynomial_ring_constructor.py:60(PolynomialRing)
3 0.008 0.003 0.169 0.056 minimal_model.py:302(Min)
19104 0.006 0.000 0.006 0.000 {isinstance}
2157 0.004 0.000 0.005 0.000 re.py:226(_compile)
}}}
so it looks like just constructing the polynomials is an expensive
proposition already. `bCheck` does take quite a bit of time by itself too,
so there may be some algorithmic issues too. Perhaps we don't care about
performance at this point?
(Ah, I see: there are lots of polynomial rings constructed *inside*
functions. That shouldn't happen)
Some possible packaging problems:
- I think the file name `sage/schemes/projective/minimal_model.py` will
cause problems later on: there are all kinds of projective schemes that
have their own concept of minimality, so I think it should be
`endP1_minimal_model` or something more appetizing.
- `phi.is_minimal_model` reads a little strange: `phi` is supposed to be
an endomorphism on a `P1` (with coordinate choice, i.e., with `0,1,infty`
marked), not a model of one. Would is_PGL_minimal be better (or perhaps
is_minimal)?
--
Ticket URL: <http://trac.sagemath.org/ticket/15392#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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