1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
|
setRandomSeed 0;
needsPackage "MonodromySolver"
needs "cyclic.m2"
runNaiveDynamicMonodromy = polys -> (
(p0,x0) := createSeedPair polySystem polys;
targetSystem := x0#SolutionSystem;
MV := computeMixedVolume (ideal(targetSystem))_*;
nextP := ((p0)->point {apply(#coordinates p0, i->exp(2*pi*ii*random RR))});
sols := pointArray {x0};
PathTrackCount := 0;
<< "Mixed volume: " << MV << endl;
while length sols < MV do (
petalSystem := polySystem specializeSystem (nextP(p0),polys);
PathTrackCount = PathTrackCount + length sols;
sols1 := select(track(
targetSystem,
petalSystem,
points sols,
NumericalAlgebraicGeometry$gamma=>random CC),
s->status s==Regular);
PathTrackCount = PathTrackCount + length sols1;
newSols := select(track(
petalSystem,
targetSystem,
sols1,
NumericalAlgebraicGeometry$gamma=>random CC),
s->status s==Regular);
for sol in newSols do (
if not member(sol,sols) then (
appendPoint(sols,sol);
);
);
<< "#sols: " << length sols << endl;
);
if length sols > MV then (
print "FAILED!!!";
infinity
) else (
<< "#Path tracks: " << PathTrackCount << endl;
PathTrackCount
)
)
end
restart
needs "naive-dynamic.m2"
L = for i to 10 list
runNaiveDynamicMonodromy parametrizedCyclic 7
sum L / 10. -- 7486
restart
load "naive-dynamic.m2"
elapsedTime runNaiveDynamicMonodromy parametrizedCyclic 10
restart
load "naive-dynamic.m2"
elapsedTime runNaiveDynamicMonodromy parametrizedCyclic 11
restart
load "naive-dynamic.m2"
load "large-examples/noon10.m2"
elapsedTime runNaiveDynamicMonodromy parametrizedNoon 10
-- #Path tracks: 495692
-- 7651.17 seconds elapsed
|
