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needsPackage "MonodromySolver"
-- copied from ExampleIdeals.m2
cyclicRoots = (n,kk) -> (
R := kk[vars(0..n-1)];
ideal apply(1..n-1, d-> sum(0..n-1, i -> product(d, k -> R_((i+k)%n))))
+ ideal(product gens R - 1))
parametrizedCyclic = n -> (
S := gens cyclicRoots(n,CC);
R := ring S;
polys := flatten entries S;
ind := flatten apply(#polys,i-> -- indices for parameters
apply(exponents polys#i, t->(i,t))
);
AR := CC[apply(ind,i->A_i)][gens R];
polysP := for i to #polys-1 list -- system with parameteric coefficients and same support
sum(exponents polys#i, t->A_(i,t)*AR_(t));
polySystem transpose matrix {polysP}
);
end
--------------------------------------------------------------
-- push F11 starting on the line below
restart
load "cyclic.m2"
polys = parametrizedCyclic 7;
-* each case is a quadruple (
type of graph,
#nodes,
#edges,
"edge selection strategy" => "potential" -- "potential" = null if potential is not used
)
*-
setRandomSeed 0
testTriples = {
(completeGraphInit, 2, 3),
(completeGraphInit, 2, 4),
(completeGraphInit, 2, 5),
(completeGraphInit, 3, 2),
(completeGraphInit, 4, 1),
(completeGraphInit, 5, 1),
(flowerGraphInit, 3, 2), -- two petals
(flowerGraphInit, 4, 2),
(flowerGraphInit, 5, 2),
(flowerGraphInit, 3, 3),
(flowerGraphInit, 4, 3)
}
testOptions = {
selectRandomEdgeAndDirection => null,
selectBestEdgeAndDirection => potentialLowerBound,
selectBestEdgeAndDirection => potentialE
}
(p0,x0) = createSeedPair polySystem polys;
mixedVolume = computeMixedVolume specializeSystem (p0,polys)
numSeeds = 10
file = openOut (currentFileDirectory | "cyclic-7" | ".output")
file << "\\begin{array}{|c||" << concatenate(#testTriples:"c|") << "} " << endl;
for opt in testOptions do (
file << opt;
for triple in testTriples do (
(init,nnodes,nedges) := triple;
pairs := apply(numSeeds, seed -> (
setRandomSeed seed;
(p0,x0) := createSeedPair polySystem polys;
(node,numPaths) := monodromySolve(polys,p0,{x0},
GraphInitFunction=>init,
NumberOfNodes=>nnodes,
NumberOfEdges=>nedges,
SelectEdgeAndDirection=>first opt,
Potential=>last opt,
TargetSolutionCount=>mixedVolume);
(length node.PartialSols == mixedVolume, numPaths)
));
success := select(pairs,p->first p);
if #success > 0 then
(file << " & " << 100.*#success/#pairs << "%" << ",\\ " << toRR sum(success,p->last p)/#success) else
(file << " & " << 100.*#success/#pairs << "%" << ",\\ - ")
);
file << "\\\\" << endl;
)
file << "\\end{array}" << endl;
close file
end
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