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20 lines
554 B
Julia
20 lines
554 B
Julia
1 year ago
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module Homogenize
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using TypedPolynomials
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export homogenize, homogenized_start_system
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function homogenize(F)
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@polyvar h
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return [sum([h^(maxdegree(p)-maxdegree(t))*t for t in p.terms]) for p in F]
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end
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function homogenized_start_system(F)
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degrees = [maxdegree(p) for p in F]
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@polyvar h
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G = [x_i^d - h^d for (d, x_i) in zip(degrees, variables(F))]
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r = [[exp(2im*pi/d)^k for k=0:d-1] for d in degrees]
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roots = vec([vcat(collect(root), 1) for root in collect(Iterators.product(r...))])
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return (G, roots)
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end
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end
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