38 lines
852 B
Julia
38 lines
852 B
Julia
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using LinearAlgebra
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using AbstractAlgebra
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function printgood(msg)
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printstyled("✓", color = :green)
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println(" ", msg)
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end
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function printbad(msg)
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printstyled("✗", color = :red)
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println(" ", msg)
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end
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F, gens = rational_function_field(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
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x = gens[1]
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t = gens[2:4]
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# three mutually tangent spheres which are all perpendicular to the x, y plane
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M = matrix_space(F, 7, 7)
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gram = M(F[
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1 -1 -1 -1 -1 t[1] t[2];
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-1 1 -1 -1 -1 x t[3]
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-1 -1 1 -1 -1 -1 -1;
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-1 -1 -1 1 -1 -1 -1;
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-1 -1 -1 -1 1 -1 -1;
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t[1] x -1 -1 -1 1 -1;
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t[2] t[3] -1 -1 -1 -1 1
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])
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r, p, L, U = lu(gram)
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if isone(p)
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printgood("Found a solution")
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else
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printbad("Didn't find a solution")
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end
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solution = transpose(L)
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mform = U * inv(solution)
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