30 lines
654 B
Julia
30 lines
654 B
Julia
using LinearAlgebra
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using AbstractAlgebra
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F, (a, b, c) = rational_function_field(Generic.Rationals{BigInt}(), ["a", "b", "c"])
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M = matrix_space(F, 5, 5)
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# three mutually tangent spheres which are all perpendicular to the x, y plane
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gram = M(F.([
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-1 0 0 0 0;
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0 -1 a b c;
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0 a -1 1 1;
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0 b 1 -1 1;
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0 c 1 1 -1;
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]))
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r, p, L, U = lu(gram)
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solution = transpose(p * L)
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mform = U * inv(transpose(L))
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concrete = [evaluate(entry, [0, 1, -3//4]) for entry in solution]
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std_basis = [
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0 0 0 1 1;
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0 0 0 1 -1;
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1 0 0 0 0;
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0 1 0 0 0;
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0 0 1 0 0
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]
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std_solution = M(F.(std_basis)) * solution
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std_concrete = std_basis * concrete |