27 lines
603 B
Python
27 lines
603 B
Python
F = QQ['a', 'b', 'c'].fraction_field()
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a, b, c = F.gens()
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# three mutually tangent spheres which are all perpendicular to the x, y plane
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gram = matrix([
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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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P, L, U = gram.LU()
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solution = (P * L).transpose()
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mform = U * L.transpose().inverse()
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concrete = solution.subs({a: 0, b: 1, c: -3/4})
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std_basis = matrix([
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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 = std_basis * solution
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std_concrete = std_basis * concrete |