dyna3/engine-proto/gram-test/gram-test.sage

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2024-02-21 03:35:24 +00:00
F = QQ['a', 'b', 'c'].fraction_field()
a, b, c = F.gens()
# three mutually tangent spheres which are all perpendicular to the x, y plane
gram = matrix([
[-1, 0, 0, 0, 0],
[0, -1, a, b, c],
[0, a, -1, 1, 1],
[0, b, 1, -1, 1],
[0, c, 1, 1, -1]
])
P, L, U = gram.LU()
solution = (P * L).transpose()
mform = U * L.transpose().inverse()
concrete = solution.subs({a: 0, b: 1, c: -3/4})
std_basis = matrix([
[0, 0, 0, 1, 1],
[0, 0, 0, 1, -1],
[1, 0, 0, 0, 0],
[0, 1, 0, 0, 0],
[0, 0, 1, 0, 0]
])
std_solution = std_basis * solution
std_concrete = std_basis * concrete