engine-proto/gram-test/gram-test.jl

@@ -1,77 +0,0 @@
-using LinearAlgebra
-using AbstractAlgebra
-
-function printgood(msg)
-  printstyled("✓", color = :green)
-  println(" ", msg)
-end
-
-function printbad(msg)
-  printstyled("✗", color = :red)
-  println(" ", msg)
-end
-
-F, gens = rational_function_field(Generic.Rationals{BigInt}(), ["a₁", "a₂", "b₁", "b₂", "c₁", "c₂"])
-a = gens[1:2]
-b = gens[3:4]
-c = gens[5:6]
-
-# three mutually tangent spheres which are all perpendicular to the x, y plane
-gram = [
-  -1  1  1;
-   1 -1  1;
-   1  1 -1
-]
-
-eig = eigen(gram)
-n_pos = count(eig.values .> 0.5)
-n_neg = count(eig.values .< -0.5)
-if n_pos + n_neg == size(gram, 1)
-  printgood("Non-degenerate subspace")
-else
-  printbad("Degenerate subspace")
-end
-sig_rem = Int64[ones(2-n_pos); -ones(3-n_neg)]
-unk = hcat(a, b, c)
-M = matrix_space(F, 5, 5)
-big_gram = M(F.([
-  diagm(sig_rem) unk;
-  transpose(unk) gram
-]))
-
-r, p, L, U = lu(big_gram)
-if isone(p)
-  printgood("Found a solution")
-else
-  printbad("Didn't find a solution")
-end
-solution = transpose(L)
-mform = U * inv(solution)
-
-vals = [0, 0, 0, 1, 0, -3//4]
-solution_ex = [evaluate(entry, vals) for entry in solution]
-mform_ex = [evaluate(entry, vals) for entry in mform]
-
-std_basis = [
-  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 = M(F.(std_basis)) * solution
-std_solution_ex = std_basis * solution_ex
-
-println("Minkowski form:")
-display(mform_ex)
-
-big_gram_recovered = transpose(solution_ex) * mform_ex * solution_ex
-valid = all(iszero.(
-  [evaluate(entry, vals) for entry in big_gram] - big_gram_recovered
-))
-if valid
-  printgood("Recovered Gram matrix:")
-else
-  printbad("Didn't recover Gram matrix. Instead, got:")
-end
-display(big_gram_recovered)

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

@@ -1,27 +0,0 @@
-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