Part 1: polygon inequality for random real tensors (mu = smaller eigenvalue of M_i M_i^T)
  n=3 samples=20000  max_i (mu_i - sum_{j!=i} mu_j) = 1.110e-16   max polygon defect of f(d) at t=1 = 3.331e-16
  n=4 samples=20000  max_i (mu_i - sum_{j!=i} mu_j) = 1.110e-16   max polygon defect of f(d) at t=1 = 1.110e-16
  n=5 samples=20000  max_i (mu_i - sum_{j!=i} mu_j) = 1.110e-16   max polygon defect of f(d) at t=1 = 5.551e-17
  n=6 samples=4000  max_i (mu_i - sum_{j!=i} mu_j) = 3.469e-18   max polygon defect of f(d) at t=1 = 0.000e+00
  n=7 samples=4000  max_i (mu_i - sum_{j!=i} mu_j) = -3.428e-06   max polygon defect of f(d) at t=1 = -9.563e-07

Part 2: explicit real tensors (nonnegative, supported on even-weight strings) attaining P_n
  n=2: 60 random rational lambda in P_n realised exactly; float |det(MM^T) - lambda(1-lambda)| max = 1.11e-16
  n=3: 60 random rational lambda in P_n realised exactly; float |det(MM^T) - lambda(1-lambda)| max = 1.39e-16
  n=4: 60 random rational lambda in P_n realised exactly; float |det(MM^T) - lambda(1-lambda)| max = 1.11e-16
  n=5: 60 random rational lambda in P_n realised exactly; float |det(MM^T) - lambda(1-lambda)| max = 1.67e-16
  n=6: 60 random rational lambda in P_n realised exactly; float |det(MM^T) - lambda(1-lambda)| max = 1.94e-16
  n=7: 20 random rational lambda in P_n realised exactly; float |det(MM^T) - lambda(1-lambda)| max = 1.11e-16
  n=8: 20 random rational lambda in P_n realised exactly; float |det(MM^T) - lambda(1-lambda)| max = 1.39e-16

Example: lambda = ['1/10', '1/10', '1/10', '3/10']  weights: {(0, 3): '1/5', (1, 3): '1/5', (2, 3): '1/5'}
  p(x) on even-weight strings: {'0000': '7/10', '0011': '1/10', '0101': '1/10', '1001': '1/10'}
  Gram determinants d = lambda(1-lambda) = ['9/100', '9/100', '9/100', '21/100']
ALL CHECKS PASSED
