def assertReductionWorks(t, filename): M = import_matrix_from_file(filename) x, eps = SR.var("x eps") t.assertIn(x, M.variables()) M_pranks = singularities(M, x).values() t.assertNotEqual(M_pranks, [0] * len(M_pranks)) #1 Fuchsify m, t1 = simplify_by_factorization(M, x) Mf, t2 = fuchsify(m, x) Tf = t1 * t2 t.assertTrue((Mf - transform(M, x, Tf)).simplify_rational().is_zero()) Mf_pranks = singularities(Mf, x).values() t.assertEqual(Mf_pranks, [0] * len(Mf_pranks)) #2 Normalize t.assertFalse(is_normalized(Mf, x, eps)) m, t1 = simplify_by_factorization(Mf, x) Mn, t2 = normalize(m, x, eps) Tn = t1 * t2 t.assertTrue((Mn - transform(Mf, x, Tn)).simplify_rational().is_zero()) t.assertTrue(is_normalized(Mn, x, eps)) #3 Factorize t.assertIn(eps, Mn.variables()) m, t1 = simplify_by_factorization(Mn, x) Mc, t2 = factorize(m, x, eps, seed=3) Tc = t1 * t2 t.assertTrue((Mc - transform(Mn, x, Tc)).simplify_rational().is_zero()) t.assertNotIn(eps, (Mc / eps).simplify_rational().variables())
def test_normalize_4(t): # Test with non-zero normalized eigenvalues x, e = SR.var("x eps") M = matrix([[1 / x / 2, 0], [0, 0]]) with t.assertRaises(FuchsiaError): N, T = normalize(M, x, e)
def test_normalize_3(t): # Test with non-zero normalized eigenvalues x = SR.var("x") e = SR.var("epsilon") M = matrix([[(1 - e) / x, 0], [0, (1 + e) / 3 / x]]) with t.assertRaises(FuchsiaError): N, T = normalize(M, x, e)
def test_normalize_5(t): # An unnormalizable example by A. A. Bolibrukh x, e = SR.var("x eps") b = import_matrix_from_file("test/data/bolibrukh.mtx") f, ft = fuchsify(b, x) f_pranks = singularities(f, x).values() t.assertEqual(f_pranks, [0] * len(f_pranks)) with t.assertRaises(FuchsiaError): n, nt = normalize(f, x, e)
def test_normalize_1(t): # Test with apparent singularities at 0 and oo, but not at 1. x = SR.var("x") M = matrix([[1 / x, 5 / (x - 1), 0, 6 / (x - 1)], [0, 2 / x, 0, 0], [0, 0, 3 / x, 7 / (x - 1)], [6 / (x - 1), 0, 0, 1 / x]]) N, T = normalize(M, x, SR.var("epsilon")) N = N.simplify_rational() t.assertEqual(N, transform(M, x, T).simplify_rational()) for point, prank in singularities(N, x).iteritems(): R = matrix_c0(N, x, point, prank) evlist = R.eigenvalues() t.assertEqual(evlist, [0] * len(evlist))
def test_pap_3_52_slow(t): x, eps = SR.var("x eps") M = import_matrix_from_file("test/data/pap_3_52.mtx") N, T = normalize(M, x, eps) N = N.simplify_rational() t.assertEqual(N, transform(M, x, T).simplify_rational())