def assertIsReduced(t, m_path, x_name, eps_name):
M = fuchsia.import_matrix_from_file(m_path)
x = SR.var(x_name)
eps = SR.var(eps_name)
pranks = fuchsia.singularities(M, x).values()
t.assertEqual(pranks, [0]*len(pranks))
t.assertTrue(eps not in (M/eps).simplify_rational().variables())
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_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 assertReductionWorks(test, filename, fuchsian=False):
m = import_matrix_from_file(filename)
x, eps = SR.var("x eps")
test.assertIn(x, m.variables())
if not fuchsian:
m_pranks = singularities(m, x).values()
test.assertNotEqual(m_pranks, [0]*len(m_pranks))
mt, t = epsilon_form(m, x, eps)
test.assertTrue((mt-transform(m, x, t)).simplify_rational().is_zero())
test.assertTrue(is_fuchsian(mt, x))
test.assertTrue(is_normalized(mt, x, eps))
test.assertNotIn(eps, (mt/eps).simplify_rational().variables())
def assertNormalizeBlocksWorks(test, filename):
x, eps = SR.var("x eps")
m = import_matrix_from_file(filename)
test.assertIn(x, m.variables())
test.assertIn(eps, m.variables())
test.assertFalse(is_normalized(m, x, eps))
m_pranks = singularities(m, x).values()
test.assertNotEqual(m_pranks, [0] * len(m_pranks))
m, t, b = block_triangular_form(m)
mt, tt = reduce_diagonal_blocks(m, x, eps, b=b)
t = t * tt
test.assertTrue(
(mt - transform(m, x, t)).simplify_rational().is_zero())
test.assertTrue(are_diagonal_blocks_reduced(mt, b, x, eps))
import sage.all
print "Welcome to the Normalize Assistant!"
def print_usage():
print "Usage:"
print " normalize.py <matrix>"
if len(sys.argv) != 2:
print "invalid arguments: normalize.py needs exactly 1 argument"
print_usage()
exit(1)
fname = sys.argv[1]
if not os.path.isfile(fname):
print "'%s' does not exist or is not a file" % fname
exit(1)
fuchsia.logger.setLevel(logging.INFO)
m0 = fuchsia.import_matrix_from_file(fname)
x, ep = sage.all.var("x ep")
print "You are normalizing matrix '%s' in (%s, %s)" % (fname, x, ep)
m = fuchsia.FuchsianSystem.from_M(m0, x, ep)
na = fuchsia.NormalizeAssistant(m)
na.start()
def test_import_matrix_from_file_1(t):
x, eps = SR.var("x eps")
m = import_matrix_from_file("test/data/henn_324.m")
t.assertEqual(set(m.variables()), set([x, eps]))
t.assertEqual(m, matrix([[eps / x, 0], [-1 / x**2, eps / (x + 1)]]))
def assertIsFuchsian(t, m_path, x_name):
M = fuchsia.import_matrix_from_file(m_path)
x = SR.var(x_name)
pranks = fuchsia.singularities(M, x).values()
t.assertEqual(pranks, [0]*len(pranks))
def assertTransformation(t, m1_path, x_name, t_path, m2_path):
M1 = fuchsia.import_matrix_from_file(m1_path)
T = fuchsia.import_matrix_from_file(t_path)
M2 = fuchsia.import_matrix_from_file(m2_path)
t.assertEqual(M2.simplify_rational(),
fuchsia.transform(M1, SR.var(x_name), T).simplify_rational())
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())