def test_saddle(self):
lie = LieAlgebra(1)
diag = Diagonalizer(lie)
q = lie.q
p = lie.p
orig = q(0)*p(0)
eq_type = 's'
comp = Complexifier(lie, eq_type)
r2c = comp.calc_sub_complex_into_real()
c2r = comp.calc_sub_real_into_complex()
comp = orig.substitute(r2c)
real = comp.substitute(c2r)
diff = orig-real
for m, c in diff.powers_and_coefficients():
self.assert_(abs(c)<1.0e-15)
def test_saddle(self):
lie = LieAlgebra(1)
diag = Diagonalizer(lie)
q = lie.q
p = lie.p
orig = q(0) * p(0)
eq_type = 's'
comp = Complexifier(lie, eq_type)
r2c = comp.calc_sub_complex_into_real()
c2r = comp.calc_sub_real_into_complex()
comp = orig.substitute(r2c)
real = comp.substitute(c2r)
diff = orig - real
for m, c in diff.powers_and_coefficients():
self.assert_(abs(c) < 1.0e-15)
def test_centre_saddle(self):
lie = LieAlgebra(2)
diag = Diagonalizer(lie)
q = lie.q
p = lie.p
cent = (0.5*q(0)**2)+(0.5*p(0)**2)
sadd = (1.0*q(1))*(1.0*p(1))
orig = cent + sadd
self.assertEquals(len(orig), 3)
eq_type = 'cs'
comp = Complexifier(lie, eq_type)
r2c = comp.calc_sub_complex_into_real()
c2r = comp.calc_sub_real_into_complex()
comp = orig.substitute(r2c)
self.assertEquals(len(comp), 2)
real = comp.substitute(c2r)
diff = orig-real
for m, c in diff.powers_and_coefficients():
self.assert_(abs(c)<1.0e-15)
def test_centre_saddle(self):
lie = LieAlgebra(2)
diag = Diagonalizer(lie)
q = lie.q
p = lie.p
cent = (0.5 * q(0)**2) + (0.5 * p(0)**2)
sadd = (1.0 * q(1)) * (1.0 * p(1))
orig = cent + sadd
self.assertEquals(len(orig), 3)
eq_type = 'cs'
comp = Complexifier(lie, eq_type)
r2c = comp.calc_sub_complex_into_real()
c2r = comp.calc_sub_real_into_complex()
comp = orig.substitute(r2c)
self.assertEquals(len(comp), 2)
real = comp.substitute(c2r)
diff = orig - real
for m, c in diff.powers_and_coefficients():
self.assert_(abs(c) < 1.0e-15)
def test_centre(self):
lie = LieAlgebra(1)
diag = Diagonalizer(lie)
q = lie.q
p = lie.p
orig = (0.5*q(0)**2)+(0.5*p(0)**2)
self.assertEquals(len(orig), 2)
eq_type = 'c'
comp = Complexifier(lie, eq_type)
r2c = comp.calc_sub_complex_into_real()
c2r = comp.calc_sub_real_into_complex()
comp = orig.substitute(r2c)
self.assertEquals(len(comp), 1)
for m, c in comp.powers_and_coefficients():
self.assert_(c.real == 0.0)
self.assert_(m[0] == 1)
self.assert_(m[1] == 1)
real = comp.substitute(c2r)
diff = orig-real
for m, c in diff.powers_and_coefficients():
self.assert_(abs(c)<1.0e-15)
def test_centre(self):
lie = LieAlgebra(1)
diag = Diagonalizer(lie)
q = lie.q
p = lie.p
orig = (0.5 * q(0)**2) + (0.5 * p(0)**2)
self.assertEquals(len(orig), 2)
eq_type = 'c'
comp = Complexifier(lie, eq_type)
r2c = comp.calc_sub_complex_into_real()
c2r = comp.calc_sub_real_into_complex()
comp = orig.substitute(r2c)
self.assertEquals(len(comp), 1)
for m, c in comp.powers_and_coefficients():
self.assert_(c.real == 0.0)
self.assert_(m[0] == 1)
self.assert_(m[1] == 1)
real = comp.substitute(c2r)
diff = orig - real
for m, c in diff.powers_and_coefficients():
self.assert_(abs(c) < 1.0e-15)