def create_linear_system(symbol, superscript, sym_group='622', tdim=2):
sg = RedSgSymOps()
print(sg.symops['6parZ3'])
symops = sg(sym_group)
symop = symops[0]
R = Matrix(symop)
Rsym = Matrix([[Symbol('R_{{{},{}}}'.format(i, j)) for j in range(1, 4)]
for i in range(1, 4)])
print('Rsym=\n', latex(Rsym))
print('R=\n', latex(R))
print(symop)
ivm, vm = SymbolicTensor.voigt_map(2)
print(ivm)
print(vm)
indices0 = list(product(range(3), repeat=tdim))
indices1 = list(product(range(1, 4), repeat=tdim))
print(indices0)
print(indices1)
lhs = Matrix([[Rsym[I, i] * Rsym[J, j] for (i, j) in indices0]
for (I, J) in indices0])
print(latex(lhs))
vec = Matrix([[Symbol('c_{{{},{}}}'.format(i, j))] for (i, j) in indices1])
print(latex(vec))
vvec = Matrix([[Symbol('c_{{{}}}'.format(vm[k] + 1))] for k in indices0])
print(latex(vvec))
lines = []
frac_lines = []
redfrac_lines = []
symbol += '^{{{}}}'.format(superscript)
for (I, J) in indices:
line = '&'.join([
"{}_{{{}{}}} {}_{{{}{}}}".format(symbol, I, i, symbol, J, j)
for (i, j) in indices
])
lines.append(line)
Iint = int(I) - 1
Jint = int(J) - 1
frac_line = '&'.join([
"{} \cdot {}".format(symop[Iint, int(i) - 1], symop[Jint,
int(j) - 1])
for (i, j) in indices
])
frac_line = frac_line.replace('sqrt(3)', '\\sqrt{3}')
frac_lines.append(frac_line)
redfrac_line = '&'.join([
"{}".format(4 * symop[Iint, int(i) - 1] *
symop[Jint, int(j) - 1]) for (i, j) in indices
])
redfrac_line = redfrac_line.replace('sqrt(3)', '\\sqrt{3}')
redfrac_lines.append(redfrac_line)
print('\\\\'.join(lines))
print('\\\\'.join(frac_lines))
print('\\\\'.join(redfrac_lines))
def test_voigt_map(self):
exact_vm = {
(1, 1): 1,
(2, 2): 2,
(3, 3): 3,
(2, 3): 4,
(3, 2): 4,
(1, 3): 5,
(3, 1): 5,
(1, 2): 6,
(2, 1): 6
}
exact_ivm = {
1: (1, 1),
2: (2, 2),
3: (3, 3),
4: (2, 3),
5: (1, 3),
6: (1, 2)
}
approx_ivm, approx_vm = SymbolicTensor.voigt_map(dim=2, start=1)
assert_equal(approx_vm, exact_vm)
assert_equal(approx_ivm, exact_ivm)