def test_equivalent_internal_lines_VT2conjT2_ambiguous_order():
# These diagrams invokes _determine_ambiguous() because the
# dummies can not be ordered unambiguously by the key alone
i, j, k, l, m, n = symbols('i j k l m n', below_fermi=True, cls=Dummy)
a, b, c, d, e, f = symbols('a b c d e f', above_fermi=True, cls=Dummy)
p1, p2, p3, p4 = symbols('p1 p2 p3 p4', above_fermi=True, cls=Dummy)
h1, h2, h3, h4 = symbols('h1 h2 h3 h4', below_fermi=True, cls=Dummy)
from sympy.utilities.iterables import variations
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
# v(abcd)t(abij)t(cdij)
template = v(p1, p2, p3, p4)*t(p1, p2, i, j)*t(p3, p4, i, j)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
template = v(p1, p2, p3, p4)*t(p1, p2, j, i)*t(p3, p4, i, j)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_index_permutations_with_dummies():
a, b, c, d = symbols('a b c d')
p, q, r, s = symbols('p q r s', cls=Dummy)
f, g = map(Function, 'fg')
P = PermutationOperator
# No dummy substitution necessary
expr = f(a, b, p, q) - f(b, a, p, q)
assert simplify_index_permutations(
expr, [P(a, b)]) == P(a, b)*f(a, b, p, q)
# Cases where dummy substitution is needed
expected = P(a, b)*substitute_dummies(f(a, b, p, q))
expr = f(a, b, p, q) - f(b, a, q, p)
result = simplify_index_permutations(expr, [P(a, b)])
assert expected == substitute_dummies(result)
expr = f(a, b, q, p) - f(b, a, p, q)
result = simplify_index_permutations(expr, [P(a, b)])
assert expected == substitute_dummies(result)
# A case where nothing can be done
expr = f(a, b, q, p) - g(b, a, p, q)
result = simplify_index_permutations(expr, [P(a, b)])
assert expr == result
def test_dummy_order_inner_outer_lines_VT1T1T1T1_AT():
ii, jj = symbols('i j', below_fermi=True)
aa, bb = symbols('a b', above_fermi=True)
k, l = symbols('k l', below_fermi=True, cls=Dummy)
c, d = symbols('c d', above_fermi=True, cls=Dummy)
# Coupled-Cluster T2 terms with V*T1*T1*T1*T1
# non-equivalent substitutions (change of sign)
exprs = [
# permut t <=> swapping external lines
atv(k, l, c, d)*att(c, ii)*att(d, jj)*att(aa, k)*att(bb, l),
atv(k, l, c, d)*att(c, jj)*att(d, ii)*att(aa, k)*att(bb, l),
atv(k, l, c, d)*att(c, ii)*att(d, jj)*att(bb, k)*att(aa, l),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == -substitute_dummies(permut)
# equivalent substitutions
exprs = [
atv(k, l, c, d)*att(c, ii)*att(d, jj)*att(aa, k)*att(bb, l),
# permut t <=> swapping external lines
atv(k, l, c, d)*att(c, jj)*att(d, ii)*att(bb, k)*att(aa, l),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT2conjT2_ambiguous_order_AT():
# These diagrams invokes _determine_ambiguous() because the
# dummies can not be ordered unambiguously by the key alone
i, j, k, l, m, n = symbols("i j k l m n", below_fermi=True, cls=Dummy)
a, b, c, d, e, f = symbols("a b c d e f", above_fermi=True, cls=Dummy)
p1, p2, p3, p4 = symbols("p1 p2 p3 p4", above_fermi=True, cls=Dummy)
h1, h2, h3, h4 = symbols("h1 h2 h3 h4", below_fermi=True, cls=Dummy)
from sympy.utilities.iterables import variations
# atv(abcd)att(abij)att(cdij)
template = atv(p1, p2, p3, p4) * att(p1, p2, i, j) * att(p3, p4, i, j)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
template = atv(p1, p2, p3, p4) * att(p1, p2, j, i) * att(p3, p4, i, j)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_equivalent_internal_lines_VT1T1_AT():
i, j, k, l = symbols('i j k l', below_fermi=True, cls=Dummy)
a, b, c, d = symbols('a b c d', above_fermi=True, cls=Dummy)
exprs = [ # permute v. Different dummy order. Not equivalent.
atv(i, j, a, b) * att(a, i) * att(b, j),
atv(j, i, a, b) * att(a, i) * att(b, j),
atv(i, j, b, a) * att(a, i) * att(b, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v. Different dummy order. Equivalent
atv(i, j, a, b) * att(a, i) * att(b, j),
atv(j, i, b, a) * att(a, i) * att(b, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [ # permute t. Same dummy order, not equivalent.
atv(i, j, a, b) * att(a, i) * att(b, j),
atv(i, j, a, b) * att(b, i) * att(a, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Different dummy order, equivalent
atv(i, j, a, b) * att(a, i) * att(b, j),
atv(j, i, a, b) * att(a, j) * att(b, i),
atv(i, j, b, a) * att(b, i) * att(a, j),
atv(j, i, b, a) * att(b, j) * att(a, i),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT1T1_AT():
i, j, k, l = symbols('i j k l', below_fermi=True, cls=Dummy)
a, b, c, d = symbols('a b c d', above_fermi=True, cls=Dummy)
exprs = [ # permute v. Different dummy order. Not equivalent.
atv(i, j, a, b)*att(a, i)*att(b, j),
atv(j, i, a, b)*att(a, i)*att(b, j),
atv(i, j, b, a)*att(a, i)*att(b, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v. Different dummy order. Equivalent
atv(i, j, a, b)*att(a, i)*att(b, j),
atv(j, i, b, a)*att(a, i)*att(b, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [ # permute t. Same dummy order, not equivalent.
atv(i, j, a, b)*att(a, i)*att(b, j),
atv(i, j, a, b)*att(b, i)*att(a, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Different dummy order, equivalent
atv(i, j, a, b)*att(a, i)*att(b, j),
atv(j, i, a, b)*att(a, j)*att(b, i),
atv(i, j, b, a)*att(b, i)*att(a, j),
atv(j, i, b, a)*att(b, j)*att(a, i),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_pqrs_AT():
ii, jj = symbols('i j')
aa, bb = symbols('a b')
k, l = symbols('k l', cls=Dummy)
c, d = symbols('c d', cls=Dummy)
exprs = [
atv(k, l, c, d) * att(aa, c, ii, k) * att(bb, d, jj, l),
atv(l, k, c, d) * att(aa, c, ii, l) * att(bb, d, jj, k),
atv(k, l, d, c) * att(aa, d, ii, k) * att(bb, c, jj, l),
atv(l, k, d, c) * att(aa, d, ii, l) * att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_pqrs_AT():
ii, jj = symbols('i j')
aa, bb = symbols('a b')
k, l = symbols('k l', cls=Dummy)
c, d = symbols('c d', cls=Dummy)
exprs = [
atv(k, l, c, d)*att(aa, c, ii, k)*att(bb, d, jj, l),
atv(l, k, c, d)*att(aa, c, ii, l)*att(bb, d, jj, k),
atv(k, l, d, c)*att(aa, d, ii, k)*att(bb, c, jj, l),
atv(l, k, d, c)*att(aa, d, ii, l)*att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_substitute_dummies_substitution_order():
i, j, k, l = symbols("i j k l", below_fermi=True, cls=Dummy)
f = Function("f")
from sympy.utilities.iterables import variations
for permut in variations([i, j, k, l], 4):
assert substitute_dummies(f(*permut) - f(i, j, k, l)) == 0
def test_substitute_dummies_substitution_order():
i, j, k, l = symbols("i j k l", below_fermi=True, cls=Dummy)
f = Function("f")
from sympy.utilities.iterables import variations
for permut in variations([i, j, k, l], 4):
assert substitute_dummies(f(*permut) - f(i, j, k, l)) == 0
def test_dummy_order_inner_outer_lines_VT1T1T1_AT():
ii = symbols('i', below_fermi=True)
aa = symbols('a', above_fermi=True)
k, l = symbols('k l', below_fermi=True, cls=Dummy)
c, d = symbols('c d', above_fermi=True, cls=Dummy)
# Coupled-Cluster T1 terms with V*T1*T1*T1
# t^{a}_{k} t^{c}_{i} t^{d}_{l} v^{lk}_{dc}
exprs = [
# permut v and t <=> swapping internal lines, equivalent
# irrespective of symmetries in v
atv(k, l, c, d)*att(c, ii)*att(d, l)*att(aa, k),
atv(l, k, c, d)*att(c, ii)*att(d, k)*att(aa, l),
atv(k, l, d, c)*att(d, ii)*att(c, l)*att(aa, k),
atv(l, k, d, c)*att(d, ii)*att(c, k)*att(aa, l),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_dummy_order_inner_outer_lines_VT1T1T1_AT():
ii = symbols("i", below_fermi=True)
aa = symbols("a", above_fermi=True)
k, l = symbols("k l", below_fermi=True, cls=Dummy)
c, d = symbols("c d", above_fermi=True, cls=Dummy)
# Coupled-Cluster T1 terms with V*T1*T1*T1
# t^{a}_{k} t^{c}_{i} t^{d}_{l} v^{lk}_{dc}
exprs = [
# permut v and t <=> swapping internal lines, equivalent
# irrespective of symmetries in v
atv(k, l, c, d) * att(c, ii) * att(d, l) * att(aa, k),
atv(l, k, c, d) * att(c, ii) * att(d, k) * att(aa, l),
atv(k, l, d, c) * att(d, ii) * att(c, l) * att(aa, k),
atv(l, k, d, c) * att(d, ii) * att(c, k) * att(aa, l),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def get_two_body_equation(equation_h, equation_u):
two_body_eq = wicks(
Fd(j) * F(b) * Fd(i) * F(a) * equation_u, **wicks_kwargs)
p = PermutationOperator
two_body_eq = simplify_index_permutations(two_body_eq, [p(i, j), p(a, b)])
two_body_eq = substitute_dummies(two_body_eq, **sub_kwargs)
return two_body_eq
def get_one_body_equation(equation_h, equation_u):
one_body_eq = wicks(
Fd(j) * F(b) * Fd(i) * F(a) * equation_h, **wicks_kwargs)
p = PermutationOperator
one_body_eq = simplify_index_permutations(one_body_eq, [p(a, b), p(i, j)])
one_body_eq = substitute_dummies(one_body_eq, **sub_kwargs)
return one_body_eq
def level(H, expr):
pretty_dummies_dict = {
'above': 'defg',
'below': 'lmno',
'general': 'pqrst'
}
#display(Markdown
# (rf"""Calculating 4 nested commutators"""))
C = Commutator
T1, T2 = get_CC_operators()
T = T1 + T2
comm1 = wicks(C(H, T))
comm1 = evaluate_deltas(comm1)
comm1 = substitute_dummies(comm1)
T1, T2 = get_CC_operators()
T = T1 + T2
comm2 = wicks(C(comm1, T))
comm2 = evaluate_deltas(comm2)
comm2 = substitute_dummies(comm2)
T1, T2 = get_CC_operators()
T = T1 + T2
comm3 = wicks(C(comm2, T))
comm3 = evaluate_deltas(comm3)
comm3 = substitute_dummies(comm3)
T1, T2 = get_CC_operators()
T = T1 + T2
comm4 = wicks(C(comm3, T))
comm4 = evaluate_deltas(comm4)
comm4 = substitute_dummies(comm4)
eq = H + comm1 + comm2 / 2 + comm3 / 6 + comm4 / 24
eq = eq.expand()
eq = evaluate_deltas(eq)
eq = substitute_dummies(eq,
new_indices=True,
pretty_indices=pretty_dummies_dict)
return eq
def test_internal_external_pqrs():
ii, jj = symbols("i j")
aa, bb = symbols("a b")
k, l = symbols("k l", cls=Dummy)
c, d = symbols("c d", cls=Dummy)
v = Function("v")
t = Function("t")
dums = _get_ordered_dummies
exprs = [
v(k, l, c, d) * t(aa, c, ii, k) * t(bb, d, jj, l),
v(l, k, c, d) * t(aa, c, ii, l) * t(bb, d, jj, k),
v(k, l, d, c) * t(aa, d, ii, k) * t(bb, c, jj, l),
v(l, k, d, c) * t(aa, d, ii, l) * t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def computeHausdorff(H):
print("Calculating 4 nested commutators")
C = Commutator
T1, T2 = get_T_operators()
T = T2
print("commutator 1...")
comm1 = wicks(C(H, T))
comm1 = evaluate_deltas(comm1)
comm1 = substitute_dummies(comm1)
T1, T2 = get_T_operators()
T = T2
print("commutator 2...")
comm2 = wicks(C(comm1, T))
comm2 = evaluate_deltas(comm2)
comm2 = substitute_dummies(comm2)
T1, T2 = get_T_operators()
T = T2
print("commutator 3...")
comm3 = wicks(C(comm2, T))
comm3 = evaluate_deltas(comm3)
comm3 = substitute_dummies(comm3)
T1, T2 = get_T_operators()
T = T2
print("commutator 4...")
comm4 = wicks(C(comm3, T))
comm4 = evaluate_deltas(comm4)
comm4 = substitute_dummies(comm4)
print("construct Hausdorff expansion...")
eq = H + comm1 + comm2 / 2 + comm3 / 6 + comm4 / 24
eq = eq.expand()
eq = evaluate_deltas(eq)
eq = substitute_dummies(eq,
new_indices=True,
pretty_indices=pretty_dummies_dict)
print("*********************")
print()
return eq
def test_internal_external_pqrs():
ii, jj = symbols("i j")
aa, bb = symbols("a b")
k, l = symbols("k l", cls=Dummy)
c, d = symbols("c d", cls=Dummy)
v = Function("v")
t = Function("t")
dums = _get_ordered_dummies
exprs = [
v(k, l, c, d) * t(aa, c, ii, k) * t(bb, d, jj, l),
v(l, k, c, d) * t(aa, c, ii, l) * t(bb, d, jj, k),
v(k, l, d, c) * t(aa, d, ii, k) * t(bb, c, jj, l),
v(l, k, d, c) * t(aa, d, ii, l) * t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_pqrs():
ii, jj = symbols('i j')
aa, bb = symbols('a b')
k, l = symbols('k l', cls=Dummy)
c, d = symbols('c d', cls=Dummy)
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
exprs = [
v(k, l, c, d)*t(aa, c, ii, k)*t(bb, d, jj, l),
v(l, k, c, d)*t(aa, c, ii, l)*t(bb, d, jj, k),
v(k, l, d, c)*t(aa, d, ii, k)*t(bb, c, jj, l),
v(l, k, d, c)*t(aa, d, ii, l)*t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_pqrs():
ii, jj = symbols('i j')
aa, bb = symbols('a b')
k, l = symbols('k l', cls=Dummy)
c, d = symbols('c d', cls=Dummy)
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
exprs = [
v(k, l, c, d)*t(aa, c, ii, k)*t(bb, d, jj, l),
v(l, k, c, d)*t(aa, c, ii, l)*t(bb, d, jj, k),
v(k, l, d, c)*t(aa, d, ii, k)*t(bb, c, jj, l),
v(l, k, d, c)*t(aa, d, ii, l)*t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def compute_hausdorff(h, cluster_func, num_terms=4):
commutator = Commutator
comm_term = h
equation = comm_term
for i in range(num_terms):
t = sum(cluster_func())
comm_term = wicks(commutator(comm_term, t))
comm_term = substitute_dummies(evaluate_deltas(comm_term))
equation += comm_term / factorial(i + 1)
equation = equation.expand()
equation = evaluate_deltas(equation)
equation = substitute_dummies(equation,
new_indices=True,
pretty_indices=pretty_dummies)
return equation
def test_equivalent_internal_lines_VT2_AT():
i, j, k, l = symbols("i j k l", below_fermi=True, cls=Dummy)
a, b, c, d = symbols("a b c d", above_fermi=True, cls=Dummy)
exprs = [
# permute v. Same dummy order, not equivalent.
atv(i, j, a, b) * att(a, b, i, j),
atv(j, i, a, b) * att(a, b, i, j),
atv(i, j, b, a) * att(a, b, i, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permute t.
atv(i, j, a, b) * att(a, b, i, j),
atv(i, j, a, b) * att(b, a, i, j),
atv(i, j, a, b) * att(a, b, j, i),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Relabelling of dummies should be equivalent.
atv(i, j, a, b) * att(a, b, i, j),
atv(j, i, a, b) * att(a, b, j, i),
atv(i, j, b, a) * att(b, a, i, j),
atv(j, i, b, a) * att(b, a, j, i),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_VT2T2_AT():
ii, jj = symbols("i j", below_fermi=True)
aa, bb = symbols("a b", above_fermi=True)
k, l = symbols("k l", below_fermi=True, cls=Dummy)
c, d = symbols("c d", above_fermi=True, cls=Dummy)
dums = _get_ordered_dummies
exprs = [
atv(k, l, c, d) * att(aa, c, ii, k) * att(bb, d, jj, l),
atv(l, k, c, d) * att(aa, c, ii, l) * att(bb, d, jj, k),
atv(k, l, d, c) * att(aa, d, ii, k) * att(bb, c, jj, l),
atv(l, k, d, c) * att(aa, d, ii, l) * att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d) * att(aa, c, ii, k) * att(d, bb, jj, l),
atv(l, k, c, d) * att(aa, c, ii, l) * att(d, bb, jj, k),
atv(k, l, d, c) * att(aa, d, ii, k) * att(c, bb, jj, l),
atv(l, k, d, c) * att(aa, d, ii, l) * att(c, bb, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d) * att(c, aa, ii, k) * att(bb, d, jj, l),
atv(l, k, c, d) * att(c, aa, ii, l) * att(bb, d, jj, k),
atv(k, l, d, c) * att(d, aa, ii, k) * att(bb, c, jj, l),
atv(l, k, d, c) * att(d, aa, ii, l) * att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_VT2T2_AT():
ii, jj = symbols('ij', below_fermi=True)
aa, bb = symbols('ab', above_fermi=True)
k, l = symbols('k l', below_fermi=True, cls=Dummy)
c, d = symbols('c d', above_fermi=True, cls=Dummy)
dums = _get_ordered_dummies
exprs = [
atv(k, l, c, d) * att(aa, c, ii, k) * att(bb, d, jj, l),
atv(l, k, c, d) * att(aa, c, ii, l) * att(bb, d, jj, k),
atv(k, l, d, c) * att(aa, d, ii, k) * att(bb, c, jj, l),
atv(l, k, d, c) * att(aa, d, ii, l) * att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d) * att(aa, c, ii, k) * att(d, bb, jj, l),
atv(l, k, c, d) * att(aa, c, ii, l) * att(d, bb, jj, k),
atv(k, l, d, c) * att(aa, d, ii, k) * att(c, bb, jj, l),
atv(l, k, d, c) * att(aa, d, ii, l) * att(c, bb, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d) * att(c, aa, ii, k) * att(bb, d, jj, l),
atv(l, k, c, d) * att(c, aa, ii, l) * att(bb, d, jj, k),
atv(k, l, d, c) * att(d, aa, ii, k) * att(bb, c, jj, l),
atv(l, k, d, c) * att(d, aa, ii, l) * att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_VT2T2_AT():
ii, jj = symbols("i j", below_fermi=True)
aa, bb = symbols("a b", above_fermi=True)
k, l = symbols("k l", below_fermi=True, cls=Dummy)
c, d = symbols("c d", above_fermi=True, cls=Dummy)
exprs = [
atv(k, l, c, d) * att(aa, c, ii, k) * att(bb, d, jj, l),
atv(l, k, c, d) * att(aa, c, ii, l) * att(bb, d, jj, k),
atv(k, l, d, c) * att(aa, d, ii, k) * att(bb, c, jj, l),
atv(l, k, d, c) * att(aa, d, ii, l) * att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d) * att(aa, c, ii, k) * att(d, bb, jj, l),
atv(l, k, c, d) * att(aa, c, ii, l) * att(d, bb, jj, k),
atv(k, l, d, c) * att(aa, d, ii, k) * att(c, bb, jj, l),
atv(l, k, d, c) * att(aa, d, ii, l) * att(c, bb, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d) * att(c, aa, ii, k) * att(bb, d, jj, l),
atv(l, k, c, d) * att(c, aa, ii, l) * att(bb, d, jj, k),
atv(k, l, d, c) * att(d, aa, ii, k) * att(bb, c, jj, l),
atv(l, k, d, c) * att(d, aa, ii, l) * att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT2_AT():
i, j, k, l = symbols("i j k l", below_fermi=True, cls=Dummy)
a, b, c, d = symbols("a b c d", above_fermi=True, cls=Dummy)
exprs = [
# permute v. Same dummy order, not equivalent.
atv(i, j, a, b) * att(a, b, i, j),
atv(j, i, a, b) * att(a, b, i, j),
atv(i, j, b, a) * att(a, b, i, j),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permute t.
atv(i, j, a, b) * att(a, b, i, j),
atv(i, j, a, b) * att(b, a, i, j),
atv(i, j, a, b) * att(a, b, j, i),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Relabelling of dummies should be equivalent.
atv(i, j, a, b) * att(a, b, i, j),
atv(j, i, a, b) * att(a, b, j, i),
atv(i, j, b, a) * att(b, a, i, j),
atv(j, i, b, a) * att(b, a, j, i),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_VT2T2_AT():
ii, jj = symbols('i j', below_fermi=True)
aa, bb = symbols('a b', above_fermi=True)
k, l = symbols('k l', below_fermi=True, cls=Dummy)
c, d = symbols('c d', above_fermi=True, cls=Dummy)
exprs = [
atv(k, l, c, d)*att(aa, c, ii, k)*att(bb, d, jj, l),
atv(l, k, c, d)*att(aa, c, ii, l)*att(bb, d, jj, k),
atv(k, l, d, c)*att(aa, d, ii, k)*att(bb, c, jj, l),
atv(l, k, d, c)*att(aa, d, ii, l)*att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d)*att(aa, c, ii, k)*att(d, bb, jj, l),
atv(l, k, c, d)*att(aa, c, ii, l)*att(d, bb, jj, k),
atv(k, l, d, c)*att(aa, d, ii, k)*att(c, bb, jj, l),
atv(l, k, d, c)*att(aa, d, ii, l)*att(c, bb, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
atv(k, l, c, d)*att(c, aa, ii, k)*att(bb, d, jj, l),
atv(l, k, c, d)*att(c, aa, ii, l)*att(bb, d, jj, k),
atv(k, l, d, c)*att(d, aa, ii, k)*att(bb, c, jj, l),
atv(l, k, d, c)*att(d, aa, ii, l)*att(bb, c, jj, k),
]
for permut in exprs[1:]:
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT2conjT2():
# this diagram requires special handling in TCE
i, j, k, l, m, n = symbols('i j k l m n', below_fermi=True, cls=Dummy)
a, b, c, d, e, f = symbols('a b c d e f', above_fermi=True, cls=Dummy)
p1, p2, p3, p4 = symbols('p1 p2 p3 p4', above_fermi=True, cls=Dummy)
h1, h2, h3, h4 = symbols('h1 h2 h3 h4', below_fermi=True, cls=Dummy)
from sympy.utilities.iterables import variations
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
# v(abcd)t(abij)t(ijcd)
template = v(p1, p2, p3, p4)*t(p1, p2, i, j)*t(i, j, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
template = v(p1, p2, p3, p4)*t(p1, p2, j, i)*t(j, i, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
# v(abcd)t(abij)t(jicd)
template = v(p1, p2, p3, p4)*t(p1, p2, i, j)*t(j, i, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
template = v(p1, p2, p3, p4)*t(p1, p2, j, i)*t(i, j, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_equivalent_internal_lines_VT2conjT2():
# this diagram requires special handling in TCE
i, j, k, l, m, n = symbols("i j k l m n", below_fermi=True, cls=Dummy)
a, b, c, d, e, f = symbols("a b c d e f", above_fermi=True, cls=Dummy)
p1, p2, p3, p4 = symbols("p1 p2 p3 p4", above_fermi=True, cls=Dummy)
h1, h2, h3, h4 = symbols("h1 h2 h3 h4", below_fermi=True, cls=Dummy)
from sympy.utilities.iterables import variations
v = Function("v")
t = Function("t")
dums = _get_ordered_dummies
# v(abcd)t(abij)t(ijcd)
template = v(p1, p2, p3, p4) * t(p1, p2, i, j) * t(i, j, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
template = v(p1, p2, p3, p4) * t(p1, p2, j, i) * t(j, i, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
# v(abcd)t(abij)t(jicd)
template = v(p1, p2, p3, p4) * t(p1, p2, i, j) * t(j, i, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
template = v(p1, p2, p3, p4) * t(p1, p2, j, i) * t(i, j, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], next(permutator)))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert dums(base) != dums(expr)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_dummy_order_inner_outer_lines_VT1T1T1():
ii = symbols('i', below_fermi=True)
aa = symbols('a', above_fermi=True)
k, l = symbols('k l', below_fermi=True, cls=Dummy)
c, d = symbols('c d', above_fermi=True, cls=Dummy)
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
# Coupled-Cluster T1 terms with V*T1*T1*T1
# t^{a}_{k} t^{c}_{i} t^{d}_{l} v^{lk}_{dc}
exprs = [
# permut v and t <=> swapping internal lines, equivalent
# irrespective of symmetries in v
v(k, l, c, d)*t(c, ii)*t(d, l)*t(aa, k),
v(l, k, c, d)*t(c, ii)*t(d, k)*t(aa, l),
v(k, l, d, c)*t(d, ii)*t(c, l)*t(aa, k),
v(l, k, d, c)*t(d, ii)*t(c, k)*t(aa, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_dummy_order_inner_outer_lines_VT1T1T1():
ii = symbols("i", below_fermi=True)
aa = symbols("a", above_fermi=True)
k, l = symbols("k l", below_fermi=True, cls=Dummy)
c, d = symbols("c d", above_fermi=True, cls=Dummy)
v = Function("v")
t = Function("t")
dums = _get_ordered_dummies
# Coupled-Cluster T1 terms with V*T1*T1*T1
# t^{a}_{k} t^{c}_{i} t^{d}_{l} v^{lk}_{dc}
exprs = [
# permut v and t <=> swapping internal lines, equivalent
# irrespective of symmetries in v
v(k, l, c, d) * t(c, ii) * t(d, l) * t(aa, k),
v(l, k, c, d) * t(c, ii) * t(d, k) * t(aa, l),
v(k, l, d, c) * t(d, ii) * t(c, l) * t(aa, k),
v(l, k, d, c) * t(d, ii) * t(c, k) * t(aa, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT1T1():
i, j, k, l = symbols('i j k l', below_fermi=True, cls=Dummy)
a, b, c, d = symbols('a b c d', above_fermi=True, cls=Dummy)
f = Function('f')
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
exprs = [ # permute v. Different dummy order. Not equivalent.
v(i, j, a, b) * t(a, i) * t(b, j),
v(j, i, a, b) * t(a, i) * t(b, j),
v(i, j, b, a) * t(a, i) * t(b, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v. Different dummy order. Equivalent
v(i, j, a, b) * t(a, i) * t(b, j),
v(j, i, b, a) * t(a, i) * t(b, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [ # permute t. Same dummy order, not equivalent.
v(i, j, a, b) * t(a, i) * t(b, j),
v(i, j, a, b) * t(b, i) * t(a, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) == dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Different dummy order, equivalent
v(i, j, a, b) * t(a, i) * t(b, j),
v(j, i, a, b) * t(a, j) * t(b, i),
v(i, j, b, a) * t(b, i) * t(a, j),
v(j, i, b, a) * t(b, j) * t(a, i),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT1T1():
i,j,k,l = symbols('i j k l',below_fermi=True, cls=Dummy)
a,b,c,d = symbols('a b c d',above_fermi=True, cls=Dummy)
f = Function('f')
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
exprs = [ # permute v. Different dummy order. Not equivalent.
v(i, j, a, b)*t(a, i)*t(b, j),
v(j, i, a, b)*t(a, i)*t(b, j),
v(i, j, b, a)*t(a, i)*t(b, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v. Different dummy order. Equivalent
v(i, j, a, b)*t(a, i)*t(b, j),
v(j, i, b, a)*t(a, i)*t(b, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [ # permute t. Same dummy order, not equivalent.
v(i, j, a, b)*t(a, i)*t(b, j),
v(i, j, a, b)*t(b, i)*t(a, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) == dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Different dummy order, equivalent
v(i, j, a, b)*t(a, i)*t(b, j),
v(j, i, a, b)*t(a, j)*t(b, i),
v(i, j, b, a)*t(b, i)*t(a, j),
v(j, i, b, a)*t(b, j)*t(a, i),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT2conjT2_AT():
# this diagram requires special handling in TCE
i,j,k,l,m,n = symbols('i j k l m n',below_fermi=True, cls=Dummy)
a,b,c,d,e,f = symbols('a b c d e f',above_fermi=True, cls=Dummy)
p1,p2,p3,p4 = symbols('p1 p2 p3 p4',above_fermi=True, cls=Dummy)
h1,h2,h3,h4 = symbols('h1 h2 h3 h4',below_fermi=True, cls=Dummy)
from sympy.utilities.iterables import variations
# atv(abcd)att(abij)att(ijcd)
template = atv(p1, p2, p3, p4)*att(p1, p2, i, j)*att(i, j, p3, p4)
permutator = variations([a,b,c,d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
template = atv(p1, p2, p3, p4)*att(p1, p2, j, i)*att(j, i, p3, p4)
permutator = variations([a,b,c,d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
# atv(abcd)att(abij)att(jicd)
template = atv(p1, p2, p3, p4)*att(p1, p2, i, j)*att(j, i, p3, p4)
permutator = variations([a,b,c,d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
template = atv(p1, p2, p3, p4)*att(p1, p2, j, i)*att(i, j, p3, p4)
permutator = variations([a,b,c,d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_dummy_order_inner_outer_lines_VT1T1T1T1():
ii, jj = symbols('i j', below_fermi=True)
aa, bb = symbols('a b', above_fermi=True)
k, l = symbols('k l', below_fermi=True, cls=Dummy)
c, d = symbols('c d', above_fermi=True, cls=Dummy)
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
# Coupled-Cluster T2 terms with V*T1*T1*T1*T1
exprs = [
# permut t <=> swapping external lines, not equivalent
# except if v has certain symmetries.
v(k, l, c, d)*t(c, ii)*t(d, jj)*t(aa, k)*t(bb, l),
v(k, l, c, d)*t(c, jj)*t(d, ii)*t(aa, k)*t(bb, l),
v(k, l, c, d)*t(c, ii)*t(d, jj)*t(bb, k)*t(aa, l),
v(k, l, c, d)*t(c, jj)*t(d, ii)*t(bb, k)*t(aa, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permut v <=> swapping external lines, not equivalent
# except if v has certain symmetries.
#
# Note that in contrast to above, these permutations have identical
# dummy order. That is because the proximity to external indices
# has higher influence on the canonical dummy ordering than the
# position of a dummy on the factors. In fact, the terms here are
# similar in structure as the result of the dummy substitions above.
v(k, l, c, d)*t(c, ii)*t(d, jj)*t(aa, k)*t(bb, l),
v(l, k, c, d)*t(c, ii)*t(d, jj)*t(aa, k)*t(bb, l),
v(k, l, d, c)*t(c, ii)*t(d, jj)*t(aa, k)*t(bb, l),
v(l, k, d, c)*t(c, ii)*t(d, jj)*t(aa, k)*t(bb, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) == dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permut t and v <=> swapping internal lines, equivalent.
# Canonical dummy order is different, and a consistent
# substitution reveals the equivalence.
v(k, l, c, d)*t(c, ii)*t(d, jj)*t(aa, k)*t(bb, l),
v(k, l, d, c)*t(c, jj)*t(d, ii)*t(aa, k)*t(bb, l),
v(l, k, c, d)*t(c, ii)*t(d, jj)*t(bb, k)*t(aa, l),
v(l, k, d, c)*t(c, jj)*t(d, ii)*t(bb, k)*t(aa, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_dummy_order_inner_outer_lines_VT1T1T1T1():
ii, jj = symbols("i j", below_fermi=True)
aa, bb = symbols("a b", above_fermi=True)
k, l = symbols("k l", below_fermi=True, cls=Dummy)
c, d = symbols("c d", above_fermi=True, cls=Dummy)
v = Function("v")
t = Function("t")
dums = _get_ordered_dummies
# Coupled-Cluster T2 terms with V*T1*T1*T1*T1
exprs = [
# permut t <=> swapping external lines, not equivalent
# except if v has certain symmetries.
v(k, l, c, d) * t(c, ii) * t(d, jj) * t(aa, k) * t(bb, l),
v(k, l, c, d) * t(c, jj) * t(d, ii) * t(aa, k) * t(bb, l),
v(k, l, c, d) * t(c, ii) * t(d, jj) * t(bb, k) * t(aa, l),
v(k, l, c, d) * t(c, jj) * t(d, ii) * t(bb, k) * t(aa, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permut v <=> swapping external lines, not equivalent
# except if v has certain symmetries.
#
# Note that in contrast to above, these permutations have identical
# dummy order. That is because the proximity to external indices
# has higher influence on the canonical dummy ordering than the
# position of a dummy on the factors. In fact, the terms here are
# similar in structure as the result of the dummy substitutions above.
v(k, l, c, d) * t(c, ii) * t(d, jj) * t(aa, k) * t(bb, l),
v(l, k, c, d) * t(c, ii) * t(d, jj) * t(aa, k) * t(bb, l),
v(k, l, d, c) * t(c, ii) * t(d, jj) * t(aa, k) * t(bb, l),
v(l, k, d, c) * t(c, ii) * t(d, jj) * t(aa, k) * t(bb, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) == dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permut t and v <=> swapping internal lines, equivalent.
# Canonical dummy order is different, and a consistent
# substitution reveals the equivalence.
v(k, l, c, d) * t(c, ii) * t(d, jj) * t(aa, k) * t(bb, l),
v(k, l, d, c) * t(c, jj) * t(d, ii) * t(aa, k) * t(bb, l),
v(l, k, c, d) * t(c, ii) * t(d, jj) * t(bb, k) * t(aa, l),
v(l, k, d, c) * t(c, jj) * t(d, ii) * t(bb, k) * t(aa, l),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT2conjT2_AT():
# this diagram requires special handling in TCE
i, j, k, l, m, n = symbols("i j k l m n", below_fermi=True, cls=Dummy)
a, b, c, d, e, f = symbols("a b c d e f", above_fermi=True, cls=Dummy)
p1, p2, p3, p4 = symbols("p1 p2 p3 p4", above_fermi=True, cls=Dummy)
h1, h2, h3, h4 = symbols("h1 h2 h3 h4", below_fermi=True, cls=Dummy)
from sympy.utilities.iterables import variations
# atv(abcd)att(abij)att(ijcd)
template = atv(p1, p2, p3, p4) * att(p1, p2, i, j) * att(i, j, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
template = atv(p1, p2, p3, p4) * att(p1, p2, j, i) * att(j, i, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
# atv(abcd)att(abij)att(jicd)
template = atv(p1, p2, p3, p4) * att(p1, p2, i, j) * att(j, i, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
template = atv(p1, p2, p3, p4) * att(p1, p2, j, i) * att(i, j, p3, p4)
permutator = variations([a, b, c, d], 4)
base = template.subs(zip([p1, p2, p3, p4], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_equivalent_internal_lines_VT2():
i, j, k, l = symbols('i j k l', below_fermi=True, cls=Dummy)
a, b, c, d = symbols('a b c d', above_fermi=True, cls=Dummy)
f = Function('f')
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
exprs = [
# permute v. Same dummy order, not equivalent.
#
# This test show that the dummy order may not be sensitive to all
# index permutations. The following expressions have identical
# structure as the resulting terms from of the dummy subsitutions
# in the test above. Here, all expressions have the same dummy
# order, so they cannot be simplified by means of dummy
# substitution. In order to simplify further, it is necessary to
# exploit symmetries in the objects, for instance if t or v is
# antisymmetric.
v(i, j, a, b) * t(a, b, i, j),
v(j, i, a, b) * t(a, b, i, j),
v(i, j, b, a) * t(a, b, i, j),
v(j, i, b, a) * t(a, b, i, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) == dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permute t.
v(i, j, a, b) * t(a, b, i, j),
v(i, j, a, b) * t(b, a, i, j),
v(i, j, a, b) * t(a, b, j, i),
v(i, j, a, b) * t(b, a, j, i),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Relabelling of dummies should be equivalent.
v(i, j, a, b) * t(a, b, i, j),
v(j, i, a, b) * t(a, b, j, i),
v(i, j, b, a) * t(b, a, i, j),
v(j, i, b, a) * t(b, a, j, i),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_equivalent_internal_lines_VT2():
i,j,k,l = symbols('i j k l',below_fermi=True, cls=Dummy)
a,b,c,d = symbols('a b c d',above_fermi=True, cls=Dummy)
f = Function('f')
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
exprs = [
# permute v. Same dummy order, not equivalent.
#
# This test show that the dummy order may not be sensitive to all
# index permutations. The following expressions have identical
# structure as the resulting terms from of the dummy subsitutions
# in the test above. Here, all expressions have the same dummy
# order, so they cannot be simplified by means of dummy
# substitution. In order to simplify further, it is necessary to
# exploit symmetries in the objects, for instance if t or v is
# antisymmetric.
v(i, j, a, b)*t(a, b, i, j),
v(j, i, a, b)*t(a, b, i, j),
v(i, j, b, a)*t(a, b, i, j),
v(j, i, b, a)*t(a, b, i, j),
]
for permut in exprs[1:]:
assert dums(exprs[0]) == dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [
# permute t.
v(i, j, a, b)*t(a, b, i, j),
v(i, j, a, b)*t(b, a, i, j),
v(i, j, a, b)*t(a, b, j, i),
v(i, j, a, b)*t(b, a, j, i),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) != substitute_dummies(permut)
exprs = [ # permute v and t. Relabelling of dummies should be equivalent.
v(i, j, a, b)*t(a, b, i, j),
v(j, i, a, b)*t(a, b, j, i),
v(i, j, b, a)*t(b, a, i, j),
v(j, i, b, a)*t(b, a, j, i),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_dummy_order_ambiguous():
aa, bb = symbols('ab', above_fermi=True)
i, j, k, l, m = symbols('i j k l m', below_fermi=True, cls=Dummy)
a, b, c, d, e = symbols('a b c d e', above_fermi=True, cls=Dummy)
p, q = symbols('p q', cls=Dummy)
p1, p2, p3, p4 = symbols('p1 p2 p3 p4', above_fermi=True, cls=Dummy)
p5, p6, p7, p8 = symbols('p5 p6 p7 p8', above_fermi=True, cls=Dummy)
h1, h2, h3, h4 = symbols('h1 h2 h3 h4', below_fermi=True, cls=Dummy)
h5, h6, h7, h8 = symbols('h5 h6 h7 h8', below_fermi=True, cls=Dummy)
A = Function('A')
B = Function('B')
dums = _get_ordered_dummies
from sympy.utilities.iterables import variations
# A*A*A*A*B -- ordering of p5 and p4 is used to figure out the rest
template = A(p1, p2) * A(p4, p1) * A(p2, p3) * A(p3, p5) * B(p5, p4)
permutator = variations([a, b, c, d, e], 5)
base = template.subs(zip([p1, p2, p3, p4, p5], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4, p5], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
# A*A*A*A*A -- an arbitrary index is assigned and the rest are figured out
template = A(p1, p2) * A(p4, p1) * A(p2, p3) * A(p3, p5) * A(p5, p4)
permutator = variations([a, b, c, d, e], 5)
base = template.subs(zip([p1, p2, p3, p4, p5], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4, p5], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
# A*A*A -- ordering of p5 and p4 is used to figure out the rest
template = A(p1, p2, p4, p1) * A(p2, p3, p3, p5) * A(p5, p4)
permutator = variations([a, b, c, d, e], 5)
base = template.subs(zip([p1, p2, p3, p4, p5], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4, p5], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_dummy_order_ambiguous():
aa, bb = symbols('ab', above_fermi=True)
i, j, k, l, m = symbols('i j k l m', below_fermi=True, cls=Dummy)
a, b, c, d, e = symbols('a b c d e', above_fermi=True, cls=Dummy)
p, q = symbols('p q', cls=Dummy)
p1,p2,p3,p4 = symbols('p1 p2 p3 p4',above_fermi=True, cls=Dummy)
p5,p6,p7,p8 = symbols('p5 p6 p7 p8',above_fermi=True, cls=Dummy)
h1,h2,h3,h4 = symbols('h1 h2 h3 h4',below_fermi=True, cls=Dummy)
h5,h6,h7,h8 = symbols('h5 h6 h7 h8',below_fermi=True, cls=Dummy)
A = Function('A')
B = Function('B')
dums = _get_ordered_dummies
from sympy.utilities.iterables import variations
# A*A*A*A*B -- ordering of p5 and p4 is used to figure out the rest
template = A(p1, p2)*A(p4, p1)*A(p2, p3)*A(p3, p5)*B(p5, p4)
permutator = variations([a,b,c,d,e], 5)
base = template.subs(zip([p1, p2, p3, p4, p5], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4, p5], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
# A*A*A*A*A -- an arbitrary index is assigned and the rest are figured out
template = A(p1, p2)*A(p4, p1)*A(p2, p3)*A(p3, p5)*A(p5, p4)
permutator = variations([a,b,c,d,e], 5)
base = template.subs(zip([p1, p2, p3, p4, p5], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4, p5], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
# A*A*A -- ordering of p5 and p4 is used to figure out the rest
template = A(p1, p2, p4, p1)*A(p2, p3, p3, p5)*A(p5, p4)
permutator = variations([a,b,c,d,e], 5)
base = template.subs(zip([p1, p2, p3, p4, p5], permutator.next()))
for permut in permutator:
subslist = zip([p1, p2, p3, p4, p5], permut)
expr = template.subs(subslist)
assert substitute_dummies(expr) == substitute_dummies(base)
def test_internal_external_VT2T2():
ii, jj = symbols('i j', below_fermi=True)
aa, bb = symbols('a b', above_fermi=True)
k, l = symbols('k l', below_fermi=True, cls=Dummy)
c, d = symbols('c d', above_fermi=True, cls=Dummy)
v = Function('v')
t = Function('t')
dums = _get_ordered_dummies
exprs = [
v(k, l, c, d)*t(aa, c, ii, k)*t(bb, d, jj, l),
v(l, k, c, d)*t(aa, c, ii, l)*t(bb, d, jj, k),
v(k, l, d, c)*t(aa, d, ii, k)*t(bb, c, jj, l),
v(l, k, d, c)*t(aa, d, ii, l)*t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
v(k, l, c, d)*t(aa, c, ii, k)*t(d, bb, jj, l),
v(l, k, c, d)*t(aa, c, ii, l)*t(d, bb, jj, k),
v(k, l, d, c)*t(aa, d, ii, k)*t(c, bb, jj, l),
v(l, k, d, c)*t(aa, d, ii, l)*t(c, bb, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
v(k, l, c, d)*t(c, aa, ii, k)*t(bb, d, jj, l),
v(l, k, c, d)*t(c, aa, ii, l)*t(bb, d, jj, k),
v(k, l, d, c)*t(d, aa, ii, k)*t(bb, c, jj, l),
v(l, k, d, c)*t(d, aa, ii, l)*t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_internal_external_VT2T2():
ii, jj = symbols("i j", below_fermi=True)
aa, bb = symbols("a b", above_fermi=True)
k, l = symbols("k l", below_fermi=True, cls=Dummy)
c, d = symbols("c d", above_fermi=True, cls=Dummy)
v = Function("v")
t = Function("t")
dums = _get_ordered_dummies
exprs = [
v(k, l, c, d) * t(aa, c, ii, k) * t(bb, d, jj, l),
v(l, k, c, d) * t(aa, c, ii, l) * t(bb, d, jj, k),
v(k, l, d, c) * t(aa, d, ii, k) * t(bb, c, jj, l),
v(l, k, d, c) * t(aa, d, ii, l) * t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
v(k, l, c, d) * t(aa, c, ii, k) * t(d, bb, jj, l),
v(l, k, c, d) * t(aa, c, ii, l) * t(d, bb, jj, k),
v(k, l, d, c) * t(aa, d, ii, k) * t(c, bb, jj, l),
v(l, k, d, c) * t(aa, d, ii, l) * t(c, bb, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
exprs = [
v(k, l, c, d) * t(c, aa, ii, k) * t(bb, d, jj, l),
v(l, k, c, d) * t(c, aa, ii, l) * t(bb, d, jj, k),
v(k, l, d, c) * t(d, aa, ii, k) * t(bb, c, jj, l),
v(l, k, d, c) * t(d, aa, ii, l) * t(bb, c, jj, k),
]
for permut in exprs[1:]:
assert dums(exprs[0]) != dums(permut)
assert substitute_dummies(exprs[0]) == substitute_dummies(permut)
def test_substitute_dummies_without_dummies():
i, j = symbols('i,j')
assert substitute_dummies(att(i, j) + 2) == att(i, j) + 2
assert substitute_dummies(att(i, j) + 1) == att(i, j) + 1
def main():
print
print "Calculates the Coupled-Cluster energy- and amplitude equations"
print "See 'An Introduction to Coupled Cluster Theory' by"
print "T. Daniel Crawford and Henry F. Schaefer III"
print "http://www.ccc.uga.edu/lec_top/cc/html/review.html"
print
# setup hamiltonian
p, q, r, s = symbols("pqrs", dummy=True)
f = AntiSymmetricTensor("f", (p,), (q,))
pr = NO((Fd(p) * F(q)))
v = AntiSymmetricTensor("v", (p, q), (r, s))
pqsr = NO(Fd(p) * Fd(q) * F(s) * F(r))
H = f * pr
# Uncomment the next line to use a 2-body hamiltonian:
# H=f*pr + Number(1,4)*v*pqsr
print "Using the hamiltonian:", latex(H)
print "Calculating nested commutators"
C = Commutator
T1, T2 = get_CC_operators()
T = T1 + T2
print "comm1..."
comm1 = wicks(C(H, T), simplify_dummies=True, simplify_kronecker_deltas=True)
T1, T2 = get_CC_operators()
T = T1 + T2
print "comm2..."
comm2 = wicks(C(comm1, T), simplify_dummies=True, simplify_kronecker_deltas=True)
T1, T2 = get_CC_operators()
T = T1 + T2
print "comm3..."
comm3 = wicks(C(comm2, T), simplify_dummies=True, simplify_kronecker_deltas=True)
T1, T2 = get_CC_operators()
T = T1 + T2
print "comm4..."
comm4 = wicks(C(comm3, T), simplify_dummies=True, simplify_kronecker_deltas=True)
print "construct Hausdoff expansion..."
eq = H + comm1 + comm2 / 2 + comm3 / 6 + comm4 / 24
eq = eq.expand()
eq = evaluate_deltas(eq)
eq = substitute_dummies(eq, new_indices=True, reverse_order=False, pretty_indices=pretty_dummies_dict)
print "*********************"
print
print "extracting CC equations from full Hbar"
i, j, k, l = symbols("ijkl", below_fermi=True)
a, b, c, d = symbols("abcd", above_fermi=True)
print
print "CC Energy:"
print latex(wicks(eq, simplify_dummies=True, keep_only_fully_contracted=True))
print
print "CC T1:"
eqT1 = wicks(NO(Fd(i) * F(a)) * eq, simplify_kronecker_deltas=True, keep_only_fully_contracted=True)
eqT1 = substitute_dummies(eqT1, reverse_order=False)
print latex(eqT1)
print
print "CC T2:"
eqT2 = wicks(
NO(Fd(i) * Fd(j) * F(b) * F(a)) * eq,
simplify_dummies=True,
keep_only_fully_contracted=True,
simplify_kronecker_deltas=True,
)
P = PermutationOperator
eqT2 = simplify_index_permutations(eqT2, [P(a, b), P(i, j)])
print latex(eqT2)
def test_substitute_dummies_new_indices():
i, j = symbols("i j", below_fermi=True, cls=Dummy)
a, b = symbols("a b", above_fermi=True, cls=Dummy)
p, q = symbols("p q", cls=Dummy)
f = Function("f")
assert substitute_dummies(f(i, a, p) - f(j, b, q), new_indices=True) == 0
def test_substitute_dummies_SQ_operator():
i, j = symbols("i j", cls=Dummy)
assert substitute_dummies(att(i, j) * Fd(i) * F(j) - att(j, i) * Fd(j) * F(i)) == 0
def test_substitute_dummies_without_dummies():
i, j = symbols("i,j")
assert substitute_dummies(att(i, j) + 2) == att(i, j) + 2
assert substitute_dummies(att(i, j) + 1) == att(i, j) + 1
def test_substitute_dummies_SQ_operator():
i, j = symbols('i j', cls=Dummy)
assert substitute_dummies(att(i, j)*Fd(i)*F(j)
- att(j, i)*Fd(j)*F(i)) == 0
T_2 = sum(get_ccsd_t_operators()) T_t = sum(get_ccsd_t_operators(ast_symb="t(t)")) T_t_2 = sum(get_ccsd_t_operators(ast_symb="t(t)")) L = sum(get_ccsd_lambda_operators()) L_t = sum(get_ccsd_lambda_operators(ast_symb="l(t)")) tilde_t_eq = Rational(1, 1) tilde_t_eq += eval_equation(-L_t * T_t) tilde_t_eq += eval_equation(L_t * T) tilde_t_eq += eval_equation(-L_t * T_t * T) tilde_t_eq += eval_equation(Rational(1, 2) * L_t * T_t * T_t_2) tilde_t_eq += eval_equation(Rational(1, 2) * L_t * T * T_2) tilde_t_eq = tilde_t_eq.expand() tilde_t_eq = evaluate_deltas(tilde_t_eq) tilde_t_eq = substitute_dummies(tilde_t_eq, **sub_kwargs) tilde_eq = Rational(1, 1) tilde_eq += eval_equation(-L * T) tilde_eq += eval_equation(L * T_t) tilde_eq += eval_equation(-L * T * T_t) tilde_eq += eval_equation(Rational(1, 2) * L * T * T_2) tilde_eq += eval_equation(Rational(1, 2) * L * T_t * T_t_2) tilde_eq = tilde_eq.expand() tilde_eq = evaluate_deltas(tilde_eq) tilde_eq = substitute_dummies(tilde_eq, **sub_kwargs) print(latex(tilde_t_eq)) print(latex(tilde_eq))
def test_substitute_dummies_new_indices():
i, j = symbols("i j", below_fermi=True, cls=Dummy)
a, b = symbols("a b", above_fermi=True, cls=Dummy)
p, q = symbols("p q", cls=Dummy)
f = Function("f")
assert substitute_dummies(f(i, a, p) - f(j, b, q), new_indices=True) == 0
def test_substitute_dummies_NO_operator():
i, j = symbols("i j", cls=Dummy)
assert substitute_dummies(att(i, j) * NO(Fd(i) * F(j)) - att(j, i) * NO(Fd(j) * F(i))) == 0
def test_substitute_dummies_new_indices():
i, j = symbols('i j', below_fermi=True, cls=Dummy)
a, b = symbols('a b', above_fermi=True, cls=Dummy)
p, q = symbols('p q', cls=Dummy)
f = Function('f')
assert substitute_dummies(f(i, a, p) - f(j, b, q), new_indices=True) == 0
def test_substitute_dummies_NO_operator():
i, j = symbols('i j', cls=Dummy)
assert substitute_dummies(att(i, j)*NO(Fd(i)*F(j))
- att(j, i)*NO(Fd(j)*F(i))) == 0
def main():
print()
print("Calculates the Coupled-Cluster energy- and amplitude equations")
print("See 'An Introduction to Coupled Cluster Theory' by")
print("T. Daniel Crawford and Henry F. Schaefer III")
print("http://www.ccc.uga.edu/lec_top/cc/html/review.html")
print()
# setup hamiltonian
p, q, r, s = symbols('p,q,r,s', cls=Dummy)
f = AntiSymmetricTensor('f', (p,), (q,))
pr = NO((Fd(p)*F(q)))
v = AntiSymmetricTensor('v', (p, q), (r, s))
pqsr = NO(Fd(p)*Fd(q)*F(s)*F(r))
H = f*pr + Rational(1, 4)*v*pqsr
print("Using the hamiltonian:", latex(H))
print("Calculating 4 nested commutators")
C = Commutator
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 1...")
comm1 = wicks(C(H, T))
comm1 = evaluate_deltas(comm1)
comm1 = substitute_dummies(comm1)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 2...")
comm2 = wicks(C(comm1, T))
comm2 = evaluate_deltas(comm2)
comm2 = substitute_dummies(comm2)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 3...")
comm3 = wicks(C(comm2, T))
comm3 = evaluate_deltas(comm3)
comm3 = substitute_dummies(comm3)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 4...")
comm4 = wicks(C(comm3, T))
comm4 = evaluate_deltas(comm4)
comm4 = substitute_dummies(comm4)
print("construct Hausdoff expansion...")
eq = H + comm1 + comm2/2 + comm3/6 + comm4/24
eq = eq.expand()
eq = evaluate_deltas(eq)
eq = substitute_dummies(eq, new_indices=True,
pretty_indices=pretty_dummies_dict)
print("*********************")
print()
print("extracting CC equations from full Hbar")
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
print()
print("CC Energy:")
print(latex(wicks(eq, simplify_dummies=True,
keep_only_fully_contracted=True)))
print()
print("CC T1:")
eqT1 = wicks(NO(Fd(i)*F(a))*eq, simplify_kronecker_deltas=True, keep_only_fully_contracted=True)
eqT1 = substitute_dummies(eqT1)
print(latex(eqT1))
print()
print("CC T2:")
eqT2 = wicks(NO(Fd(i)*Fd(j)*F(b)*F(a))*eq, simplify_dummies=True, keep_only_fully_contracted=True, simplify_kronecker_deltas=True)
P = PermutationOperator
eqT2 = simplify_index_permutations(eqT2, [P(a, b), P(i, j)])
print(latex(eqT2))
T1,T2 = get_CC_operators()
T = T1+ T2
print "comm3..."
comm3 = wicks(C(comm2,T),simplify_dummies=True, simplify_kronecker_deltas=True)
T1,T2 = get_CC_operators()
T = T1+ T2
print "comm4..."
comm4 = wicks(C(comm3,T),simplify_dummies=True, simplify_kronecker_deltas=True)
print "construct Hausdoff expansion..."
eq = H + comm1+comm2/2+comm3/6+comm4/24
eq = eq.expand()
eq = evaluate_deltas(eq)
eq = substitute_dummies(eq, new_indices=True, reverse_order=False)
print "*********************"
print
print "extracting CC equations from full Hbar"
i,j,k,l = symbols('ijkl',below_fermi=True)
a,b,c,d = symbols('abcd',above_fermi=True)
print
print "CC Energy:"
print latex(wicks(eq, simplify_dummies=True,
keep_only_fully_contracted=True))
print
print "CC T1:"
eqT1 = wicks(NO(Fd(i)*F(a))*eq, simplify_kronecker_deltas=True, keep_only_fully_contracted=True)
eqT1 = substitute_dummies(eqT1,reverse_order=False)
print latex(eqT1)
def test_substitute_dummies_new_indices():
i, j = symbols('i j', below_fermi=True, cls=Dummy)
a, b = symbols('a b', above_fermi=True, cls=Dummy)
p, q = symbols('p q', cls=Dummy)
f = Function('f')
assert substitute_dummies(f(i, a, p) - f(j, b, q), new_indices=True) == 0
def main():
print()
print("Calculates the Coupled-Cluster energy- and amplitude equations")
print("See 'An Introduction to Coupled Cluster Theory' by")
print("T. Daniel Crawford and Henry F. Schaefer III")
print(
"Reference to a Lecture Series: http://vergil.chemistry.gatech.edu/notes/sahan-cc-2010.pdf"
)
print()
# setup hamiltonian
p, q, r, s = symbols('p,q,r,s', cls=Dummy)
f = AntiSymmetricTensor('f', (p, ), (q, ))
pr = NO(Fd(p) * F(q))
v = AntiSymmetricTensor('v', (p, q), (r, s))
pqsr = NO(Fd(p) * Fd(q) * F(s) * F(r))
H = f * pr + Rational(1, 4) * v * pqsr
print("Using the hamiltonian:", latex(H))
print("Calculating 4 nested commutators")
C = Commutator
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 1...")
comm1 = wicks(C(H, T))
comm1 = evaluate_deltas(comm1)
comm1 = substitute_dummies(comm1)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 2...")
comm2 = wicks(C(comm1, T))
comm2 = evaluate_deltas(comm2)
comm2 = substitute_dummies(comm2)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 3...")
comm3 = wicks(C(comm2, T))
comm3 = evaluate_deltas(comm3)
comm3 = substitute_dummies(comm3)
T1, T2 = get_CC_operators()
T = T1 + T2
print("commutator 4...")
comm4 = wicks(C(comm3, T))
comm4 = evaluate_deltas(comm4)
comm4 = substitute_dummies(comm4)
print("construct Hausdorff expansion...")
eq = H + comm1 + comm2 / 2 + comm3 / 6 + comm4 / 24
eq = eq.expand()
eq = evaluate_deltas(eq)
eq = substitute_dummies(eq,
new_indices=True,
pretty_indices=pretty_dummies_dict)
print("*********************")
print()
print("extracting CC equations from full Hbar")
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
print()
print("CC Energy:")
print(
latex(wicks(eq, simplify_dummies=True,
keep_only_fully_contracted=True)))
# print("HERE")
# print("HERE")
# print("HERE")
# print(pycode(wicks(eq, simplify_dummies=True,
# keep_only_fully_contracted=True)))
# with open("cc_energy.py", "w") as f:
# f.
with open("ccsd.jl", "w") as f:
eq_energy = wicks(eq,
simplify_dummies=True,
keep_only_fully_contracted=True)
f.write(julia_code(eq_energy))
print()
print("CC T1:")
eqT1 = wicks(NO(Fd(i) * F(a)) * eq,
simplify_kronecker_deltas=True,
keep_only_fully_contracted=True)
eqT1 = substitute_dummies(eqT1)
print(latex(eqT1))
print()
print("CC T2:")
eqT2 = wicks(NO(Fd(i) * Fd(j) * F(b) * F(a)) * eq,
simplify_dummies=True,
keep_only_fully_contracted=True,
simplify_kronecker_deltas=True)
# P = PermutationOperator
# eqT2 = simplify_index_permutations(eqT2, [P(a, b), P(i, j)])
print(latex(eqT2))
print(latex(simplify(eqT2)))