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# rename_dummies tests
def test01():
__cdbkernel__=create_scope()
{m,n,p,q}::Indices("one").
{a,b,c,d}::Indices("two").
ex:= A_{m} A^{m} + B_{m} C^{m} + A_{n} A^{n} + Q_{c d} R^{d c}.
rename_dummies(ex, "one", "two")
tst:= 2 A_{a} A^{a} + B_{a} C^{a} + Q_{c d} R^{d c} - @(ex).
assert tst == 0, tst
print("Test 01 passed")
test01()
def test02a():
__cdbkernel__=create_scope()
{n,p,q}::Indices("one").
{m,n,p,q,r,s,t}::Indices("two").
ex:= A_{r} = A_{m r} A^{m} + A_{n r} A^{n} + A_{s r} A^{s}.
rename_dummies(ex, "two", "one")
assert ex == $A_{r} = 3A_{n r} A^{n}$, ex
print("Test 02a passed")
test02a()
def test02b():
__cdbkernel__ = create_scope()
{a, b, c, d, e, f}::Indices("one").
{\alpha, \beta, \gamma, \delta}::Indices("two")
ex1 := A_{a a \alpha \alpha};
rename_dummies(ex1, "two", "one")
assert ex1 == $A_{a a b b}$
ex2 := A_{a a \alpha \alpha};
rename_dummies(ex2, "one", "two")
assert ex2 == $A_{\beta \beta \alpha \alpha}$
print("Test 02b passed")
test02b()
# expand_dummies tests
def test03():
__cdbkernel__ = create_scope()
{t, x}::Coordinate.
{\mu, \nu, \rho}::Indices(vector, values={t, x}).
ex := A_{\mu} A^{\mu}.
expand_dummies(ex)
assert ex == $A_{t}A^{t} + A_{x}A^{x}$, ex
print("Test 03 passed")
test03()
def test04():
__cdbkernel__ = create_scope()
{t, x}::Coordinate.
{\mu, \nu, \rho}::Indices(vector, values={t, x}).
ex := g^{\mu \nu} A_{\nu}.
expand_dummies(ex)
assert ex == $g^{\mu t} A_{t} + g^{\mu x} A_{x}$, ex
print("Test 04 passed")
test04()
def test05():
__cdbkernel__ = create_scope()
{t, x, y, z}::Coordinate.
{\mu, \nu, \rho, \lambda}::Indices(vector, values={t, x, y, z}).
mink := g_{t t} = -1, g_{x x} = 1, g_{y y} = 1, g_{z z} = 1.
ex := g_{\mu \rho} g_{\mu \lambda} k^{\rho} k^{\lambda}.
expand_dummies(ex, mink)
assert ex == $k^{t}k^{t} + k^{x}k^{x} + k^{y}k^{y} + k^{z}k^{z}$, ex
print("Test 05 passed")
test05()
def test06():
__cdbkernel__ = create_scope()
{t, x}::Coordinate.
{\mu, \nu, \rho, \lambda}::Indices(vector, values={t, x}).
components := A_{t t} = a1, A_{x x} = a2, B_{x t} = b.
ex := A_{\mu \nu}B_{\mu \nu}.
expand_dummies(ex, components, False)
assert ex == $a1 B_{t t} + A_{x t} b + A_{t x} B_{t x} + a2 B_{x x}$, ex
print("Test 06 passed")
test06()
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