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def test01():
__cdbkernel__=create_scope()
{a,b,c,d}::Indices(type1);
{m,n,p,q}::Indices(type2);
A::ImplicitIndex(A_{m n});
C::ImplicitIndex(C_{m n});
D::ImplicitIndex(D_{a b});
ex:= D C A D;
sort_product(_)
tst:= C A D D - @(ex);
assert(tst==0)
print("Test 01 passed")
test01()
def test02():
__cdbkernel__=create_scope()
{a,b,c,d}::Indices(spinor);
Tr{#}::Trace(indices=spinor);
A::ImplicitIndex(A_{a b});
B::ImplicitIndex(B_{a b});
ex:= Tr( A B A C B ) - Tr( C );
untrace(_)
tst:= C Tr( A B A B ) - C Tr(1) - @(ex);
assert(tst==0)
print("Test 02 passed")
test02()
def test03():
__cdbkernel__=create_scope()
{a,b,c,d}::Indices(spinor);
\sigma^{\mu}::ImplicitIndex(\sigma^{\mu a}_{b});
Tr{#}::Trace(indices=spinor);
ex:= Tr( \sigma^{\mu} q \sigma^{\nu} );
untrace(_)
tst:= q Tr( \sigma^{\mu} \sigma^{\nu} ) - @(ex);
assert(tst==0)
print("Test 03 passed")
test03()
def test04():
__cdbkernel__=create_scope()
{a,b}::Indices(spinor);
{m,n}::Indices(vector);
Tr{#}::Trace(indices=spinor);
A::ImplicitIndex(A_{a b});
B::ImplicitIndex(B_{m n});
A::Traceless(indices=spinor);
B::Traceless(indices=vector);
ex:=Tr( A ) + Tr( B );
canonicalise(_)
tst:= Tr( B ) - @(ex);
assert(tst==0)
print("Test 04 passed")
test04()
def test05():
__cdbkernel__=create_scope()
{a,b,c,d}::Indices(vector);
ex:=(A)_{a b} (B)_{b c} (C)_{c d};
combine(_)
tst:= (A B C)_{a d} - @(ex);
assert(tst==0)
print("Test 05 passed")
test05()
def test06():
__cdbkernel__=create_scope()
{a,b}::Indices(vector);
ex:=(A)_{a b} (B)_{b a};
combine(_)
tst:= (B A)_{b b} - @(ex);
assert(tst==0)
print("Test 06 passed")
test06()
def test07():
__cdbkernel__=create_scope()
{a,b}::Indices(vector);
Tr{#}::Trace(indices=vector);
ex:=(A)_{a b} (B)_{b a};
combine(_, trace_op=$Tr$)
tst:= Tr( B A ) - @(ex);
assert(tst==0)
print("Test 07 passed")
test07()
def test08():
__cdbkernel__=create_scope()
{a,b}::Indices(vector);
{A,B}::AntiCommuting;
ex:=(A)_{a b} (B)_{b a};
combine(_)
tst:= \indexbracket{-B A}_{b b} - @(ex);
assert(tst==0)
print("Test 08 passed")
test08()
def test09():
__cdbkernel__=create_scope()
{m,n}::Indices(vector);
{a,b,c}::Indices(spinor, position=fixed);
\Gamma^{m}::ImplicitIndex(\Gamma^{m a}_{b});
\Gamma^{m}::Matrix;
ex:=(\Gamma^{m} \Gamma^{n})^{a}_{c};
expand(_)
tst:= (\Gamma^{m})^{a}_{b} (\Gamma^{n})^{b}_{c} - @(ex);
assert(tst==0)
print("Test 09 passed")
test09()
def test10():
__cdbkernel__=create_scope()
{a,b}::Indices(vector);
ex:=(u)_{a} (M)^{a b} (v)_{b};
combine(_)
tst:= \indexbracket(u M v) - @(ex);
assert(tst==0)
print("Test 10 passed")
if sys.platform == "darwin":
print("Skipping test 10, segfault on Darwin.")
else:
test10()
def test11():
__cdbkernel__=create_scope()
{a,b,c}::Indices(vector);
ex:=(B)_{b c} (A)_{a b};
combine(_)
tst:= (A B)_{a c} - @(ex);
assert(tst==0)
print("Test 11 passed")
test11()
def test12():
__cdbkernel__=create_scope()
{a,b}::Indices(vector);
Tr{#}::Trace(indices=vector);
A::ImplicitIndex(A_{a b});
B::ImplicitIndex(B_{a b});
{A_{a b}, B_{a b}, C, D}::AntiCommuting;
ex:=Tr( A C B D );
untrace(_)
sort_product(_)
tst:= -C D Tr( A B ) - @(ex);
assert(tst==0)
print("Test 12 passed")
test12()
def test13():
__cdbkernel__=create_scope()
{a,b}::Indices(vector);
Tr{#}::Trace(indices=vector);
A::ImplicitIndex(A_{a b});
B::ImplicitIndex(B_{a b});
{A_{a b}, B_{a b}}::AntiCommuting;
ex:=Tr( B A );
sort_product(_)
tst:= Tr( -A B ) - @(ex);
assert(tst==0)
print("Test 13 passed")
test13()
def test14():
__cdbkernel__=create_scope()
{A,B,C}::ImplicitIndex;
ex:=(B A C)_{a a};
sort_product(_)
tst:= (A C B)_{a a} - @(ex);
assert(tst==0)
print("Test 14 passed")
test14()
def test15():
__cdbkernel__=create_scope()
{\mu,\nu,\rho}::Indices(vector).
{a^{\mu},b^{\mu},c^{\mu}}::NonCommuting.
tr{#}::Trace.
ex:=tr(a^{\mu} b^{\nu} c^{\rho} a^{\mu} b^{\rho} c^{\nu}+b^{\mu} c^{\nu} a^{\rho} b^{\nu} c^{\mu} a^{\rho}+c^{\mu} a^{\nu} b^{\mu} c^{\rho} a^{\nu} b^{\rho});
sort_product(_)
rename_dummies(_)
tst:= 3 tr( a^{\mu} b^{\nu} c^{\rho} a^{\mu} b^{\rho} c^{\nu} ) - @(ex);
assert(tst==0)
print("Test 15 passed")
test15()
def test16():
__cdbkernel__=create_scope()
{\mu,\nu,\rho}::Indices(vector).
{a^{\mu},b^{\mu},c^{\mu}}::NonCommuting.
tr{#}::Trace.
ex:=tr( b^{\mu} c^{\nu} a^{\rho} b^{\nu} c^{\mu} a^{\rho} );
sort_product(_)
rename_dummies(_)
tst:= tr( a^{\mu} b^{\nu} c^{\rho} a^{\mu} b^{\rho} c^{\nu} ) - @(ex);
assert(tst==0)
print("Test 16 passed")
test16()
def test17():
__cdbkernel__=create_scope()
{A,B}::ImplicitIndex.
tr{#}::Trace.
ex:=tr( A B B A );
sort_product(_)
tst:= tr( A A B B ) - @(ex);
assert(tst==0)
print("Test 17 passed")
test17()
def test18():
__cdbkernel__=create_scope()
{\mu,\nu}::Indices(vector).
tr{#}::Trace.
{a^{\mu},b^{\mu}}::NonCommuting.
{a^{\mu},b^{\mu}}::SelfNonCommuting.
ex:=tr{a^{\mu} b^{\mu} b^{\nu} a^{\nu}} - tr{a^{\mu} a^{\nu} b^{\nu} b^{\mu} };
sort_product(_)
rename_dummies(_)
assert(ex==0)
print("Test 18 passed")
test18()
def test19():
__cdbkernel__=create_scope()
i::ImaginaryI;
A::ImplicitIndex.
tr{#}::Trace.
ex:= i tr(i A);
untrace(_, repeat=True)
tst:= -tr(A) - @(ex);
assert("Test 19 passed")
test19()
def test20():
__cdbkernel__=create_scope()
{\mu,\nu}::Indices(vector).
tr{#}::Trace.
ex:=A A tr{u^{\mu} u^{\nu}} tr{u^{\nu} u^{\mu}}- B B tr{u^{\mu} u^{\nu}} tr{u^{\mu} u^{\nu}};
collect_factors(_)
tst:= A**2 tr{u^{\mu} u^{\nu}} tr{u^{\nu} u^{\mu}}- B**2 tr{u^{\mu} u^{\nu}} tr{u^{\mu} u^{\nu}} - @(ex);
assert(tst==0)
print("Test 20 passed")
test20()
def test21():
__cdbkernel__=create_scope()
{\mu,\nu}::Indices(vector).
A^{\mu\nu}::Symmetric.
B^{\mu\nu}::AntiSymmetric.
tr{#}::Trace.
B^{\mu\nu}::ImplicitIndex.
\epsilon^{\mu\nu\rho\sigma}::EpsilonTensor.
ex:=A^{\mu\nu} tr{B^{\mu\nu}};
canonicalise(_)
assert ex==0
print("Test 21a passed")
ex:=\epsilon^{\mu\nu\rho\sigma} tr{A^{\mu\nu} B^{\rho\sigma}};
canonicalise(_)
assert ex==0
print("Test 21b passed")
ex:=\epsilon^{\mu\nu\rho\sigma} A^{\nu\mu} B^{\rho\sigma};
canonicalise(_)
assert ex==0
print("Test 21c passed")
ex:=\epsilon^{\mu\nu\rho\sigma} tr{ A^{\nu\mu} B^{\rho\sigma} };
canonicalise(_)
assert ex==0
print("Test 21d passed")
ex:=\epsilon^{\mu\nu\rho\sigma} tr{ A^{\nu\mu} B^{\rho\sigma} + A^{\mu\nu} B^{\rho\sigma} };
# FIXME: this does not work with repeat=True?
canonicalise(_)
canonicalise(_)
assert ex==0
print("Test 21e passed")
test21()
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