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def test01():
__cdbkernel__=create_scope()
{m, n, p, q, r}::Indices(vector, position=fixed).
{m, n, p, q, r}::Integer(0..9).
g_{m n}::Metric.
g^{m n}::InverseMetric.
g_{m}^{n}::KroneckerDelta.
g^{m}_{n}::KroneckerDelta.
obj10:= g_{m p} g^{p m};
eliminate_metric(_);
eliminate_kronecker(_);
tst10:= 10 - @(obj10);
assert(tst10==0)
print("Test 01 passed")
test01()
def test02():
__cdbkernel__=create_scope()
{m, n, p, q, r}::Indices(vector, position=fixed).
g_{m n}::Metric.
g^{m n}::InverseMetric.
obj11b:= 3 g_{m p} g^{m p};
eliminate_metric(_);
tst11b:= 3 g_{p}^{p} - @(obj11b);
assert(tst11b==0)
print("Test 02 passed")
test02()
# Eliminating metrics in presence of derivatives.
def test03():
__cdbkernel__=create_scope()
{m, n, p, q, r}::Indices(vector, position=fixed).
g_{m n}::Metric.
\partial{#}::Derivative.
obj12a:= g_{m n} \partial_{p}{ A^{n} };
eliminate_metric(_);
tst12a:= \partial_{p}{ A_{m} } - @(obj12a);
assert(tst12a==0)
print("Test 03 passed")
test03()
def test04():
__cdbkernel__=create_scope()
{m, n, p, q, r}::Indices(vector, position=fixed).
g_{m n}::Metric.
\partial{#}::Derivative.
g_{m n}::Depends(\partial{#}).
obj12b:= g_{m n} \partial_{p}{ A^{n} };
eliminate_metric(_);
tst12b:= g_{m n} \partial_{p}{ A^{n} } - @(obj12b);
assert(tst12b==0)
print("Test 04 passed")
test04()
# Reported bug with eliminate_metric.
# {a,b,c,d,e,i,j,k}::Indices(curved).
# g^{a b}::InverseMetric.
# \nabla{#}::Derivative.
# h_{a b}::Symmetric.
# ex:=g^{a k} * \nabla_{b}{h_{k c}} +g^{a k} * \nabla_{c}{h_{k b}};
# eliminate_metric(_);
def test05():
__cdbkernel__=create_scope()
{ m, n, p }::Indices(flat, position=fixed).
{ \mu, \nu, \rho, \sigma, \kappa }::Indices(curved, position=fixed).
obj:= H_{m n p} ( B^{m n p} + H^{m n p} );
rewrite_indices(_, $H_{\mu\nu\rho}$, $e_{m}^{\mu}$);
tst:= H_{\mu \nu \rho} * ( B^{m n p} + H^{m n p} ) * e_{m}^{\mu} * e_{n}^{\nu} * e_{p}^{\rho} - @(obj);
assert(tst==0)
print("Test 05 passed")
test05()
def test06():
__cdbkernel__=create_scope()
{ m, n, p }::Indices(flat).
{ \mu, \nu, \rho, \mu# }::Indices(curved, position=fixed).
obj:= H_{m n p} [ B^{m n p} + H^{m n p} ];
rewrite_indices(_, $H_{\mu\nu\rho}$, $e_{m \mu}$);
tst:= H_{m n p} [ B^{m n p} + H^{m n p} ] - @(obj);
assert(tst==0)
print("Test 06 passed")
test06()
def test08():
__cdbkernel__=create_scope()
{ m,n,p,q,r,s,t,u }::Indices(curved, position=fixed).
obj:= B_{m n p} B^{m n q} C_{q};
rewrite_indices(_, $B_{m n p}$, $g^{m n}$);
tst:= B_{m n p} B_{r s t} C_{q} g^{m r} g^{n s} g^{q t} - @(obj);
assert(tst==0)
print("Test 08 passed")
test08()
def test09():
__cdbkernel__=create_scope()
{ m,n,p,q,r,s,t,u }::Indices(curved, position=free).
obj:= B_{m n p} B_{m n q} C_{q};
rewrite_indices(_, $B_{m n p}$, $g^{m n}$);
tst:= B_{m n p} B_{m n q} C_{q} - @(obj);
assert(tst==0)
print("Test 09 passed")
test09()
def test10():
__cdbkernel__=create_scope()
{m,n,p,q,r,s}::Indices(curved, position=fixed).
ex:=H_{m n p};
rewrite_indices(_, $H^{m n p}$, $g_{m n}$);
tst:=H^{q r s} g_{m q} g_{n r} g_{p s} - @(ex);
assert(tst==0)
print("Test 10 passed")
test10()
def test11():
__cdbkernel__=create_scope()
{a, b, c, d, e, f}::Indices(position=fixed).
\eta_{a b}::Metric.
ex:=F_{a}^{b} G_{b c} + F^{b d}G_{d a c b};
rewrite_indices(_, $F_{a b}$, $\eta^{a b}$);
tst:=F_{a d} G_{b c} \eta^{b d} + F_{e f} G_{d a c b} \eta^{b e} \eta^{d f} - @(ex);
assert(tst==0)
print("Test 11 passed")
test11()
def test12():
__cdbkernel__=create_scope()
x::Coordinate.
{a, b}::Indices(position=fixed).
{a, b}::Integer(0..3).
g_{a b}::Metric.
g^{a b}::InverseMetric.
g^{\mu?}_{\nu?}::KroneckerDelta.
g_{\mu?}^{\nu?}::KroneckerDelta.
\hat{#}::Accent.
ex:=\hat{g^{a b}} \hat{g_{a b}};
eliminate_metric(_);
eliminate_kronecker(_);
tst:= 4 - @(ex);
assert(tst==0)
print("Test 12 passed")
test12()
def test13():
__cdbkernel__=create_scope()
{ m, n, p }::Indices(flat).
{ \mu, \nu, \rho }::Indices(curved).
e^{m}_{\mu}::Vielbein.
ex:= H_{m n p} e^{m}_{\mu} e^{p}_{\rho};
eliminate_vielbein(_, repeat=True);
tst:= H_{\mu n \rho} - @(ex);
assert(tst==0)
print("Test 13 passed")
test13()
def test14():
__cdbkernel__=create_scope()
{a,b,c,d,e,f}::Indices(position=fixed);
g_{a b}::Metric().
g^{a b}::InverseMetric().
A:=X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f};
eliminate_metric(_, repeat=True)
tst:= X^{f} - @(A);
assert(tst==0)
print("Test 14a passed")
A:=X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f};
eliminate_metric(_, repeat=True, redundant=True)
tst:= X_{e} g^{e f} - @(A);
assert(tst==0)
print("Test 14b passed")
test14()
# { m, n, p }::Indices(flat).
# { \mu, \nu, \rho }::Indices(curved).
# e^{m}_{\mu}::Vielbein.
# e_{m}^{\mu}::InverseVielbein.
# ex:= e_{m}^{\mu} e^{m}_{\nu};
# eliminate_vielbein(_);
# def post_process(ex):
# substitute(ex, $\delta^{0}_{\alpha} -> 0$)
# return ex
#
# {a,b,c,d,e}::Indices(fourD, position=independent);
# {a,b,c,d,e}::Integer(0..4);
# {\alpha,\beta,\gamma,\delta,\epsilon}::Indices(threeD, position=independent, parent=fourD);
# {\alpha,\beta,\gamma,\delta,\epsilon}::Integer(1..3);
# \delta{#}::KroneckerDelta();
# ex := \gamma^{\alpha \beta} \delta^{0}_{d} \delta^{d}_{\alpha};
# eliminate_kronecker(ex, repeat=False);
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