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def test01():
__cdbkernel__=create_scope()
\partial{#}::PartialDerivative;
a::Depends(\partial{#});
ex:= \int{ \partial_{0}{a} \partial_{0}{a} }{x};
integrate_by_parts(_, $a$)
tst:= \int{ -a \partial_{0 0}{a} }{x} - @(ex);
assert(tst==0)
print("Test 01 passed")
test01()
def test02():
__cdbkernel__=create_scope()
\partial{#}::PartialDerivative;
a::Depends(\partial{#});
ex:= \int{ a \partial_{0}{\partial_{0}{a}} }{x};
integrate_by_parts(_, $\partial_{0}{a}$)
tst:= \int{ - \partial_{0}{a} \partial_{0}{a} }{x} - @(ex);
assert(tst==0)
print("Test 02 passed")
test02()
def test03():
__cdbkernel__=create_scope()
\nabla{#}::Derivative;
a::Depends(\nabla{#});
ex:= \int{ a \nabla_{0}{\nabla_{0}{a}} }{x};
integrate_by_parts(_, $a$)
tst:= \int{ a \nabla_{0}{\nabla_{0}{a}} }{x} - @(ex);
assert(tst==0)
print("Test 03 passed")
test03()
def test04():
__cdbkernel__=create_scope()
\partial{#}::PartialDerivative;
ex:= \int{ a \partial_{0 0}{b} c }{x};
integrate_by_parts(_, $b$)
tst:= \int{ a \partial_{0 0}{b} c }{x} - @(ex);
assert(tst==0)
print("Test 04 passed")
test04()
def test05():
__cdbkernel__=create_scope()
\partial{#}::PartialDerivative;
ex:= \int{ A_{i j} }{x};
integrate_by_parts(_, $h$)
tst:= \int{ A_{i j} }{x} - @(ex);
assert(tst==0)
print("Test 05a passed")
ex:= \int{ h A_{i j} }{x};
integrate_by_parts(_, $h$)
tst:= \int{ h A_{i j} }{x} - @(ex);
assert(tst==0)
print("Test 05b passed")
\partial{#}::PartialDerivative;
ex:= \int{ A_{i j} + \partial_{i j}{h} }{x};
integrate_by_parts(_, $h$)
tst:= \int{ A_{i j} }{x} - @(ex);
assert(tst==0)
print("Test 05c passed")
test05()
def test06():
__cdbkernel__=create_scope()
\partial{#}::Derivative;
\tau::Coordinate;
{t,r}::Depends(\partial{#});
\delta{#}::Accent;
ex:=\int{ \partial{\delta{t}} \partial{t} r }{\tau};
integrate_by_parts(ex, $\delta{t}$)
tst:= - \int{ \delta{t} \partial{ \partial{t} r} }{\tau} - @(ex);
assert(tst==0)
print("Test 06 passed")
test06()
def test07():
__cdbkernel__=create_scope()
{A,B,C,D,E,F,F#}::Indices(full);
{a,b,c,d,e,f,f#}::Indices(space1);
{m,n,o,p,q,r,r#}::Indices(space2);
\partial{#}::PartialDerivative.
\delta{#}::Accent.
F_{A B C}::AntiSymmetric.
F_{a b c}::AntiSymmetric.
F_{m n p}::AntiSymmetric.
F_{#}::Depends(\partial{#}).
ex:=\int{ c_{0} \partial_{a d}{ \delta{F_{a b c}}} F_{d b c}
+ 2 c_{1} \partial_{a c}{ \delta{F_{m a b}}} F_{m c b} }{x};
integrate_by_parts(ex, $\partial_{n?}{\delta{F_{m? a b}}}$)
tst:=\int{ -\partial_{a}{c_{0}} \partial_{d}{\delta{F_{a b c}}} F_{d b c}
- c_{0} \partial_{d}{\delta{F_{a b c}}} \partial_{a}{ F_{d b c} }
- 2 \partial_{a}{c_{1}} \partial_{c}{\delta{F_{m a b}}} F_{m c b}
- 2 c_{1} \partial_{c}{\delta{F_{m a b}}} \partial_{a}{ F_{m c b} } }{x} - @(ex);
assert(tst==0)
print("Test 07 passed")
test07()
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