def test_make_grad(self):
ga, e_1, e_2, e_3 = Ga.build('e*1|2|3',
g=[1, 1, 1],
coords=symbols('x y z'))
r = ga.mv(ga.coord_vec)
assert ga.make_grad(r) == ga.grad
assert ga.make_grad(r, cmpflg=True) == ga.rgrad
x = ga.mv('x', 'vector')
B = ga.mv('B', 'bivector')
dx = ga.make_grad(x)
dB = ga.make_grad(B)
# GA4P, eq. (6.29)
for a in [ga.mv(1), e_1, e_1 ^ e_2]:
r = a.i_grade
assert dx * (x ^ a) == (ga.n - r) * a
assert dx * (x * a) == ga.n * a
# derivable via the product rule
assert dx * (x * x) == 2 * x
assert dx * (x * x * x) == (2 * x) * x + (x * x) * ga.n
assert dB * (B * B) == 2 * B
assert dB * (B * B * B) == (2 * B) * B + (B * B) * ga.n
# an arbitrary chained expression to check we do not crash
assert dB * dx * (B * x) == -3
assert dx * dB * (x * B) == -3
assert dx * dB * (B * x) == 9
assert dB * dx * (x * B) == 9
def make_vector(a, n=3, ga=None):
if isinstance(a, str):
v = zero
for i in range(n):
a_i = Symbol(a + str(i + 1))
v += a_i * ga.basis[i]
v = ga.mv(v)
return (F(v))
else:
return (F(a))
def make_vector(a, n=3, ga=None):
if isinstance(a,str):
v = zero
for i in range(n):
a_i = Symbol(a+str(i+1))
v += a_i*ga.basis[i]
v = ga.mv(v)
return(F(v))
else:
return(F(a))