def test_GenericVector_check_Metric():
syms = symbols("t x y z")
t, x, y, z = syms
obj = GenericVector([t, x, y, z],
syms=syms,
config="u",
parent_metric=None)
obj.change_config("u", None)
def test_GenericVector_change_config_theoretical_test():
# https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors#Definition
a, b, th = symbols("a b theta")
metric = euclidean_space_metric()
# defining a contravariant vector
cnvec = GenericVector([a, b], metric.syms, config="u", parent_metric=metric)
covec = cnvec.change_config("l") # get contravariant vector
assert simplify(covec.tensor()[0] - (a + b * cos(th))) == 0
assert simplify(covec.tensor()[1] - (b + a * cos(th))) == 0
def test_GenericVector_check_ValueErrors():
a, b = symbols("a b")
syms = symbols("e1 e2")
# input a tensor with wring rank
try:
arr = [[a, b], [b, 1]]
v1 = GenericVector(arr, syms, "l")
boolstore = False
except ValueError:
boolstore = True
assert boolstore
# input a wrong length config
try:
arr = [a, b]
v2 = GenericVector(arr, syms, "uu")
boolstore = False
except ValueError:
boolstore = True
assert boolstore
def get_vector():
syms = symbols("t x y z")
t, x, y, z = syms
return GenericVector([t, x, y, z], syms=syms, config="u")