def test_from_str(self):
coords = symbols('x y', real=True)
g, e1, e2 = Ga.build('e*1|2', coords=coords, g=[1, 1])
a1 = g.mv('a1', 'vector')
a2 = g.mv('a2', 'vector')
a1x, a1y = a1.get_coefs(1)
a2x, a2y = a2.get_coefs(1)
# one-d
T = Mlt('T', g, nargs=1)
v = T(a1)
# Two new symbols created
Tx, Ty = sorted(v.free_symbols - {a1x, a1y}, key=lambda x: x.sort_key())
assert v == (
Tx * a1x +
Ty * a1y
)
# two-d
T = Mlt('T', g, nargs=2)
v = T(a1, a2)
# four new symbols created
Txx, Txy, Tyx, Tyy = sorted(v.free_symbols - {a1x, a1y, a2x, a2y}, key=lambda x: x.sort_key())
assert v == (
Txx * a1x * a2x +
Txy * a1x * a2y +
Tyx * a1y * a2x +
Tyy * a1y * a2y
)
def test_basic(self):
# from TensorDef.py
coords = symbols('t x y z', real=True)
st4d, g0, g1, g2, g3 = Ga.build('gamma*t|x|y|z', g=[1, -1, -1, -1],
coords=coords)
A = st4d.mv('T', 'bivector')
def TA(a1, a2):
return A | (a1 ^ a2)
T = Mlt(TA, st4d)
# tests begin
a1 = st4d.mv('a1', 'vector')
a2 = st4d.mv('a2', 'vector')
a3 = st4d.mv('a3', 'vector')
a4 = st4d.mv('a4', 'vector')
# calling the Mlt is like calling the function
assert T(a1, a2) == TA(a1, a2)
# for addition, argument slots are reused
assert (T + T)(a1, a2) == T(a1, a2) + T(a1, a2)
assert (T - T)(a1, a2) == T(a1, a2) - T(a1, a2)
# for multiplication, argument slots are chained
assert (T * T)(a1, a2, a3, a4) == TA(a1, a2) * T(a3, a4)
assert (T ^ T)(a1, a2, a3, a4) == TA(a1, a2) ^ T(a3, a4)
assert (T | T)(a1, a2, a3, a4) == TA(a1, a2) | T(a3, a4)
# Test linearity properties. Note that this behavior is implied by our
# test that T and TA are equivalent above, but it does exercise
# `Mlt.__call__` with compound expressions as arguments.
alpha = st4d.mv('alpha', 'scalar')
b = st4d.mv('b', 'vector')
assert T(alpha * a1, a2) == alpha * T(a1, a2)
assert T(a1, alpha * a2) == alpha * T(a1, a2)
assert T(a1 + b, a2) == T(a1, a2) + T(b, a2)
assert T(a1, a2 + b) == T(a1, a2) + T(a1, b)
def test_deprecations(self):
g = Ga('e*a|b', g=[1, 1])
with pytest.warns(DeprecationWarning):
assert Mlt.extact_basis_indexes(g) == ['a', 'b']
import sys
from sympy import symbols, sin, cos
from galgebra.printer import Format, xpdf, Get_Program, Print_Function
from galgebra.ga import Ga
from galgebra.lt import Mlt
coords = symbols('t x y z', real=True)
(st4d, g0, g1, g2, g3) = Ga.build('gamma*t|x|y|z',
g=[1, -1, -1, -1],
coords=coords)
A = st4d.mv('T', 'bivector')
def TA(a1, a2):
return A | (a1 ^ a2)
T = Mlt(TA, st4d) # Define multi-linear function