def test_extract_plane_and_line():
metric = '# # # 0 0,'+ \
'# # # 0 0,'+ \
'# # # 0 0,'+ \
'0 0 0 0 2,'+ \
'0 0 0 2 0'
MV.setup('p1 p2 p3 n nbar', metric, debug=0)
MV.set_str_format(1)
ZERO_MV = MV()
P1 = F(p1)
P2 = F(p2)
P3 = F(p3)
L = P1 ^ P2 ^ n
delta = (L | n) | nbar
delta_test = 2 * p1 - 2 * p2
diff = delta - delta_test
diff.compact()
assert diff == ZERO_MV
C = P1 ^ P2 ^ P3
delta = ((C ^ n) | n) | nbar
delta_test = 2 * (p1 ^ p2) - 2 * (p1 ^ p3) + 2 * (p2 ^ p3)
diff = delta - delta_test
diff.compact()
assert diff == ZERO_MV
def test_vector_extraction():
metric = ' 0 -1 #,'+ \
'-1 0 #,'+ \
' # # #,'
MV.setup('P1 P2 a', metric)
ZERO_MV = MV()
B = P1 ^ P2
Bsq = B * B
ap = a - (a ^ B) * B
Ap = ap + ap * B
Am = ap - ap * B
Ap_test = (-2 * P2dota) * P1
Am_test = (-2 * P1dota) * P2
Ap.compact()
Am.compact()
Ap_test.compact()
Am_test.compact()
assert Ap == Ap_test
assert Am == Am_test
Ap2 = Ap * Ap
Am2 = Am * Am
Ap2.compact()
Am2.compact()
assert Ap2 == ZERO_MV
assert Am2 == ZERO_MV
def make_vector(a, n=3):
if type(a) == types.StringType:
sym_str = ''
for i in range(n):
sym_str += a + str(i) + ' '
sym_lst = make_symbols(sym_str)
sym_lst.append(ZERO)
sym_lst.append(ZERO)
a = MV(sym_lst, 'vector')
return (F(a))
def test_geometry():
metric = '1 0 0 0 0,'+ \
'0 1 0 0 0,'+ \
'0 0 1 0 0,'+ \
'0 0 0 0 2,'+ \
'0 0 0 2 0'
MV.setup('e0 e1 e2 n nbar', metric, debug=0)
e = n + nbar
#conformal representation of points
ZERO_MV = MV()
A = make_vector(e0) # point a = (1,0,0) A = F(a)
B = make_vector(e1) # point b = (0,1,0) B = F(b)
C = make_vector(-1 * e0) # point c = (-1,0,0) C = F(c)
D = make_vector(e2) # point d = (0,0,1) D = F(d)
X = make_vector('x', 3)
Circle = A ^ B ^ C ^ X
Line = A ^ B ^ n ^ X
Sphere = A ^ B ^ C ^ D ^ X
Plane = A ^ B ^ n ^ D ^ X
Circle_test = -x2 * (e0 ^ e1 ^ e2 ^ n) + x2 * (
e0 ^ e1 ^ e2 ^ nbar) + HALF * (-1 + x0**2 + x1**2 +
x2**2) * (e0 ^ e1 ^ n ^ nbar)
diff = Circle - Circle_test
diff.compact()
assert diff == ZERO_MV
Line_test = -x2*(e0^e1^e2^n)+HALF*(-1+x0+x1)*(e0^e1^n^nbar)+(HALF*x2)*(e0^e2^n^nbar)+\
(-HALF*x2)*(e1^e2^n^nbar)
diff = Line - Line_test
diff.compact()
assert diff == ZERO_MV
Sphere_test = HALF * (1 - x0**2 - x1**2 - x2**2) * (e0 ^ e1 ^ e2 ^ n
^ nbar)
diff = Sphere - Sphere_test
diff.compact()
assert diff == ZERO_MV
Plane_test = HALF * (1 - x0 - x1 - x2) * (e0 ^ e1 ^ e2 ^ n ^ nbar)
diff = Plane - Plane_test
diff.compact()
assert diff == ZERO_MV
