def test_substitution():
MV.setup('e_x e_y e_z','1 0 0, 0 1 0, 0 0 1',offset=1)
make_symbols('x y z')
X = x*e_x+y*e_y+z*e_z
Y = X.subs([(x,2),(y,3),(z,4)])
assert Y == 2*e_x+3*e_y+4*e_z
def test_substitution():
MV.setup('e_x e_y e_z','1 0 0, 0 1 0, 0 0 1',offset=1)
make_symbols('x y z')
X = x*e_x+y*e_y+z*e_z
Y = X.subs([(x,2),(y,3),(z,4)])
assert Y == 2*e_x+3*e_y+4*e_z
def test_substitution():
MV.setup("e_x e_y e_z", "1 0 0, 0 1 0, 0 0 1", offset=1)
make_symbols("x y z")
X = x * e_x + y * e_y + z * e_z
Y = X.subs([(x, 2), (y, 3), (z, 4)])
assert Y == 2 * e_x + 3 * e_y + 4 * e_z
def test_rmul():
"""
Test for commutative scalar multiplication. Leftover from when sympy and
numpy were not working together and __mul__ and __rmul__ would not give the
same answer.
"""
MV.setup('x y z')
make_symbols('a b c')
assert 5*x == x*5
assert HALF*x == x*HALF
assert a*x == x*a
def test_rmul():
"""
Test for communitive scalar multiplication. Leftover from when sympy and
numpy were not working together and __mul__ and __rmul__ would not give the
same answer.
"""
MV.setup('x y z')
make_symbols('a b c')
assert 5*x == x*5
assert HALF*x == x*HALF
assert a*x == x*a
def test_constructor():
"""
Test various multivector constructors
"""
MV.setup('e_1 e_2 e_3','[1,1,1]')
make_symbols('x')
assert str(S(1)) == '1'
assert str(S(x)) == 'x'
assert str(MV('a','scalar')) == 'a'
assert str(MV('a','vector')) == 'a__0*e_1+a__1*e_2+a__2*e_3'
assert str(MV('a','pseudo')) == 'a*e_1e_2e_3'
assert str(MV('a','spinor')) == 'a+a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3'
assert str(MV('a')) == 'a+a__0*e_1+a__1*e_2+a__2*e_3+a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3+a__012*e_1e_2e_3'
assert str(MV([2,'a'],'grade')) == 'a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3'
assert str(MV('a','grade2')) == 'a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3'
def test_constructor():
"""
Test various multivector constructors
"""
MV.setup('e_1 e_2 e_3','[1,1,1]')
make_symbols('x')
assert str(S(1)) == '1'
assert str(S(x)) == 'x'
assert str(MV('a','scalar')) == 'a'
assert str(MV('a','vector')) == 'a__0*e_1+a__1*e_2+a__2*e_3'
assert str(MV('a','pseudo')) == 'a*e_1e_2e_3'
assert str(MV('a','spinor')) == 'a+a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3'
assert str(MV('a')) == 'a+a__0*e_1+a__1*e_2+a__2*e_3+a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3+a__012*e_1e_2e_3'
assert str(MV([2,'a'],'grade')) == 'a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3'
assert str(MV('a','grade2')) == 'a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3'
def test_constructor():
"""
Test various multivector constructors
"""
MV.setup("e_1 e_2 e_3", "[1,1,1]")
make_symbols("x")
assert str(S(1)) == "1"
assert str(S(x)) == "x"
assert str(MV("a", "scalar")) == "a"
assert str(MV("a", "vector")) == "a__0*e_1+a__1*e_2+a__2*e_3"
assert str(MV("a", "pseudo")) == "a*e_1e_2e_3"
assert str(MV("a", "spinor")) == "a+a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3"
assert str(MV("a")) == "a+a__0*e_1+a__1*e_2+a__2*e_3+a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3+a__012*e_1e_2e_3"
assert str(MV([2, "a"], "grade")) == "a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3"
assert str(MV("a", "grade2")) == "a__01*e_1e_2+a__02*e_1e_3+a__12*e_2e_3"
def make_vector(a,n = 3):
if type(a) == str:
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_derivative():
coords = make_symbols('x y z')
MV.setup('e','1 0 0, 0 1 0, 0 0 1',coords=coords)
X = x*e_x+y*e_y+z*e_z
a = MV('a','vector')
assert ((X|a).grad()) == a
assert ((X*X).grad()) == 2*X
assert (X*X*X).grad() == 5*X*X
assert X.grad_int() == 3
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_derivative():
coords = make_symbols('x y z')
MV.setup('e','1 0 0, 0 1 0, 0 0 1',coords=coords)
X = x*e_x+y*e_y+z*e_z
a = MV('a','vector')
assert ((X|a).grad()) == a
assert ((X*X).grad()) == 2*X
assert (X*X*X).grad() == 5*X*X
assert X.grad_int() == 3
def make_vector(a, n=3):
if type(a) == str:
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_derivative():
coords = make_symbols("x y z")
MV.setup("e", "1 0 0, 0 1 0, 0 0 1", coords=coords)
X = x * e_x + y * e_y + z * e_z
a = MV("a", "vector")
assert ((X | a).grad()) == a
assert ((X * X).grad()) == 2 * X
assert (X * X * X).grad() == 5 * X * X
assert X.grad_int() == 3
print 'Example: non-euclidian distance calculation'
metric = '0 # #,# 0 #,# # 1'
MV.setup('X Y e',metric)
MV.set_str_format(1)
L = X^Y^e
B = L*e
Bsq = (B*B)()
print 'L = X^Y^e is a non-euclidian line'
print 'B = L*e =',B
BeBr =B*e*B.rev()
print 'B*e*B.rev() =',BeBr
print 'B^2 =',Bsq
print 'L^2 =',(L*L)()
make_symbols('s c Binv M S C alpha')
Bhat = Binv*B # Normalize translation generator
R = c+s*Bhat # Rotor R = exp(alpha*Bhat/2)
print 's = sinh(alpha/2) and c = cosh(alpha/2)'
print 'R = exp(alpha*B/(2*|B|)) =',R
Z = R*X*R.rev()
Z.expand()
Z.collect([Binv,s,c,XdotY])
print 'R*X*R.rev() =',Z
W = Z|Y
W.expand()
W.collect([s*Binv])
print '(R*X*rev(R)).Y =',W
M = 1/Bsq
W.subs(Binv**2,M)
W.simplify()
