本文整理汇总了Python中sympy.galgebra.ga.MV类的典型用法代码示例。如果您正苦于以下问题：Python MV类的具体用法？Python MV怎么用？Python MV使用的例子？那么恭喜您, 这里精选的类代码示例或许可以为您提供帮助。
在下文中一共展示了MV类的20个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: test_basic_multivector_operations
def test_basic_multivector_operations():
with GA_Printer():
(ex, ey, ez) = MV.setup('e*x|y|z')
A = MV('A', 'mv')
assert str(A) == 'A + A__x*e_x + A__y*e_y + A__z*e_z + A__xy*e_x^e_y + A__xz*e_x^e_z + A__yz*e_y^e_z + A__xyz*e_x^e_y^e_z'
assert str(A) == 'A + A__x*e_x + A__y*e_y + A__z*e_z + A__xy*e_x^e_y + A__xz*e_x^e_z + A__yz*e_y^e_z + A__xyz*e_x^e_y^e_z'
assert str(A) == 'A + A__x*e_x + A__y*e_y + A__z*e_z + A__xy*e_x^e_y + A__xz*e_x^e_z + A__yz*e_y^e_z + A__xyz*e_x^e_y^e_z'
X = MV('X', 'vector')
Y = MV('Y', 'vector')
assert str(X) == 'X__x*e_x + X__y*e_y + X__z*e_z'
assert str(Y) == 'Y__x*e_x + Y__y*e_y + Y__z*e_z'
assert str((X*Y)) == '(e_x.e_x)*X__x*Y__x + (e_x.e_y)*X__x*Y__y + (e_x.e_y)*X__y*Y__x + (e_x.e_z)*X__x*Y__z + (e_x.e_z)*X__z*Y__x + (e_y.e_y)*X__y*Y__y + (e_y.e_z)*X__y*Y__z + (e_y.e_z)*X__z*Y__y + (e_z.e_z)*X__z*Y__z + (X__x*Y__y - X__y*Y__x)*e_x^e_y + (X__x*Y__z - X__z*Y__x)*e_x^e_z + (X__y*Y__z - X__z*Y__y)*e_y^e_z'
assert str((X ^ Y)) == '(X__x*Y__y - X__y*Y__x)*e_x^e_y + (X__x*Y__z - X__z*Y__x)*e_x^e_z + (X__y*Y__z - X__z*Y__y)*e_y^e_z'
assert str((X | Y)) == '(e_x.e_x)*X__x*Y__x + (e_x.e_y)*X__x*Y__y + (e_x.e_y)*X__y*Y__x + (e_x.e_z)*X__x*Y__z + (e_x.e_z)*X__z*Y__x + (e_y.e_y)*X__y*Y__y + (e_y.e_z)*X__y*Y__z + (e_y.e_z)*X__z*Y__y + (e_z.e_z)*X__z*Y__z'
(ex, ey) = MV.setup('e*x|y')
X = MV('X', 'vector')
A = MV('A', 'spinor')
assert str(X) == 'X__x*e_x + X__y*e_y'
assert str(A) == 'A + A__xy*e_x^e_y'
assert str((X | A)) == '(-A__xy*((e_x.e_y)*X__x + (e_y.e_y)*X__y))*e_x + (A__xy*((e_x.e_x)*X__x + (e_x.e_y)*X__y))*e_y'
assert str((X < A)) == '(-A__xy*((e_x.e_y)*X__x + (e_y.e_y)*X__y))*e_x + (A__xy*((e_x.e_x)*X__x + (e_x.e_y)*X__y))*e_y'
assert str((A > X)) == '(A__xy*((e_x.e_y)*X__x + (e_y.e_y)*X__y))*e_x + (-A__xy*((e_x.e_x)*X__x + (e_x.e_y)*X__y))*e_y'
(ex, ey) = MV.setup('e*x|y', metric='[1,1]')
X = MV('X', 'vector')
A = MV('A', 'spinor')
assert str(X) == 'X__x*e_x + X__y*e_y'
assert str(A) == 'A + A__xy*e_x^e_y'
assert str((X*A)) == '(A*X__x - A__xy*X__y)*e_x + (A*X__y + A__xy*X__x)*e_y'
assert str((X | A)) == '-A__xy*X__y*e_x + A__xy*X__x*e_y'
assert str((X < A)) == '-A__xy*X__y*e_x + A__xy*X__x*e_y'
assert str((X > A)) == 'A*X__x*e_x + A*X__y*e_y'
assert str((A*X)) == '(A*X__x + A__xy*X__y)*e_x + (A*X__y - A__xy*X__x)*e_y'
assert str((A | X)) == 'A__xy*X__y*e_x - A__xy*X__x*e_y'
assert str((A < X)) == 'A*X__x*e_x + A*X__y*e_y'
assert str((A > X)) == 'A__xy*X__y*e_x - A__xy*X__x*e_y'
return
开发者ID:AALEKH，项目名称:sympy，代码行数:51，代码来源:test_ga.py
示例2: Distorted_manifold_with_scalar_function
def Distorted_manifold_with_scalar_function():
Print_Function()
coords = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('ex ey ez', metric='[1,1,1]', coords=coords)
mfvar = (u, v) = symbols('u v')
X = 2*u*ex + 2*v*ey + (u**3 + v**3/2)*ez
MF = Manifold(X, mfvar, I=MV.I)
(eu, ev) = MF.Basis()
g = (v + 1)*log(u)
dg = MF.Grad(g)
print('g =', g)
print('dg =', dg)
print('dg(1,0) =', dg.subs({u: 1, v: 0}))
G = u*eu + v*ev
dG = MF.Grad(G)
print('G =', G)
print('P(G) =', MF.Proj(G))
print('zcoef =', simplify(2*(u**2 + v**2)*(-4*u**2 - 4*v**2 - 1)))
print('dG =', dG)
print('P(dG) =', MF.Proj(dG))
PS = u*v*eu ^ ev
print('PS =', PS)
print('dPS =', MF.Grad(PS))
print('P(dPS) =', MF.Proj(MF.Grad(PS)))
return
开发者ID:AdrianPotter，项目名称:sympy，代码行数:27，代码来源:manifold_check.py
示例3: test_vector_extraction
def test_vector_extraction():
"""
Show that conformal bivector encodes two points. See D&L Section 10.4.1
"""
metric = ' 0 -1 #,' + \
'-1 0 #,' + \
' # # #,'
P1, P2, a = MV.setup('P1 P2 a', metric)
"""
P1 and P2 are null vectors and hence encode points in conformal space.
Show that P1 and P2 can be extracted from the bivector B = P1^P2. a is a
third vector in the conformal space with a.B not 0.
"""
B = P1 ^ P2
Bsq = B*B
ap = a - (a ^ B)*B
Ap = ap + ap*B
Am = ap - ap*B
P1dota = Symbol('(P1.a)')
P2dota = Symbol('(P2.a)')
Ap_test = (-2*P2dota)*P1
Am_test = (-2*P1dota)*P2
assert Ap == Ap_test
assert Am == Am_test
Ap2 = Ap*Ap
Am2 = Am*Am
assert Ap2 == S.Zero
assert Am2 == S.Zero
开发者ID:AALEKH，项目名称:sympy，代码行数:29，代码来源:test_ga.py
示例4: Test_Reciprocal_Frame
def Test_Reciprocal_Frame():
Print_Function()
coords = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('ex ey ez', metric='[1,1,1]', coords=coords)
mfvar = (u, v) = symbols('u v')
eu = ex + ey
ev = ex - ey
(eu_r, ev_r) = ReciprocalFrame([eu, ev])
oprint('Frame', (eu, ev), 'Reciprocal Frame', (eu_r, ev_r))
print('eu.eu_r =', eu | eu_r)
print('eu.ev_r =', eu | ev_r)
print('ev.eu_r =', ev | eu_r)
print('ev.ev_r =', ev | ev_r)
eu = ex + ey + ez
ev = ex - ey
(eu_r, ev_r) = ReciprocalFrame([eu, ev])
oprint('Frame', (eu, ev), 'Reciprocal Frame', (eu_r, ev_r))
print('eu.eu_r =', eu | eu_r)
print('eu.ev_r =', eu | ev_r)
print('ev.eu_r =', ev | eu_r)
print('ev.ev_r =', ev | ev_r)
return
开发者ID:AdrianPotter，项目名称:sympy，代码行数:31，代码来源:manifold_check.py
示例5: test_conformal_representations_of_circles_lines_spheres_and_planes
def test_conformal_representations_of_circles_lines_spheres_and_planes():
global n, nbar
with GA_Printer():
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'
(e1, e2, e3, n, nbar) = MV.setup('e_1 e_2 e_3 n nbar', metric)
e = n + nbar
#conformal representation of points
A = make_vector(e1)
B = make_vector(e2)
C = make_vector(-e1)
D = make_vector(e3)
X = make_vector('x', 3)
assert str(A) == 'e_1 + 1/2*n - 1/2*nbar'
assert str(B) == 'e_2 + 1/2*n - 1/2*nbar'
assert str(C) == '-e_1 + 1/2*n - 1/2*nbar'
assert str(D) == 'e_3 + 1/2*n - 1/2*nbar'
assert str(X) == 'x1*e_1 + x2*e_2 + x3*e_3 + ((x1**2 + x2**2 + x3**2)/2)*n - 1/2*nbar'
assert str((A ^ B ^ C ^ X)) == '-x3*e_1^e_2^e_3^n + x3*e_1^e_2^e_3^nbar + ((x1**2 + x2**2 + x3**2 - 1)/2)*e_1^e_2^n^nbar'
assert str((A ^ B ^ n ^ X)) == '-x3*e_1^e_2^e_3^n + ((x1 + x2 - 1)/2)*e_1^e_2^n^nbar + x3/2*e_1^e_3^n^nbar - x3/2*e_2^e_3^n^nbar'
assert str((((A ^ B) ^ C) ^ D) ^ X) == '((-x1**2 - x2**2 - x3**2 + 1)/2)*e_1^e_2^e_3^n^nbar'
assert str((A ^ B ^ n ^ D ^ X)) == '((-x1 - x2 - x3 + 1)/2)*e_1^e_2^e_3^n^nbar'
L = (A ^ B ^ e) ^ X
assert str(L) == '-x3*e_1^e_2^e_3^n - x3*e_1^e_2^e_3^nbar + (-x1**2/2 + x1 - x2**2/2 + x2 - x3**2/2 - 1/2)*e_1^e_2^n^nbar + x3*e_1^e_3^n^nbar - x3*e_2^e_3^n^nbar'
return
开发者ID:AALEKH，项目名称:sympy，代码行数:33，代码来源:test_ga.py
示例6: test_derivatives_in_spherical_coordinates
def test_derivatives_in_spherical_coordinates():
with GA_Printer():
X = (r, th, phi) = symbols("r theta phi")
curv = [[r * cos(phi) * sin(th), r * sin(phi) * sin(th), r * cos(th)], [1, r, r * sin(th)]]
(er, eth, ephi, grad) = MV.setup("e_r e_theta e_phi", metric="[1,1,1]", coords=X, curv=curv)
f = MV("f", "scalar", fct=True)
A = MV("A", "vector", fct=True)
B = MV("B", "grade2", fct=True)
assert str(f) == "f"
assert str(A) == "A__r*e_r + A__theta*e_theta + A__phi*e_phi"
assert str(B) == "B__rtheta*e_r^e_theta + B__rphi*e_r^e_phi + B__thetaphi*e_theta^e_phi"
assert str(grad * f) == "D{r}f*e_r + D{theta}f/r*e_theta + D{phi}f/(r*sin(theta))*e_phi"
assert (
str(grad | A)
== "D{r}A__r + 2*A__r/r + A__theta*cos(theta)/(r*sin(theta)) + D{theta}A__theta/r + D{phi}A__phi/(r*sin(theta))"
)
assert (
str(-MV.I * (grad ^ A))
== "((A__phi*cos(theta)/sin(theta) + D{theta}A__phi - D{phi}A__theta/sin(theta))/r)*e_r + (-D{r}A__phi - A__phi/r + D{phi}A__r/(r*sin(theta)))*e_theta + (D{r}A__theta + A__theta/r - D{theta}A__r/r)*e_phi"
)
assert (
str(grad ^ B)
== "(D{r}B__thetaphi - B__rphi*cos(theta)/(r*sin(theta)) + 2*B__thetaphi/r - D{theta}B__rphi/r + D{phi}B__rtheta/(r*sin(theta)))*e_r^e_theta^e_phi"
)
return
开发者ID:guanlongtianzi，项目名称:sympy，代码行数:29，代码来源:test_ga.py
示例7: test_extract_plane_and_line
def test_extract_plane_and_line():
"""
Show that conformal trivector encodes planes and lines. See D&L section
10.4.2
"""
metric = '# # # 0 0,' + \
'# # # 0 0,' + \
'# # # 0 0,' + \
'0 0 0 0 2,' + \
'0 0 0 2 0'
p1, p2, p3, n, nbar = MV.setup('p1 p2 p3 n nbar', metric, debug=0)
P1 = F(p1, n, nbar)
P2 = F(p2, n, nbar)
P3 = F(p3, n, nbar)
#Line through p1 and p2
L = P1 ^ P2 ^ n
delta = (L | n) | nbar
delta_test = 2*p1 - 2*p2
diff = delta - delta_test
assert diff == S.Zero
#Plane through p1, p2, and p3
C = P1 ^ P2 ^ P3
delta = ((C ^ n) | n) | nbar
delta_test = 2*(p1 ^ p2) - 2*(p1 ^ p3) + 2*(p2 ^ p3)
diff = delta - delta_test
assert diff == S.Zero
开发者ID:AALEKH，项目名称:sympy，代码行数:30，代码来源:test_ga.py
示例8: test_extracting_vectors_from_conformal_2_blade
def test_extracting_vectors_from_conformal_2_blade():
with GA_Printer():
metric = ' 0 -1 #,' + \
'-1 0 #,' + \
' # # #,'
(P1, P2, a) = MV.setup('P1 P2 a', metric)
B = P1 ^ P2
Bsq = B*B
assert str(Bsq) == '1'
ap = a - (a ^ B)*B
assert str(ap) == '-(P2.a)*P1 - (P1.a)*P2'
Ap = ap + ap*B
Am = ap - ap*B
assert str(Ap) == '-2*(P2.a)*P1'
assert str(Am) == '-2*(P1.a)*P2'
assert str(Ap*Ap) == '0'
assert str(Am*Am) == '0'
aB = a | B
assert str(aB) == '-(P2.a)*P1 + (P1.a)*P2'
return
开发者ID:AALEKH，项目名称:sympy，代码行数:27，代码来源:test_ga.py
示例9: test_extracting_vectors_from_conformal_2_blade
def test_extracting_vectors_from_conformal_2_blade():
with GA_Printer():
metric = " 0 -1 #," + "-1 0 #," + " # # #,"
(P1, P2, a) = MV.setup("P1 P2 a", metric)
B = P1 ^ P2
Bsq = B * B
assert str(Bsq) == "1"
ap = a - (a ^ B) * B
assert str(ap) == "-(P2.a)*P1 - (P1.a)*P2"
Ap = ap + ap * B
Am = ap - ap * B
assert str(Ap) == "-2*(P2.a)*P1"
assert str(Am) == "-2*(P1.a)*P2"
assert str(Ap * Ap) == "0"
assert str(Am * Am) == "0"
aB = a | B
assert str(aB) == "-(P2.a)*P1 + (P1.a)*P2"
return
开发者ID:guanlongtianzi，项目名称:sympy，代码行数:25，代码来源:test_ga.py
示例10: test_reciprocal_frame_test
def test_reciprocal_frame_test():
with GA_Printer():
metric = '1 # #,' + \
'# 1 #,' + \
'# # 1,'
(e1, e2, e3) = MV.setup('e1 e2 e3', metric)
E = e1 ^ e2 ^ e3
Esq = (E*E).scalar()
assert str(E) == 'e1^e2^e3'
assert str(Esq) == '(e1.e2)**2 - 2*(e1.e2)*(e1.e3)*(e2.e3) + (e1.e3)**2 + (e2.e3)**2 - 1'
Esq_inv = 1/Esq
E1 = (e2 ^ e3)*E
E2 = (-1)*(e1 ^ e3)*E
E3 = (e1 ^ e2)*E
assert str(E1) == '((e2.e3)**2 - 1)*e1 + ((e1.e2) - (e1.e3)*(e2.e3))*e2 + (-(e1.e2)*(e2.e3) + (e1.e3))*e3'
assert str(E2) == '((e1.e2) - (e1.e3)*(e2.e3))*e1 + ((e1.e3)**2 - 1)*e2 + (-(e1.e2)*(e1.e3) + (e2.e3))*e3'
assert str(E3) == '(-(e1.e2)*(e2.e3) + (e1.e3))*e1 + (-(e1.e2)*(e1.e3) + (e2.e3))*e2 + ((e1.e2)**2 - 1)*e3'
w = (E1 | e2)
w = w.expand()
assert str(w) == '0'
w = (E1 | e3)
w = w.expand()
assert str(w) == '0'
w = (E2 | e1)
w = w.expand()
assert str(w) == '0'
w = (E2 | e3)
w = w.expand()
assert str(w) == '0'
w = (E3 | e1)
w = w.expand()
assert str(w) == '0'
w = (E3 | e2)
w = w.expand()
assert str(w) == '0'
w = (E1 | e1)
w = (w.expand()).scalar()
Esq = expand(Esq)
assert str(simplify(w/Esq)) == '1'
w = (E2 | e2)
w = (w.expand()).scalar()
assert str(simplify(w/Esq)) == '1'
w = (E3 | e3)
w = (w.expand()).scalar()
assert str(simplify(w/Esq)) == '1'
return
开发者ID:AALEKH，项目名称:sympy，代码行数:60，代码来源:test_ga.py
示例11: test_derivatives_in_rectangular_coordinates
def test_derivatives_in_rectangular_coordinates():
with GA_Printer():
X = (x, y, z) = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('e_x e_y e_z', metric='[1,1,1]', coords=X)
f = MV('f', 'scalar', fct=True)
A = MV('A', 'vector', fct=True)
B = MV('B', 'grade2', fct=True)
C = MV('C', 'mv', fct=True)
assert str(f) == 'f'
assert str(A) == 'A__x*e_x + A__y*e_y + A__z*e_z'
assert str(B) == 'B__xy*e_x^e_y + B__xz*e_x^e_z + B__yz*e_y^e_z'
assert str(C) == 'C + C__x*e_x + C__y*e_y + C__z*e_z + C__xy*e_x^e_y + C__xz*e_x^e_z + C__yz*e_y^e_z + C__xyz*e_x^e_y^e_z'
assert str(grad*f) == 'D{x}f*e_x + D{y}f*e_y + D{z}f*e_z'
assert str(grad | A) == 'D{x}A__x + D{y}A__y + D{z}A__z'
assert str(grad*A) == 'D{x}A__x + D{y}A__y + D{z}A__z + (-D{y}A__x + D{x}A__y)*e_x^e_y + (-D{z}A__x + D{x}A__z)*e_x^e_z + (-D{z}A__y + D{y}A__z)*e_y^e_z'
assert str(-MV.I*(grad ^ A)) == '(-D{z}A__y + D{y}A__z)*e_x + (D{z}A__x - D{x}A__z)*e_y + (-D{y}A__x + D{x}A__y)*e_z'
assert str(grad*B) == '(-(D{y}B__xy + D{z}B__xz))*e_x + (D{x}B__xy - D{z}B__yz)*e_y + (D{x}B__xz + D{y}B__yz)*e_z + (D{z}B__xy - D{y}B__xz + D{x}B__yz)*e_x^e_y^e_z'
assert str(grad ^ B) == '(D{z}B__xy - D{y}B__xz + D{x}B__yz)*e_x^e_y^e_z'
assert str(grad | B) == '(-(D{y}B__xy + D{z}B__xz))*e_x + (D{x}B__xy - D{z}B__yz)*e_y + (D{x}B__xz + D{y}B__yz)*e_z'
assert str(grad < A) == 'D{x}A__x + D{y}A__y + D{z}A__z'
assert str(grad > A) == 'D{x}A__x + D{y}A__y + D{z}A__z'
assert str(grad < B) == '(-(D{y}B__xy + D{z}B__xz))*e_x + (D{x}B__xy - D{z}B__yz)*e_y + (D{x}B__xz + D{y}B__yz)*e_z'
assert str(grad > B) == '0'
assert str(grad < C) == 'D{x}C__x + D{y}C__y + D{z}C__z + (-(D{y}C__xy + D{z}C__xz))*e_x + (D{x}C__xy - D{z}C__yz)*e_y + (D{x}C__xz + D{y}C__yz)*e_z + D{z}C__xyz*e_x^e_y - D{y}C__xyz*e_x^e_z + D{x}C__xyz*e_y^e_z'
assert str(grad > C) == 'D{x}C__x + D{y}C__y + D{z}C__z + D{x}C*e_x + D{y}C*e_y + D{z}C*e_z'
return
开发者ID:AALEKH，项目名称:sympy，代码行数:32，代码来源:test_ga.py
示例12: test_substitution
def test_substitution():
e_x, e_y, e_z = MV.setup("e_x e_y e_z", "1 0 0, 0 1 0, 0 0 1")
x, y, z = 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
开发者ID:guanlongtianzi，项目名称:sympy，代码行数:8，代码来源:test_ga.py
示例13: test_substitution
def test_substitution():
e_x, e_y, e_z = MV.setup('e_x e_y e_z', '1 0 0, 0 1 0, 0 0 1')
x, y, z = 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
开发者ID:AALEKH，项目名称:sympy，代码行数:8，代码来源:test_ga.py
示例14: test_reciprocal_frame_test
def test_reciprocal_frame_test():
with GA_Printer():
metric = "1 # #," + "# 1 #," + "# # 1,"
(e1, e2, e3) = MV.setup("e1 e2 e3", metric)
E = e1 ^ e2 ^ e3
Esq = (E * E).scalar()
assert str(E) == "e1^e2^e3"
assert str(Esq) == "(e1.e2)**2 - 2*(e1.e2)*(e1.e3)*(e2.e3) + (e1.e3)**2 + (e2.e3)**2 - 1"
Esq_inv = 1 / Esq
E1 = (e2 ^ e3) * E
E2 = (-1) * (e1 ^ e3) * E
E3 = (e1 ^ e2) * E
assert str(E1) == "((e2.e3)**2 - 1)*e1 + ((e1.e2) - (e1.e3)*(e2.e3))*e2 + (-(e1.e2)*(e2.e3) + (e1.e3))*e3"
assert str(E2) == "((e1.e2) - (e1.e3)*(e2.e3))*e1 + ((e1.e3)**2 - 1)*e2 + (-(e1.e2)*(e1.e3) + (e2.e3))*e3"
assert str(E3) == "(-(e1.e2)*(e2.e3) + (e1.e3))*e1 + (-(e1.e2)*(e1.e3) + (e2.e3))*e2 + ((e1.e2)**2 - 1)*e3"
w = E1 | e2
w = w.expand()
assert str(w) == "0"
w = E1 | e3
w = w.expand()
assert str(w) == "0"
w = E2 | e1
w = w.expand()
assert str(w) == "0"
w = E2 | e3
w = w.expand()
assert str(w) == "0"
w = E3 | e1
w = w.expand()
assert str(w) == "0"
w = E3 | e2
w = w.expand()
assert str(w) == "0"
w = E1 | e1
w = (w.expand()).scalar()
Esq = expand(Esq)
assert str(simplify(w / Esq)) == "1"
w = E2 | e2
w = (w.expand()).scalar()
assert str(simplify(w / Esq)) == "1"
w = E3 | e3
w = (w.expand()).scalar()
assert str(simplify(w / Esq)) == "1"
return
开发者ID:guanlongtianzi，项目名称:sympy，代码行数:58，代码来源:test_ga.py
示例15: Plot_Mobius_Strip_Manifold
def Plot_Mobius_Strip_Manifold():
Print_Function()
coords = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('ex ey ez', metric='[1,1,1]', coords=coords)
mfvar = (u, v) = symbols('u v')
X = (cos(u) + v*cos(u/2)*cos(u))*ex + (sin(u) + v*cos(u/2)*sin(u))*ey + v*sin(u/2)*ez
MF = Manifold(X, mfvar, True, I=MV.I)
MF.Plot2DSurface([0.0, 6.28, 48], [-0.3, 0.3, 12], surf=False, skip=[4, 4], tan=0.15)
return
开发者ID:AdrianPotter，项目名称:sympy，代码行数:9，代码来源:manifold_check.py
示例16: test_derivative
def test_derivative():
coords = x, y, z = symbols('x y z')
e_x, e_y, e_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
开发者ID:AALEKH，项目名称:sympy，代码行数:10，代码来源:test_ga.py
示例17: test_metrics_xfail
def test_metrics_xfail():
from sympy.galgebra.ga import arbitrary_metric_conformal
metric = arbitrary_metric_conformal(3)
p1, p2, p3 = MV.setup('p1 p2 p3', metric, debug=0)
v1 = x1*p1 + y1*p2 + z1*p3
v2 = x2*p1 + y2*p2 + z2*p3
prod1 = v1*v2
prod2 = (v1|v2) + (v1^v2)
diff = prod1 - prod2
assert diff == MV(S.Zero)
开发者ID:AALEKH，项目名称:sympy，代码行数:10，代码来源:test_ga.py
示例18: test_str
def test_str():
e_1, e_2, e_3 = MV.setup('e_1 e_2 e_3', '1 0 0, 0 1 0, 0 0 1')
X = MV('x')
assert str(X) == 'x + x__1*e_1 + x__2*e_2 + x__3*e_3 + x__12*e_1^e_2 + x__13*e_1^e_3 + x__23*e_2^e_3 + x__123**e_1^e_2^e_3'
Y = MV('y', 'spinor')
assert str(Y) == 'y + y__12*e_1^e_2 + y__13*e_1^e_3 + y__23*e_2^e_3'
Z = X + Y
assert str(Z) == 'x + y + x__1*e_1 + x__2*e_2 + x__3*e_3 + (x__12 + y__12)*e_1^e_2 + (x__13 + y__13)*e_1^e_3 + (x__23 + y__23)*e_2^e_3 + x__123*e_1^e_2^e_3'
assert str(e_1 | e_1) == '1'
开发者ID:AALEKH，项目名称:sympy，代码行数:10，代码来源:test_ga.py
示例19: test_derivative
def test_derivative():
coords = x, y, z = symbols("x y z")
e_x, e_y, e_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
开发者ID:guanlongtianzi，项目名称:sympy，代码行数:10，代码来源:test_ga.py
示例20: test_rmul
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.
"""
x, y, z = MV.setup('x y z')
a, b, c = symbols('a b c')
assert 5*x == x*5
assert Rational(1, 2)*x == x*Rational(1, 2)
assert a*x == x*a
开发者ID:AALEKH，项目名称:sympy，代码行数:11，代码来源:test_ga.py
注：本文中的sympy.galgebra.ga.MV类示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。 |
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