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#!/usr/bin/env python
from __future__ import print_function
from sympy import symbols, log, simplify, diff, cos, sin
from sympy.galgebra.ga import MV, ReciprocalFrame
from sympy.galgebra.debug import oprint
from sympy.galgebra.printing import GA_Printer, enhance_print, Get_Program, Print_Function
from sympy.galgebra.manifold import Manifold
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
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
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
def Simple_manifold_with_scalar_function_derivative():
Print_Function()
coords = (x, y, z) = symbols('x y z')
basis = (e1, e2, e3, grad) = MV.setup('e_1 e_2 e_3', metric='[1,1,1]', coords=coords)
# Define surface
mfvar = (u, v) = symbols('u v')
X = u*e1 + v*e2 + (u**2 + v**2)*e3
print(X)
MF = Manifold(X, mfvar)
# Define field on the surface.
g = (v + 1)*log(u)
# Method 1: Using old Manifold routines.
VectorDerivative = (MF.rbasis[0]/MF.E_sq)*diff(g, u) + (MF.rbasis[1]/MF.E_sq)*diff(g, v)
print('Vector derivative =', VectorDerivative.subs({u: 1, v: 0}))
# Method 2: Using new Manifold routines.
dg = MF.Grad(g)
print('Vector derivative =', dg.subs({u: 1, v: 0}))
return
def dummy():
return
def main():
Get_Program(True)
with GA_Printer():
enhance_print()
Test_Reciprocal_Frame()
Distorted_manifold_with_scalar_function()
Simple_manifold_with_scalar_function_derivative()
#Plot_Mobius_Strip_Manifold()
return
if __name__ == "__main__":
main()
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