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_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_noneuclidian(): global s,c,Binv,M,S,C,alpha #set_main(sys.modules[__name__]) metric = '0 # #,'+ \ '# 0 #,'+ \ '# # 1,' MV.setup('X Y e',metric,debug=0) MV.set_str_format(1) L = X^Y^e B = L*e Bsq = (B*B)() BeBr =B*e*B.rev() 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) Z = R*X*R.rev() Z.expand() Z.collect([Binv,s,c,XdotY]) W = Z|Y W.expand() W.collect([s*Binv]) M = 1/Bsq W.subs(Binv**2,M) W.simplify() Bmag = sympy.sqrt(XdotY**2-2*XdotY*Xdote*Ydote) W.collect([Binv*c*s,XdotY]) W.subs(2*XdotY**2-4*XdotY*Xdote*Ydote,2/(Binv**2)) W.subs(2*c*s,S) W.subs(c**2,(C+1)/2) W.subs(s**2,(C-1)/2) W.simplify() W.subs(1/Binv,Bmag) W = W().expand() #print '(R*X*R.rev()).Y =',W Wd = collect(W,[C,S],exact=True,evaluate=False) #print 'Wd =',Wd Wd_1 = Wd[ONE] Wd_C = Wd[C] Wd_S = Wd[S] #print '|B| =',Bmag Wd_1 = Wd_1.subs(Bmag,1/Binv) Wd_C = Wd_C.subs(Bmag,1/Binv) Wd_S = Wd_S.subs(Bmag,1/Binv) #print 'Wd[ONE] =',Wd_1 #print 'Wd[C] =',Wd_C #print 'Wd[S] =',Wd_S lhs = Wd_1+Wd_C*C rhs = -Wd_S*S lhs = lhs**2 rhs = rhs**2 W = (lhs-rhs).expand() W = (W.subs(1/Binv**2,Bmag**2)).expand() #print 'W =',W W = (W.subs(S**2,C**2-1)).expand() W = collect(W,[C**2,C],evaluate=False) #print 'W =',W a = W[C**2] b = W[(C**2)**(sympify(1)/2)] c = W[ONE] #print 'a =',a #print 'b =',b #print 'c =',c D = (b**2-4*a*c).expand() #print 'Setting to 0 and solving for C gives:' #print 'Descriminant D = b^2-4*a*c =',D C = (-b/(2*a)).expand() #print 'C = cosh(alpha) = -b/(2*a) =',C """ Wd = collect(W,[C,S],evaluate=False) lhs = Wd[ONE]+Wd[C]*C rhs = -Wd[S]*S lhs = lhs**2 rhs = rhs**2 W = (lhs-rhs).expand() W = (W.subs(S**2,C**2-1)).expand() W = collect(W,[C**2,C],evaluate=False) a = W[C**2] b = W[abs(C)] c = W[ONE] D = (b**2-4*a*c).expand() C = (-b/(2*a)).expand() """ assert C == 1-XdotY/(Xdote*Ydote)
def test_noneuclidian(): global s, c, Binv, M, S, C, alpha #set_main(sys.modules[__name__]) metric = '0 # #,'+ \ '# 0 #,'+ \ '# # 1,' MV.setup('X Y e', metric, debug=0) MV.set_str_format(1) L = X ^ Y ^ e B = L * e Bsq = (B * B)() BeBr = B * e * B.rev() 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) Z = R * X * R.rev() Z.expand() Z.collect([Binv, s, c, XdotY]) W = Z | Y W.expand() W.collect([s * Binv]) M = 1 / Bsq W.subs(Binv**2, M) W.simplify() Bmag = sympy.sqrt(XdotY**2 - 2 * XdotY * Xdote * Ydote) W.collect([Binv * c * s, XdotY]) W.subs(2 * XdotY**2 - 4 * XdotY * Xdote * Ydote, 2 / (Binv**2)) W.subs(2 * c * s, S) W.subs(c**2, (C + 1) / 2) W.subs(s**2, (C - 1) / 2) W.simplify() W.subs(1 / Binv, Bmag) W = W().expand() #print '(R*X*R.rev()).Y =',W Wd = collect(W, [C, S], exact=True, evaluate=False) #print 'Wd =',Wd Wd_1 = Wd[ONE] Wd_C = Wd[C] Wd_S = Wd[S] #print '|B| =',Bmag Wd_1 = Wd_1.subs(Bmag, 1 / Binv) Wd_C = Wd_C.subs(Bmag, 1 / Binv) Wd_S = Wd_S.subs(Bmag, 1 / Binv) #print 'Wd[ONE] =',Wd_1 #print 'Wd[C] =',Wd_C #print 'Wd[S] =',Wd_S lhs = Wd_1 + Wd_C * C rhs = -Wd_S * S lhs = lhs**2 rhs = rhs**2 W = (lhs - rhs).expand() W = (W.subs(1 / Binv**2, Bmag**2)).expand() #print 'W =',W W = (W.subs(S**2, C**2 - 1)).expand() W = collect(W, [C**2, C], evaluate=False) #print 'W =',W a = W[C**2] b = W[(C**2)**(sympify(1) / 2)] c = W[ONE] #print 'a =',a #print 'b =',b #print 'c =',c D = (b**2 - 4 * a * c).expand() #print 'Setting to 0 and solving for C gives:' #print 'Descriminant D = b^2-4*a*c =',D C = (-b / (2 * a)).expand() #print 'C = cosh(alpha) = -b/(2*a) =',C """ Wd = collect(W,[C,S],evaluate=False) lhs = Wd[ONE]+Wd[C]*C rhs = -Wd[S]*S lhs = lhs**2 rhs = rhs**2 W = (lhs-rhs).expand() W = (W.subs(S**2,C**2-1)).expand() W = collect(W,[C**2,C],evaluate=False) a = W[C**2] b = W[abs(C)] c = W[ONE] D = (b**2-4*a*c).expand() C = (-b/(2*a)).expand() """ assert C == 1 - XdotY / (Xdote * Ydote)
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)) if __name__ == '__main__': MV.setup('a b c d e',debug=0) MV.set_str_format(1) print 'e|(a^b) =',e|(a^b) print 'e|(a^b^c) =',e|(a^b^c) print 'a*(b^c)-b*(a^c)+c*(a^b) =',a*(b^c)-b*(a^c)+c*(a^b) print 'e|(a^b^c^d) =',e|(a^b^c^d) print -d*(a^b^c)+c*(a^b^d)-b*(a^c^d)+a*(b^c^d) print (a^b)|(c^d) #sys.exit(0) """ Note that is A and B are multivectors: A*B - Geometric Product
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)) if __name__ == '__main__': MV.setup('a b c d e', debug=0) MV.set_str_format(1) print 'e|(a^b) =', e | (a ^ b) print 'e|(a^b^c) =', e | (a ^ b ^ c) print 'a*(b^c)-b*(a^c)+c*(a^b) =', a * (b ^ c) - b * (a ^ c) + c * (a ^ b) print 'e|(a^b^c^d) =', e | (a ^ b ^ c ^ d) print -d * (a ^ b ^ c) + c * (a ^ b ^ d) - b * (a ^ c ^ d) + a * (b ^ c ^ d) print(a ^ b) | (c ^ d) #sys.exit(0) """ Note that is A and B are multivectors: A*B - Geometric Product