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December 20, 2015 07:39
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| C = S(0) | |
| A = simplify(hx.diff(y) | |
| if A: | |
| B = simplify(hy.diff(y) + hy**2) | |
| if B: | |
| C = simplify(hx.diff(x) - hx**2) | |
| if C: | |
| Ax = A.diff(x) | |
| Ay = A.diff(y) | |
| Axy = Ax.diff(y) | |
| Axx = Ax.diff(x) | |
| Ayy = Ay.diff(y) | |
| D = simplify((2*Axy + hx*Ay - Ax*hy + (hx*hy + 2*A)*A)*A - 3*Ax*Ay) | |
| if not D: | |
| E1 = simplify(3*Ax**2 + ((hx**2 + 2*C)*A - 2*Axx)*A) | |
| if E1: | |
| E2 = simplify((2*Ayy + (2*B - hy**2)*A)*A - 3*Ay**2) | |
| if not E2: | |
| E3 = simplify( | |
| E1*((28*Ax + 4*hx*A)*A**3 - E1*(hy*A + Ay)) - E1.diff(x)*8*A**4) | |
| if not E3: | |
| etaval = cancel((4*A**3*(Ax - hx*A) + E1*(hy*A - Ay))/(S(2)*A*E1)) | |
| if x not in etaval: | |
| etaval = exp(integrate(etaval, y)) | |
| xival = -4*A**3*etaval/E1 | |
| if y not in xival: | |
| return [{xi: xival, eta: etaval.subs(y, func)}] | |
| else: | |
| E1 = simplify((2*Ayy + (2*B - hy**2)*A)*A - 3*Ay**2) | |
| if E1: | |
| E2 = simplify( | |
| 4*A**3*D - D**2 + E1*((2*Axx - (hx**2 + 2*C)*A)*A - 3*Ax**2)) | |
| if not E2: | |
| E3 = simplify( | |
| -(A*D)*E1.diff(y) + ((E1.diff(x) - hy*D)*A + 3*Ay*D + | |
| (A*hx - 3*Ax)*E1)*E1) | |
| if not E3: | |
| etaval = cancel(((A*hx - Ax)*E1 - (Ay + A*hy)*D)/(S(2)*A*D)) | |
| if x not in etaval: | |
| etaval = exp(integrate(etaval, y)) | |
| xival = -E1*etaval/D | |
| if y not in xival: | |
| return [{xi: xival, eta: etaval.subs(y, func)}] |
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