Here is code -
dRdtau = R.diff(tau)
print 'e_tau =',dRdtau
dRdtau_sq = (dRdtau|dRdtau)()
print 'e_tau^2 =',dRdtau_sq
dRdtau_sq = trigsimp(simplify(dRdtau_sq))
print 'e_tau^2 =',dRdtau_sq
dRdtau_sq.subs((g.diff(tau))**2-(f.diff(tau))**2,1)
print 'e_tau^2 =',dRdtau_sq
Here is output -
e_tau =
D(g(tau),tau)*e0+(D(f(tau),tau)*cos(th(tau,xth))-D(th(tau,xth),tau)*f(tau)*sin(th(tau,xth)))*e1+(D(f(tau),tau)*sin(th(tau,xth))+D(th(tau,xth),tau)*cos(th(tau,xth))*f(tau))*e2
e_tau^2 = D(g(tau), tau)**2 - (D(f(tau), tau)*cos(th(tau, xth)) -
D(th(tau, xth), tau)*f(tau)*sin(th(tau, xth)))**2 - (D(f(tau),
tau)*sin(th(tau, xth)) + D(th(tau, xth), tau)*cos(th(tau, xth))*f(tau))**2
e_tau^2 = D(g(tau), tau)**2 - D(f(tau), tau)**2 - D(th(tau, xth),
tau)**2*f(tau)**2
e_tau^2 = D(g(tau), tau)**2 - D(f(tau), tau)**2 - D(th(tau, xth),
tau)**2*f(tau)**2
A constraint is that -
D(g(tau), tau)**2 - D(f(tau), tau)**2 = 1
My use of subs does not do that. How can I make such a substitution?
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