Hi, I am new to Axiom, I am studying theoretical physics (4th grade) in Prague and I want to use the computer algebra system as a physicist and I understand that mathematicians are looking at the mathematics from a completely different angle than physicists. But anyway, I want this:
I have a diagonal matrix: gdd=Matrix(( (-exp(nu(r)),0,0,0), (0, exp(lam(r)), 0, 0), (0, 0, r**2, 0), (0, 0, 0, r**2*sin(theta)**2) )) that is a metric tensor on a 4 dimensional manifold with signature (-,+,+,+), this corresponds to g_\mu_\nu (i.e. the indices are lowered). No I want to calculate the Christoffel symbols -> riemann tensor -> ricci tensor. the x^\mu vector are variables (t, r, theta, phi). The nu(r) and lam(r) are unknown functions of "r". I am interested in the (differential) equations for the unknown functions nu(r) and lam(r) that I get by setting: R_\mu_\nu = 0 If you need some more explanation, I'll be glad to explain the details. In maple I can use the grtensor http://grtensor.org/ package, but I find the maple not suitable for me, as I want to use the symbolic manipulation in my programs and I don't want to use the ugly maple language. I found all the other symbolic packages unsuitable for me, so I wrote my own: http://code.google.com/p/sympy/ And in SymPy I can now do it quite easily: http://sympy.googlecode.com/svn/trunk/examples/relativity.py SymPy is just a general package and all I am using from it are just symbolic matrices. (I am lowering and raising indices by myself in the relativity.py example). I was curious - how could I do the same in Axiom? Thanks, Ondrej BTW, the resulting equations are: -1/4*exp(\nu(r))*exp(\lambda(r))**(-1)*\lambda'(r)*\nu'(r)+1/4*exp(\nu(r))*exp(\lambda(r))**(-1)*\nu'(r)**2+1/2*exp(\nu(r))*exp(\lambda(r))**(-1)*(\nu'(r))'+exp(\nu(r))*r**(-1)*exp(\lambda(r))**(-1)*\nu'(r) = 0 1/4*\nu'(r)*\lambda'(r)-1/2*(\nu'(r))'+r**(-1)*\lambda'(r)-1/4*\nu'(r)**2 = 0 -1/2*r*exp(\lambda(r))**(-1)*\nu'(r)+1/2*r*exp(\lambda(r))**(-1)*\lambda'(r)-sin(\theta)**(-2)*cos(\theta)**2-(-1-sin(\theta)**(-2)*cos(\theta)**2)-exp(\lambda(r))**(-1) = 0 -sin(\theta)**2*exp(\lambda(r))**(-1)+sin(\theta)**2-1/2*sin(\theta)**2*r*exp(\lambda(r))**(-1)*\nu'(r)+1/2*sin(\theta)**2*r*exp(\lambda(r))**(-1)*\lambda'(r) = 0 _______________________________________________ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
