SageManifold expand around infinity
Hi everyone, I am kind of new in sage and I can't find any help online.
I have written the following code on a Jupyter notebook:
M = Manifold(3, 'M', latex_name=r'\mathcal{M}')
Bc.<u,r,ph> = M.chart(r'u:(-oo,+oo) r:(0,+oo) ph:(0,2*pi):\phi')
e = M.default_frame()
g = M.riemannian_metric('g')
E = M.scalar_field(function('E')(u,ph), name='E')
m = M.scalar_field(function('m')(u,ph), name='m')
C = M.scalar_field(function('C')(u,ph), name='C')
Alf = M.scalar_field(function('A^l_\phi')(u,ph), name='A^l_\phi')
L = M.scalar_field(function('L')(u,ph), name='L')
f = M.scalar_field(function('f')(u,ph), name='f')
gg = M.scalar_field(function('gg')(u,ph), name='gg')
g[0,0]=2*E**2*log(r)+2*m
g[0,1]=-1+C**2/(2*r)
g[0,2]=8/3 * sqrt(r)*C*E+2*log(r)*E*Alf + L
g[2,2]=r**2
What I need here is to retrieve the asymptotic behavior for r->infinity of each of the metric's components, I would like to retrieve something like:
g[0,0].some_method_for_asymptotic_expansion(r, oo, order)
RESULT: log(r) + O(1)
I tried the .series_expansion() method but it only expands around zero, and by redefining a variable like k=1/r the method arises the error
RuntimeError: ex::series(): expansion point has unknown type
Can anyone please help me? I am kind of stuck since weeks
With e.g.
g[0,0].expr()which is a symbolic expression you'll be able to do more.@rburing thank you so much for your support, I tried to use the expr() method and substitute r with 1/z and expand for z, then substitute back but it did work only for some of my expressions. For some more complicated expressions I can't deal with it, I only need the leading term and I am not being able to solve the issue