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Substituting variable value

asked 2019-12-18 04:16:14 -0600

mattiav gravatar image

I use the following code to calculate the Kretschmann scala of the Schwartzchild spacetime:

print("Initialization of  manifold, chart, and metric. Definitions of constants.")
M=Manifold(4,'M',structure='Lorentzian')
X.<t,r,th,ph> = M.chart(r"t r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi")
m=var('m')

g=M.metric()

g[0,0]=-(1-2*m/r)
g[1,1]=1/(1-2*m/r)
g[2,2]=r^2
g[3,3]=r^2*sin(th)^2


print('Calculating Riemann tensor')
R = g.riemann()
print(R[:])
uR=R.up(g)
dR=R.down(g)

print('Calculating Kretschmann scalar')
kr= uR['^{abcd}']*dR['_{abcd}']
print(kr.expr())

It works, but now I want to substitute a value for the variable m. I have tried with:

kr.substitute(m==10)
kr.subs(m==10)
kr.substitute_expression(m==10)

but none of these work. How can I make the substituteion m=10?

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answered 2019-12-18 05:01:17 -0600

eric_g gravatar image

updated 2019-12-18 05:03:09 -0600

To use substitute, you have to be at the level of the symbolic expression underlying the scalar field kr. The symbolic expression (in the default chart) being returned by .expr(), it suffices to write

kr.expr().subs(m==10)
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Asked: 2019-12-18 04:16:14 -0600

Seen: 55 times

Last updated: Dec 18 '19