Thanks a lot!
I thought that such expansion - with parameter t, can help in
postnewton calculations. I tried to
load(itensor);
components(g([i,j],[]),g0([i,j],[])+h*g1([i,j],[])+h^2*g2([i,j],[]));
components(g([],[i,j]),g0([],[i,j])+h*g1([],[i,j])+h^2*g2([],[i,j]));
imetric(g);
ishow(ichr2([i,j],[k]))$
ishow(coeff(expand(%),h,2))$
ishow(icurvature([i,j,k],[l]))$
%,ichr2$
%,g$
expr:coeff(expand(%),h,2);
decsym(g0,2,0,[sym(all)],[]);
decsym(g1,2,0,[sym(all)],[]);
decsym(g2,2,0,[sym(all)],[]);
decsym(g0,0,2,[],[sym(all)]);
decsym(g1,0,2,[],[sym(all)]);
decsym(g2,0,2,[],[sym(all)]);
canform(%o11);
nterms(%);
and 210 term is to much too.
And it's strange to me that maxima doesn't set automatically symmetric
properties for g0, g1, g2 - these are parts of metrics which is symmetric.
Semyon.
On Mon, May 04, 2009 at 10:49:05AM -0400, Viktor T. Toth wrote:
> Semyon,
>
> Several comments:
>
> 1. I recommend using imetric(g) instead of imetric:g; the former also sets
> up the contraction properties of the metric, whereas the latter only assigns
> the metric tensor.
>
> 2. Before using coeff, you need to expand the expression in question. I
> don't think coeff can deal with unexpanded expressions.
>
> 3. Before attempting to expand an expression containing symbols like ichr2,
> you need to evaluate those symbols as they also contain implicit
> dependencies on h. Afterwards, you need to evaluate g again.
>
> 4. Make sure you specify the components for both the covariant and
> contravariant forms of the metric tensor to ensure that g is expanded
> properly in all cases.
>
> In view of these three points, try:
>
> load(itensor);
> components(g([i,j],[]),g0([i,j],[])+h*g1([i,j],[])+h^2*g2([i,j],[]));
> components(g([],[i,j]),g0([],[i,j])+h*g1([],[i,j])+h^2*g2([],[i,j]));
> imetric(g);
> ishow(ichr2([i,j],[k]))$
> ishow(coeff(expand(%),h,2))$
> ishow(icurvature([i,j,k],[l]))$
> %,ichr2$
> %,g$
> coeff(expand(%),h,2)$
> nterms(%);
>
> Your final expression is not very manageable of course, with 216 terms.
> Still, perhaps this is what you were looking for. You might consider
> attempting to set up symmetry properties for g0, g1, g2 using decsym, and
> then simplifying with canform, but it seems it only eliminates a small
> number of terms.
>
>
> Viktor
>
>
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
> On Behalf Of Semyon Glazyrin
> Sent: Monday, May 04, 2009 10:02 AM
> To: maxima at math.utexas.edu
> Subject: General Relativity calculations
>
> Hello!
>
> I'd like to do the following computations. There is a mertic, which
> has power series of h - constant scalar:
>
> g_{ik}=g0_{ik}+h*g1_{ik}+h^2*g2_{ik}
>
> and I want to calculate some expression by this metric, for example
> Riemann tensor and obtain expressions in front of h^n. But I fail in
> doing this even for Christoffel symbol
>
> Code:
>
> load(itensor)$
> components(g([i,j],[]),g0([i,j],[])+h*g1([i,j],[])+h^2*g2([i,j],[]))$
> imetric:g$
> ishow(ichr2([i,j],[k]));
> ishow(coeff(%,h,2));
> ishow(icurvature([i,j,k],[l]));
> ishow(coeff(%,h,2));
>
> answer for coeff in ichr2 is 0.
> What is the problem? I should use another function instead coeff?
> And why icurvature does not substitute Christoffel symbols?
>
> Semyon.
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