@ecterrab 

I am brand new to maple.  I teach finance and have a pastime in Cosmology. So, my initial interest in Cosmology is what is bringing me to maple.

First solution, is the self-propagation

t(tau)=1-tau; x(tau)=0

so _C2=-1, _C3=1

Second solution is the logspiral solution.

 ln( t(tau) ) = ln(_C4) - x(tau) + _C3

So, 

1 - t(tau)=exp(-x(tau))

So, I just wanted to do a polar plot where the radius would be t  between [0,1]

and the angle is given by x/t

Some of the details I didn't get right in the first time (the metric is incorrect), that said, if you could help me finish this example, I will be able to modify the metric until I get it right.

The correct metric should describe a path where the distance projection on the outermost circle is the same as the distance traversed along the radial direction. Perhaps you could also advise me about the appropriate metric.

@tomleslie @mmcdara 

I read two underscores. When I typed the two underscores,  they would disappear.

If I only type one underscore that does not disappear and I am able to get the correct result

g_[]

so, everything is fine.  Thank you a million and sorry for wasting time.

Thanks

@tomleslie 

It worked both both 1-d math and 2-d math.

It is only when I type

@mmcdara 

@mmcdara 

Screenshot 2019-09-29 12.55.32

Screenshot 2019-09-29 12.56.29

@Torre 

Thanks, it worked like a charm.

@Torre

with(DifferentialGeometry); with(Tensor);

DGsetup([r, theta, phi, w], M)

ds2 := (dw &t dw) - w^2*(dr &t dr/(-kr^2 + 1) + r*sin(theta)^2*(`dθ` &t `dθ`) + r*(`dφ` &t `dφ`))/R0^2

g1 := evalDG((dw &t dw) - w^2*(dr &t dr/(-kr^2 + 1) + r*sin(theta)^2*(`dθ` &t `dθ`) + r*(`dφ` &t `dφ`))/R0^2)

Christoffel(g1)

Error, (in DifferentialGeometry:-Tensor:-Christoffel) expected 1st argument to be a metric tensor. Received: _DG([["tensor", M, [["cov_bas", "cov_bas"], []]], [[[4, 4], 1]]])-w^2*(_DG([["tensor", M, [["cov_bas", "cov_bas"], []]], [[[1, 1], -1/(kr^2-1)]]])+r*sin(theta)^2*`dθ`^2+r*`dφ`^2)/R0^2

Since I am using a standard metric (Friedmann), I would expect this to work. It seems that the interpreter interprets dr&t dr as a tensorial product. The rest it seems to interpret as an scalar.