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These are replies submitted by ny2292000


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.

{t(tau) = _C2*tau+_C3, x(tau) = _C1}, {t(tau) = _C4*((_C1*_C2+_C1*tau+4)*(_C1*_C2+_C1*tau-4))^(1/2), x(tau) = -(1/2)*ln(_C1*_C2+_C1*tau+4)+(1/2)*ln(_C1*_C2+_C1*tau-4)+_C3}

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


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


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



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

It is only when I type


Screenshot 2019-09-29 12.55.32

Screenshot 2019-09-29 12.56.29


Thanks, it worked like a charm.


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)


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.

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