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I need to find the Killing vectors of a metric.

I initiate the session as

> restart;
> with(DifferentialGeometry); with(Tensor); with(LieAlgebras);
> DGsetup([t, r, z, phi], M);

and enter my metric as

M > g1 := evalDG(-dt &t dt ...);

I do not have an unknown function in my metric but I have two free parameters (e.g. a and b).

I use

M > K1 := KillingVectors(g1, parameters = [a, b]);

What is the distance between the trigonometrical polynomials of the form a0/2+a1*cos(Pi*x)+b1*sin(Pi*x) and the polynomials of  degree at most 1, ie c0+c1*x, in the Chebyshev metrics on the interval [-1,1] and in the L^2 metrics on the same interval?