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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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Generators sl(lambda): x y z;
Parameter, T = t^2, L = lambda^2: T L;
Relations:

[[x,y],x] - 2 x;
[[x,y],y] + 2 y;

[y,z];
[[x,y],z] + 4 z;
[x,[x,[x,[x,[x,z]]]]];

3 [[x,z],[x,[x,z]]] - 2 [z,[x,[x,[x,z]]]] - (24 L T - 96 T) y;
[z,[z,[x,z]]];
4 [[x,[x,[x,z]]],[z,[x,z]]] - 3 [[x,[x,z]],[z,[x,[x,z]]]] -
                                       (576 L T - 5184 T) z;