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0

Test this carefully n=3; eqns={x+y==0,2x-3z==0,x-y+z==0}; xform={x->2y-z,y->3x+y,z->2z-x}; f[eqns_]:=Union[Simplify[Flatten[{eqns,Map[eqns/.#&,xform]}]]]; Nest[f,eqns,n] and see if it is doing exactly what you expect. You might start with n=1 and see if the result seems correct with a single iteration. If that seems correct then try with n=2, ...


4

Define step as the function that describes how f4 evolves at each step given the values of arguments x, y, w and z: ClearAll[step] step[x_, y_, w_, z_] := w + f1[x, y, z] + f2[x, y, w, z] + f3[x, y, z] Taking 3 steps with symbolic arguments: NestList[step[x, y, w, #]&, α, 3] {α, 2 w + 4 x + 4 y + 3 α, 8 w + 16 x + 16 y + 9 α, 26 w + 52 x + 52 y ...


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