Does anybody have any idea on how to define a linearly homogeneous function? The only solution I have come up with involves using rules and 'ReplaceAll'. This solution is not adequate, as it requires a lot of fine tuning. An example: Evaluating the following code, for a suitably defined function f (linearly homogeneous) should return 'True' f[tau x,tau y]==tau f[x,y] Alternatively, evaluating In[1]:= f[mu x1,mu x2] should return Out[1]:= mu f[x1,x2] Optionaly, it would really be an added bonus if somehow the definitions would persist, in the following sense: The derivative of a linearly homogeneous function should be a homogeneous function of degree 0, i.e. evaluating In[2]:= Derivative[1,0][f][k x,k y] should return Out[2]:= Derivative[1,0][f][x,y] I would be really gratefull if someone could offer a hint towards the right direction

Thanks Sander Huisman It seems it produces the expected output for this set of inputs I think the part(s) SetAttributes[f, Orderless] (...) f[?_, ?_ y_] := ? f[1, y] did the trick, or so it seems... I'll try to verify it with some more diverse input... but it looks promisning It even seems to 'propagate' the required behaviour to the derivatives thanks for taking the time!

What should happen with f[x,x] ? Should it return x f[1,1] ? if so, than add another rule: f[\[Tau]_, \[Tau]_ ] := \[Tau] f[1, 1] Regards.

yes,evaluating In[1]:= f[x,x] should produce Out[1]:= x f[1,1] so I did make use of your later suggestion (i.e. f[t_,t_]:= t f[1,1] ) I also replaced the 'Orderless' attribute with the definition f[t_ x_,t_]:= t f[x,1] because, for the context which these definitions are made, f[a,1] == f[1,a] does not hold always. So far and for a limited but sensible range of inputs it seems to be working as it should *Unfortunately, the behavior for the derivatives so far seems not the desired one (which makes perfect sense since no defitions involve the derivatives). D[f[x , y], x] /. {x -> a x, y -> a y} evaluates to Derivative[1,0][f][a x,a y] when it would be desirable to evaluate to Derivative[1,0][f][x,y]

How to define a homogeneous function?