# Mathematica not simplifing when using FullSimplify

I am trying to simplify the following $(Z_i - Z_{i+1})^4$ using

FullSimplify[(Subscript[Z, i] - Subscript[Z, 1 + i])^4 ,
Assumptions -> {\[CapitalDelta]z > 0,
Subscript[Z, i] \[Element] Reals,
Subscript[Z, i - 1] < Subscript[Z, i] < Subscript[Z, i + 1],
Subscript[Z, i + 1] - Subscript[Z, i ] == \[CapitalDelta]z,
Subscript[Z, i] - Subscript[Z, i - 1 ] == \[CapitalDelta]z}]


The answer should be $\Delta z^4$ but it just returns the same thing that I put in. Is there something that I am missing?

-

You can use a custom transformation function:

t[e_] := Collect[e /. Subscript[z, i_] :> Subscript[z, 0] + i dz, dz]
FullSimplify[
(Subscript[z, i] - Subscript[z, i + 1] + Subscript[z, i + 10] -Subscript[z, i + 2])^4,
TransformationFunctions -> {t, Automatic}]


Or define z to have that property:

Clear@z
z[i_] := z[0] + i dz /; i =!= 0
Simplify@(z[i] - z[i + 1] + z[i + 10] - z[i + 2])^4


A bit cleaner:

Clear@z
z[i_] := z0 + i dz

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+1 z[i_] := z0 + i dz is soooo beautiful – Dr. belisarius Feb 26 '13 at 4:27