# Techniques for simplifying expressions

I am hoping to get techniques to use when faced with expressions I think may be simplified. From two symmetrical looks at a problem I ended up with two inequalities. With excess stuff removed and everything is a non-negative integer:

$$x\le\delta(A_s,X_v)+\delta(z,X_s)$$ and $$x\le\delta(X_s,A_v)+\delta(z,A_s)$$

$$\delta(z)=\begin{cases} 0 & z=2^{j}\\ 1 & otherwise \end{cases}$$ and $$\delta(x,y,\ldots)=\delta(x)\delta(y,...)$$

It would be nice to just have a single bound for $$x$$ if it's not complicated.

So I define delta as:

d[x_] := If[DigitCount[x, 2, 1] == 1, 0, 1]

I want to simplify:

x <= d[Xs]*d[Av] + d[z]*d[As] && x <= d[As]*d[Xv] + d[z]*d[Xs]

or maybe

Min[d[Xs]*d[Av] + d[z]*d[As], d[As]*d[Xv] + d[z]*d[Xs]]

What can I use to investigate this?

• I doubt very much that any simplification is possible, on the paper or with the help of MA. You seems to have some relation between Xs and As and between Xv and Av. Maybe you can do more knowing them. Sep 11 at 9:30