(*^
::[	Information =

	"This is a Mathematica Notebook file.  It contains ASCII text, and can be
	transferred by email, ftp, or other text-file transfer utility.  It should
	be read or edited using a copy of Mathematica or MathReader.  If you 
	received this as email, use your mail application or copy/paste to save 
	everything from the line containing (*^ down to the line containing ^*)
	into a plain text file.  On some systems you may have to give the file a 
	name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
	The line below identifies what version of Mathematica created this file,
	but it can be opened using any other version as well.";

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:[font = subtitle; inactive; preserveAspect; startGroup]
Transformation Rules and Definitions
:[font = text; inactive; preserveAspect]
Define transformation rules:
Replace x by 1+a:
:[font = input; preserveAspect]
1+x^2 + 3 x^3 /. x -> 1 + a
:[font = text; inactive; preserveAspect]
Replace f[2] by b:
:[font = input; preserveAspect]
{f[1],f[2],f[3]} /. f[2] -> b
:[font = text; inactive; preserveAspect]
Replace f[n] by n2:
;[s]
3:0,0;17,1;18,0;20,-1;
2:2,13,9,Times,0,12,0,0,0;1,21,13,Times,32,12,0,0,0;
:[font = input; preserveAspect]
{f[1],f[2],f[3]} /. f[n_] -> n^2
:[font = text; inactive; preserveAspect]
Define function f[n]=n2 and apply to arithmetic and algebraic:
;[s]
3:0,0;22,1;23,0;63,-1;
2:2,13,9,Times,0,12,0,0,0;1,21,13,Times,32,12,0,0,0;
:[font = input; preserveAspect]
f[n_] := n^2
:[font = input; preserveAspect]
f[3] + f[a+b]
:[font = text; inactive; preserveAspect]
Define recursive user-supplied integer factorial function;
:[font = input; preserveAspect]
fac[n_] := n fac[n-1]
:[font = input; preserveAspect]
fac[1] := 1
:[font = input; preserveAspect]
?fac
:[font = input; preserveAspect]
fac[20]
:[font = text; inactive; preserveAspect]
Define rules for user-supplied log:
:[font = input; preserveAspect]
log[x_ y_] := log[x] + log[y]
:[font = input; preserveAspect]
log[a b c d]
:[font = text; inactive; preserveAspect]
Define rules for replacements of one form by another form;
:[font = input; preserveAspect]
g/: g[i_] + g[j_] := g[i+j]
:[font = input; preserveAspect; endGroup]
g[x] + g[y] + g[z]
^*)