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Re: Boolean algebra?

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: Boolean algebra?
• From: Jack K. Cohen <jkc at keller.mines.colorado.edu>
• Date: Tue, 29 Sep 92 13:50:49 -0600

Blush.  How about my article in the Mathematica Journal, V2, #1.
Although actually, 2.0 broke my code by changing the functionality  
of PolynomialMod.  To avoid answering 1/2 dozen requests, the  
updated modules are below

... STOP READING HERE, IF YOU DON'T CARE ABOUT THIS TOPIC ...
--------
(*
Author: Jack K. Cohen, Colorado School of Mines, 1992.
*)

BeginPackage["Logic`"];

(* Declaration of public function names in logic package *)

not::usage = "not[x]"

and::usage = "x ~and~ y"

xor::usage = "x ~xor~ y  (exclusive or)"

or::usage = "x ~or~ y"

implies::usage = "x ~implies~ y"

iff::usage = "x ~iff~ y	"

reduce::usage = "reduce[x]  (simplifies expressions)"


Begin["`private`"];

Unprotect[Power]
	Power[a_, n_Integer] := a   /; n > 1
Protect[Power]

reduce[x_] := FixedPoint[PolynomialMod[#, 2]&, x]

not[x_] := 1 + x
and[x_, y_] := x y
xor[x_, y_] := x + y
or[x_, y_] := x + y + x y
implies[x_, y_] := 1 + x + x y
iff[x_, y_] := 1 + x + y

End[];

Endpackage[];
--------
(*
Author: Jack K. Cohen, Colorado School of Mines, 1992.
*)

BeginPackage["Set`"];

(* Declaration of public function names in set theory package *)

c::usage = "c[x]   (complement of x)"

i::usage = "x ~i~ y   (intersection of x and y)"

s::usage = "x ~s~ y   (symmetric difference of x and y: (x-y) U  
(y-x))"

u::usage = "x ~u~ y   (union of x and y)"

d::usage = "x ~d~ y   (difference of x and y:  (x - y))"

ss::usage = "x ~ss~ y  (x is a subset of y)"

eq::usage = "x ~eq~ y  (x equals y)"

intersection::usage = "intersection[a, n]  (a[1] ~i~ a[2] ~i~ ...  
~i~ a[n])"

union::usage = "union[a, n]  (a[1] ~u~ a[2] ~u~ ... ~u~ a[n])"

reduce::usage = "reduce[x]   (simplifies expressions)" 



Begin["`private`"];

Unprotect[Power]
	Power[a_, n_Integer] := a   /; n > 1
Protect[Power]

reduce[x_] := Expand[Simplify[Mod[x, 2]]]

c[x_] := 1 + x
i[x_, y_] := x y
s[x_, y_] := x + y
u[x_, y_] := x + y + x y
d[x_, y_] := x + x y
ss[x_, y_] := 1 + x + x y
eq[x_, y_] := 1 + x + y
intersection[a_ + b_Integer:0, n_] := reduce[Product[a[i] + b, {i,  
n}]]
union[a_ + b_Integer:0, n_] :=
	Block[{sum = 0, k},
		Do [
			sum = sum ~u~ (a[k] + b),
		{k, n}];
		Return[reduce[sum]]
	]

End[];

Endpackage[];