00100	PROJECT ON ALGEBRAIC SIMPLIFICATION
00200	
00300	
00400		Write an MLISP program to simplify algebraic expressions
00500	consisting of sums, products, differences and quotients written
00600	in the LISP S-expression notation used in class.  These expressions
00700	have the syntax
00800	
00900	<expression>	::=	<integer>|<variable>|<sum>|<product>|
01000				<difference>|<quotient>
01100	
01200	<integer>	::=	<integer as in the LISP 1.6 Manual>
01300	
01400	<variable>	::=	<LISP non-numeric atom with the flag VAR on
01500					its property list>
01600	
01700	<sum>		::=	(PLUS[ <expression>]*)
01800	
01900	<product>	::=	(TIMES[ <expression>]*)
02000	
02100	<difference>	::=	(DIFFERENCE <expression> <expression>)
02200	
02300	<quotient>	::=	(QUOTIENT <expression> <expression>)
02400	
02500		Your program should be a function called SIMPLIFY, and
02600	it should do as many as possible of the following simplifications:
02700	
02800		1. Elimination of 0 and 1 terms from sums and products
02900	respectively and elimination of products with 0 terms.
03000	
03100		2. Elimination of sums and products with only one term or
03200	no terms at all.
03300	
03400		3. Collapsing of sums of sums and products of products.
03500	
03600		4. Collection of terms with numerical coefficients and
03700	combination of coefficients.
03800