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irasnyd |
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;Written By: Ira Snyder
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;Due Date: 02-16-2005
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;Homework #: hw08
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;;; Given a list in unsorted, unreduced Polynomial
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;;; Normal Form, and returns a list in perfect PNF
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(defun PNF (L)
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(do ((L L (cdr L))
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(RET nil))
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((null L) RET)
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(setf RET (INSERT (car L) RET))
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(setf RET (DEL-ZERO-COEF RET))
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)
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)
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;;; Given a pair of numbers (in a list) and a list of pairs
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;;; this inserts the pair into the list in it's correct place
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;;; including combining coefficients
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(defun INSERT (PAIR LIST)
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(cond
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((null LIST) (cons PAIR LIST))
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((> (cadr PAIR) (cadar LIST)) (cons PAIR LIST))
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((= (cadr PAIR) (cadar LIST)) (setf (caar LIST) (+ (car PAIR) (caar LIST))) LIST)
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(t (cons (car LIST ) (INSERT PAIR (cdr LIST))))
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)
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)
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;;; Deletes all of the pairs that have zero coefficients in
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;;; a PNF list
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(defun DEL-ZERO-COEF (L)
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(cond
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((null L) nil)
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((= 0 (caar L)) (DEL-ZERO-COEF (cdr L)))
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(t (cons (car L) (DEL-ZERO-COEF (cdr L))))
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)
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)
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;;; This takes a non-negative integer, and returns a string
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;;; containing the number of spaces specified by the integer
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(defun SPACES (N)
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(do ((N N (1- N))
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(STR (format nil "")))
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((zerop N) STR)
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(setf STR (concatenate 'string STR " "))
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)
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)
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(defun WRITE-POLY (L)
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(do ((L (PNF L) (cdr L))
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(EXP (format nil ""))
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(COEF (format nil "")))
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((null L) (format t "~A~%~A~%" EXP COEF))
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(setf COEF (concatenate 'string COEF (WRITE-NUM (caar L) (cadar L))))
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(MAKE-EQUAL EXP COEF)
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(setf EXP (concatenate 'string EXP (WRITE-EXP (caar L) (cadar L))))
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(MAKE-EQUAL EXP COEF)
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)
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)
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(defun WRITE-NUM (NUM EXP)
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(cond
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((zerop EXP) (if (plusp NUM) (format nil " + ~A" NUM) (format nil " - ~A" (abs NUM))))
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((plusp NUM) (format nil " + ~A x" NUM))
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(t (format nil " - ~A x" (abs NUM)))
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)
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)
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(defun WRITE-EXP (NUM EXP)
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(cond
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((zerop EXP) nil)
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((= EXP 1) nil)
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(t (format nil "~A" EXP))
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)
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)
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;;; When called with two strings as arguments, this macro
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;;; expands to make them the same length.
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(defmacro MAKE-EQUAL (S1 S2)
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`(cond
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((> (length ,S1) (length ,S2)) (let ((DIFF (- (length ,S1) (length ,S2))))
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(setf ,S2 (concatenate 'string ,S2 (SPACES DIFF)))))
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((< (length ,S1) (length ,S2)) (let ((DIFF (- (length ,S2) (length ,S1))))
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(setf ,S1 (concatenate 'string ,S1 (SPACES DIFF)))))
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(t nil)
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)
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)
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