### Chapter 2, Building Abstractions with Data

### Section - 2.5 - Systems with Generic Operations

#### Exercise 2.90

Apparently I did not find it as difficult as it seemed from the hint. Perhaps I missed something :)

My understanding is problem requires to implement the polynomial system that can be used for both sparse and dense termlists and all operations can be performed between them. It has *not* asked to implement procedures that for the efficiency - It *only* asked to implement system which can *enable* us to later implement a polynomial system which is efficient for both dense and sparse. I believe so because as per my experience with the old problems - the problem generally gives an outline for what it seeks in the solution - here it only gave an outline to build a system which can enable operations on both term-list.

If the case is to implement the system where our polynomial also *decides* whether to use sparse or dense then it can also be implemented - we just need to think for the strategy - at how much packing is considered good for sparse and inside make-polynomial we can check with this strategy and do conversions(I have not made this change).

I made the following changes:

- Implemented two terms-list packages - ‘dense-termlist, ‘sparse-termlist
`make-term`

,`coeff`

, and`order`

are owned by the polynomial package(not by the term-list packages implemented) because they are terms not the list themselves and both packages - sparse-termlist and dense-termlist use them from the polynomial package.- There is an interesting way I worked around with the
`adjoin-term`

- this procedure have different implementation for each package and which should be the part of the respective term-list packages. But I can not apply`adjoin-term`

in generic way because it takes two arguments -`term`

, and`termlist`

- where term does not have any type tag in my implementation because I made term to be owned by polynomial package instead of termlist package(which may be debatable). So, I made`adjoin-term-proc`

- a procedure that returns a procedure! And the returned procedure takes an argument - term and adds it to the list. See the implementation for details.

Here is the complete code(Examples in the end):

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#lang sicp
(#%require (only racket/base error))
(#%require (only racket/base make-hash))
(#%require (only racket/base hash-set!))
(#%require (only racket/base hash-ref))
;Polynomial Package
(define (install-polynomial-package)
;; internal procedures
;; representation of poly
(define (make-poly variable term-list)
(cons variable term-list)
)
(define (variable p) (car p))
(define (term-list p) (cdr p))
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2) (and (variable? v1) (variable? v2) (eq? v1 v2)))
;; representation of terms and term lists
(define (adjoin-term term list)
((apply-generic 'adjoin-term-proc list) term)
)
(define (first-term terms)
(apply-generic 'first-term terms)
)
(define (rest-terms terms)
(apply-generic 'rest-terms terms)
)
(define (empty-termlist? terms)
(apply-generic 'empty-termlist? terms)
)
(define (make-term order coeff) (list order coeff))
(define (order term) (car term))
(define (coeff term) (cadr term))
(define (add-poly p1 p2)
(if (same-variable? (variable p1) (variable p2))
(make-poly (variable p1)
(add-terms (term-list p1)
(term-list p2)
)
)
(error "Polys not in same var -- ADD-POLY" (list p1 p2))
)
)
(define (mul-poly p1 p2)
(if (same-variable? (variable p1) (variable p2))
(make-poly (variable p1)
(mul-terms (term-list p1)
(term-list p2)
)
)
(error "Polys not in same var -- MUL-POLY" (list p1 p2))
)
)
(define (sub-poly p1 p2) (add-poly p1 (negate-poly p2)))
(define (negate-poly p) (make-poly (variable p) (negate-termlist (term-list p))))
(define (negate-termlist terms)
(if (empty-termlist? terms)
terms
(adjoin-term (make-term (order (first-term terms)) (apply-generic 'negate (coeff (first-term terms)))) (negate-termlist (rest-terms terms)))
)
)
(define (add-terms L1 L2)
(cond ((empty-termlist? L1) L2)
((empty-termlist? L2) L1)
(else
(let ((t1 (first-term L1)) (t2 (first-term L2)))
(cond ((> (order t1) (order t2))
(adjoin-term
t1 (add-terms (rest-terms L1) L2))
)
((< (order t1) (order t2))
(adjoin-term t2 (add-terms L1 (rest-terms L2))))
(else
(adjoin-term
(make-term (order t1)
(add (coeff t1) (coeff t2))
)
(add-terms (rest-terms L1)
(rest-terms L2)
)
)
)
)
)
)
)
)
(define (mul-terms L1 L2)
(if (empty-termlist? L1)
L1
(add-terms (mul-term-by-all-terms (first-term L1) L2)
(mul-terms (rest-terms L1) L2)
)
)
)
(define (mul-term-by-all-terms t1 L)
(if (empty-termlist? L)
L
(let ((t2 (first-term L)))
(adjoin-term
(make-term (+ (order t1) (order t2))
(mul (coeff t1) (coeff t2))
)
(mul-term-by-all-terms t1 (rest-terms L))
)
)
)
)
;; interface to rest of the system
(define (tag p) (attach-tag 'polynomial p))
(put 'add '(polynomial polynomial)
(lambda (p1 p2) (tag (add-poly p1 p2))))
(put 'sub '(polynomial polynomial)
(lambda (p1 p2) (tag (add-poly p1 (negate-poly p2)))))
(put 'mul '(polynomial polynomial)
(lambda (p1 p2) (tag (mul-poly p1 p2))))
(put 'make 'polynomial
(lambda (var terms) (tag (make-poly var terms))))
(put 'make-term 'polynomial make-term)
(put 'order 'polynomial order)
(put 'coeff 'polynomial coeff)
(put 'negate '(polynomial) (lambda (p) (tag (negate-poly p))))
(define (=is-zero? poly)
(define (iter terms)
(if (apply-generic 'empty-termlist? terms)
#t
(and (=zero? (coeff (first-term terms))) (iter (rest-terms terms)))
)
)
(iter (term-list poly))
)
(put '=zero? '(polynomial) =is-zero?)
'done)
(define (make-polynomial var terms)
((get 'make 'polynomial) var terms))
(define (make-term order coeff)
((get 'make-term 'polynomial) order coeff))
(define (order term)
((get 'order 'polynomial) term))
(define (coeff term)
((get 'coeff 'polynomial) term))
;dense-termlist package
(define (install-dense-termlist-package)
(define (adjoin-term-dense term term-list)
(define (iter count terms)
(if (= count 0)
terms
(iter (- count 1) (cons 0 terms))
)
)
(let ((cof (coeff term))
(count (- (order term) (length term-list)))
)
(cond
((=zero? cof) term-list)
((< count 0) (error "Can not add term - order of passed term is already present in the list"))
(else (cons cof (iter count term-list)))
)
)
)
(define (first-term term-list) (make-term (- (length term-list) 1) (car term-list)))
;; interface to rest of the system
(define (tag tl) (attach-tag 'dense-termlist tl))
(put 'empty-dense-termlist 'dense-termlist (lambda () (tag '())))
(put 'first-term '(dense-termlist) first-term)
(put 'rest-terms '(dense-termlist) (lambda (tl) (tag (cdr tl))))
(put 'empty-termlist? '(dense-termlist) null?)
(put 'adjoin-term-proc '(dense-termlist) (lambda(tl) (lambda(term) (tag (adjoin-term-dense term tl)))))
'done)
(define (empty-dense-termlist)
((get 'make 'dense-termlist))
)
;sparse-termlist package
(define (install-sparse-termlist-package)
(define (adjoin-term-sparse term term-list)
(if (=zero? (coeff term))
term-list
(cons term term-list)
)
)
;; interface to rest of the system
(define (tag tl) (attach-tag 'sparse-termlist tl))
(put 'empty-sparse-termlist 'dense-termlist (lambda () (tag '())))
(put 'first-term '(sparse-termlist) (lambda (tl) (car tl)))
(put 'rest-terms '(sparse-termlist) (lambda (tl) (tag (cdr tl))))
(put 'empty-termlist? '(sparse-termlist) null?)
(put 'adjoin-term-proc '(sparse-termlist) (lambda(tl) (lambda(term) (tag (adjoin-term-sparse term tl)))))
'done)
(define (empty-sparse-termlist)
((get 'make 'sparse-termlist))
)
; Code below this is the arithmetic package we built in the last section
; Arithmetic Package
(define (sine x) (sin (contents (raise-to-type 'scheme-number x))))
(define (cosine x) (cos (contents (raise-to-type 'scheme-number x))))
(define (arctan x) (atan (contents (raise-to-type 'scheme-number x))))
(define (drop arg)
(if (has-type-tag? arg)
(let ((type (type-tag arg)))
(let ((proc (get-projection type)))
(if (not (null? proc))
(let ((projected (proc arg)))
(let ((raised (raise-to-type type projected)))
(if ((get 'equ? (list type type)) (contents raised) (contents arg))
(drop projected)
arg
)
)
)
arg
)
)
)
arg
)
)
(define (apply-generic op . args)
(let ((type-tags (map type-tag args)))
(let ((proc (get op type-tags)))
(if (not (null? proc))
(drop (apply proc (map contents args)))
(let ((has-same-type
(accumulate
(lambda (a b) (and a b))
#t
(map
(lambda(x) (equal? (car type-tags) x))
(cdr type-tags)
)
)
))
(let ((highest-type (if has-same-type
(get-parent (car type-tags))
(find-highest-type type-tags)
)
))
(if (null? highest-type)
(error "Could not find a suitable ancestor" op args)
(let ((raised-args (map-until
'()
(lambda(arg)
(raise-to-type highest-type arg)
)
args
)
))
(if (not (null? raised-args))
(apply apply-generic op raised-args)
(error "Error. No suitable raise method found to raise all types into " highest-type " for raising types " type-tags)
)
)
)
)
)
)
)
)
)
(define *type-table* (make-hash))
(define (put-parent type parent)
(let ((already-set (hash-ref *type-table* (list 'parent type) '())))
(if (null? already-set)
(hash-set! *type-table* (list 'parent type) parent)
(error "Parent already defined for :" type " parent currently *present* is " already-set " the passed parent " parent)
)
)
)
(define (get-parent type)
(hash-ref *type-table* (list 'parent type) '())
)
(define (put-child type child)
(let ((already-set (hash-ref *type-table* (list 'child type) '())))
(if (null? already-set)
(hash-set! *type-table* (list 'child type) child)
(error "Child already defined for :" type " child currently *present* is " already-set " the passed child " child)
)
)
)
(define (get-child type)
(hash-ref *type-table* (list 'child type) '())
)
(define *cast-table* (make-hash))
(define (put-raise type proc)
(let ((already-set (hash-ref *cast-table* (list 'raise type) '())))
(if (null? already-set)
(hash-set! *cast-table* (list 'raise type) proc)
(error "Raise is already defined for :" type)
)
)
)
(define (get-raise type)
(hash-ref *cast-table* (list 'raise type) '())
)
(define (put-projection type proc)
(let ((already-set (hash-ref *cast-table* (list 'project type) '())))
(if (null? already-set)
(hash-set! *cast-table* (list 'project type) proc)
(error "Project is already defined for :" type)
)
)
)
(define (get-projection type)
(hash-ref *cast-table* (list 'project type) '())
)
(define (get-ancestors type)
(if (null? type)
'()
(cons type (get-ancestors (get-parent type)))
)
)
(define (contains item item-list)
(fold-left
(lambda(result new)
(or result (equal? item new))
)
#f
item-list
)
)
(define (find-highest-type type-tags)
(let ((ancestors-of-each-type (map get-ancestors type-tags)))
(let ((smallest-ancestor-set
(accumulate (lambda(new remaining)
(if (< (size new) (size remaining))
new
remaining
)
)
(car ancestors-of-each-type)
ancestors-of-each-type
)
))
(define (find-type-present-in-each-ancestors type-list)
(if (null? type-list)
'()
(let ((found (accumulate
(lambda (a b) (and a b))
#t
(map
(lambda(ancestors) (contains (car type-list) ancestors))
ancestors-of-each-type)
)
))
(if found
(car type-list)
(find-type-present-in-each-ancestors (cdr type-list))
)
)
)
)
(find-type-present-in-each-ancestors smallest-ancestor-set)
)
)
)
(define (raise-to-type type arg)
(cond ((null? arg) '())
((equal? type (type-tag arg)) arg)
(else (let ((proc (get-raise (type-tag arg))))
(if (null? proc)
'()
(raise-to-type type (proc arg))
)
)
)
)
)
(define (map-until until-val proc args)
(if (null? args)
'()
(let ((arg (car args)))
(let ((marg (proc arg)))
(if (equal? marg until-val)
'()
(cons marg (map-until until-val proc (cdr args)))
)
)
)
)
)
(define (fold-left op initial sequence)
(define (iter result rest)
(if (null? rest)
result
(iter (op result (car rest))
(cdr rest))))
(iter initial sequence))
(define (raise n)
((get-raise (type-tag n)) n)
)
;use mul as x can be rational-number also
(define (square x) (mul x x))
(define *op-table* (make-hash))
(define (put op type proc)
(hash-set! *op-table* (list op type) proc)
)
(define (get op type)
(hash-ref *op-table* (list op type) '())
)
(define (attach-tag type-tag contents)
(if (equal? 'scheme-number type-tag)
contents
(cons type-tag contents)
)
)
(define (has-type-tag? datum)
(cond
((number? datum) #t)
((pair? datum)
(contains (car datum) '(int complex rational))
)
(else #f)
)
)
(define (type-tag datum)
(cond
((number? datum) 'scheme-number)
((pair? datum) (car datum))
(else (error "Bad tagged datum -- TYPE-TAG" datum))
)
)
(define (contents datum)
(cond
((pair? datum) (cdr datum))
(error "Bad tagged datum -- CONTENTS" datum)
)
)
(define (filter predicate sequence)
(cond ((null? sequence) nil)
((predicate (car sequence))
(cons (car sequence)
(filter predicate (cdr sequence))))
(else (filter predicate (cdr sequence)))))
(define (size list)
(if (null? list) 0 (+ 1 (size (cdr list)))))
(define (list-and proc list)
(define (iter list)
(if (null? list)
#t
(let ((rs (proc (car list))))
(if (boolean? rs)
(if rs (iter (cdr list)) #f)
(error "Proc should return boolean")
)
)
)
)
(cond ((null? list) (error "Operation not defined for 0 items"))
((not (pair? list)) (error "Operation works only for lists"))
(else (iter list))
)
)
(define (accumulate op initial sequence)
(if (null? sequence)
initial
(op (car sequence)
(accumulate op initial (cdr sequence)))
)
)
;;;;;;;;;;;;;;;;;;;;;;;;
(define (install-int-package)
(define (tag x)
(attach-tag 'int x))
(put 'add '(int int)
(lambda (x y) (tag (+ x y))))
(put 'sub '(int int)
(lambda (x y) (tag (- x y))))
(put 'mul '(int int)
(lambda (x y) (tag (* x y))))
(put 'div '(int int)
(lambda (x y) (tag (/ x y))))
(put 'make 'int
(lambda (x) (tag x)))
;equ?
(put 'equ? '(int int) =)
(put 'negate '(int) -)
; raise operation
(put-raise 'int (lambda(x) (make-rational (contents x) 1)))
; set parent
(put-parent 'int 'rational)
(put '=zero? '(int) (lambda (x) (= x 0)))
'done
)
(define (make-integer n)
((get 'make 'int) n)
)
;;;;;;;;;;;;;;;;;;;;;;;;
(define (install-scheme-number-package)
(define (tag x)
(attach-tag 'scheme-number x))
(put 'add '(scheme-number scheme-number)
(lambda (x y) (tag (+ x y))))
(put 'sub '(scheme-number scheme-number)
(lambda (x y) (tag (- x y))))
(put 'mul '(scheme-number scheme-number)
(lambda (x y) (tag (* x y))))
(put 'div '(scheme-number scheme-number)
(lambda (x y) (tag (/ x y))))
(put 'make 'scheme-number
(lambda (x) (tag x)))
;equ?
(put 'equ? '(scheme-number scheme-number) =)
(put 'negate '(scheme-number) -)
;; following added to Scheme-number package
(put 'exp '(scheme-number scheme-number)
(lambda (x y) (tag (expt x y)))) ; using primitive expt
; raise operation
(put-raise 'scheme-number (lambda(x) (make-complex-from-real-imag (contents x) 0)))
; set parent
(put-parent 'scheme-number 'complex)
;a simple way to convert from real to rational is by multiplying and dividing by a
; constant but it will only be correct to 4 places of decimal(4 zeroes in 10000)
(define multiplier 10000)
; project operation
(put-projection 'scheme-number (lambda(c) (make-rational (floor (* (contents c) multiplier)) multiplier)))
; set child
(put-child 'scheme-number 'rational)
(put '=zero? '(scheme-number) (lambda (x) (= x 0)))
'done
)
(define (make-number n)
((get 'make 'scheme-number) n)
)
(define (install-rational-package)
;; internal procedures
(define (numer x) (car x))
(define (denom x) (cdr x))
(define (make-rat n d)
(if (and (integer? n) (integer? d))
(let ((nn (inexact->exact n))
(dd (inexact->exact d))
)
(let ((g (gcd nn dd)))
(cons (/ nn g) (/ dd g))
)
)
(error "Number and Denom shoud be integers" n d)
)
)
(define (add-rat x y)
(make-rat (+ (* (numer x) (denom y))
(* (numer y) (denom x)))
(* (denom x) (denom y))))
(define (sub-rat x y)
(make-rat (- (* (numer x) (denom y))
(* (numer y) (denom x)))
(* (denom x) (denom y))))
(define (mul-rat x y)
(make-rat (* (numer x) (numer y))
(* (denom x) (denom y))))
(define (div-rat x y)
(make-rat (* (numer x) (denom y))
(* (denom x) (numer y))))
;; equ?
(define (equ? x y)
(and (= (numer x) (numer y)) (= (denom x) (denom y))))
;; interface to rest of the system
(define (tag x) (attach-tag 'rational x))
(put 'add '(rational rational)
(lambda (x y) (tag (add-rat x y))))
; comment this to check the example suggested above for tree structure support
(put 'sub '(rational rational)
(lambda (x y) (tag (sub-rat x y))))
(put 'mul '(rational rational)
(lambda (x y) (tag (mul-rat x y))))
(put 'div '(rational rational)
(lambda (x y) (tag (div-rat x y))))
(put 'make 'rational
(lambda (n d) (tag (make-rat n d))))
(put 'equ? '(rational rational) equ?)
(put 'negate '(rational) (lambda (r) (make-rat (- (numer r)) (denom r))))
; raise operation
(put-raise 'rational (lambda(r) (make-number (/ (numer (contents r)) (denom (contents r))))))
; set parent
(put-parent 'rational 'scheme-number)
; project operation
(put-projection 'rational (lambda(r) (make-integer (floor (/ (numer (contents r)) (denom (contents r)))))))
; set child
(put-child 'rational 'int)
; uncomment this and comment above raise to make rational as child of complex instead of number
; (put-raise 'rational (lambda(r) (make-complex-from-real-imag (/ (numer (contents r)) (denom (contents r))) 0)))
; uncomment this and comment above raise to make rational as child of complex instead of number
; (put-parent 'rational 'complex)
(put '=zero? '(rational) (lambda (x) (= (numer x) 0)))
'done
)
(define (make-rational n d)
((get 'make 'rational) n d)
)
(define (install-complex-package)
;; imported procedures from rectangular and polar packages
(define (make-from-real-imag x y)
((get 'make-from-real-imag 'rectangular) x y))
(define (make-from-mag-ang r a)
((get 'make-from-mag-ang 'polar) r a))
;; internal procedures
(define (add-complex z1 z2)
(make-from-real-imag (add (apply-generic 'real-part z1) (apply-generic 'real-part z2))
(add (apply-generic 'imag-part z1) (apply-generic 'imag-part z2))))
(define (sub-complex z1 z2)
(make-from-real-imag (sub (apply-generic 'real-part z1) (apply-generic 'real-part z2))
(sub (apply-generic 'imag-part z1) (apply-generic 'imag-part z2))))
(define (mul-complex z1 z2)
(make-from-mag-ang (mul (apply-generic 'magnitude z1) (apply-generic 'magnitude z2))
(add (apply-generic 'angle z1) (apply-generic 'angle z2))))
(define (div-complex z1 z2)
(make-from-mag-ang (div (apply-generic 'magnitude z1) (apply-generic 'magnitude z2))
(sub (apply-generic 'angle z1) (apply-generic 'angle z2))))
(define (equ? z1 z2)
(and
(apply-generic 'equ? (apply-generic 'real-part z1) (apply-generic 'real-part z2))
(apply-generic 'equ? (apply-generic 'imag-part z1) (apply-generic 'imag-part z2))
)
)
(define (complex-negate z)
(make-from-real-imag
(apply-generic 'negate (apply-generic 'real-part z))
(apply-generic 'negate (apply-generic 'real-part z))
)
)
;; interface to rest of the system
(define (tag z) (attach-tag 'complex z))
(put 'add '(complex complex)
(lambda (z1 z2) (tag (add-complex z1 z2))))
(put 'sub '(complex complex)
(lambda (z1 z2) (tag (sub-complex z1 z2))))
(put 'mul '(complex complex)
(lambda (z1 z2) (tag (mul-complex z1 z2))))
(put 'div '(complex complex)
(lambda (z1 z2) (tag (div-complex z1 z2))))
(put 'make-from-real-imag 'complex
(lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'complex
(lambda (r a) (tag (make-from-mag-ang r a))))
(put 'equ? '(complex complex) equ?)
(put `nagate '(complex) complex-negate)
; raise operation is not defined for complex
; parent not defined for complex
; project operation
(put-projection
'complex
(lambda(c)
;note that we can not call apply-generic here because this method is used by drop and drop is used in generic
;thus it can go into a loop
;so need to take care of type-tags here only
; c is complex number(includes tag complex) cc is rectangular/angular including the type-tag
; Note that, the repurcurssions of drop lead to the point that real and imag can be any number except number
; thus raising it to the real number type (because apart from complex numbers, my understanding is any number can be raised to real number
(let ((cc (contents c)))
(raise-to-type 'scheme-number ((get 'real-part (list (type-tag cc))) (contents cc)))
)
)
)
; set child
(put-child 'complex 'scheme-number)
;; complex package:
(define (=is-zero? z)
(and
(= (apply-generic 'real-part z) 0)
(= (apply-generic 'imag-part z) 0)
)
)
(put '=zero? '(complex) =is-zero?)
'done
)
(define (sqrt x)
;note the magic of apply-generic
;it will convert that rational into real because expt is only defined in
;scheme-number package and rational can be raised to scheme-number
(exp x (make-rational 1 2))
)
(define (install-rectangular-package)
;; internal procedures
(define (real-part z) (car z))
(define (imag-part z) (cdr z))
(define (make-from-real-imag x y) (cons x y))
(define (magnitude z)
(sqrt (add (square (real-part z))
(square (imag-part z)))))
(define (angle z)
(arctan (div (imag-part z) (real-part z))))
(define (make-from-mag-ang r a)
(cons (mul r (cosine a)) (mul r (sine a))))
;; interface to the rest of the system
(define (tag x) (attach-tag 'rectangular x))
(put 'real-part '(rectangular) real-part)
(put 'imag-part '(rectangular) imag-part)
(put 'magnitude '(rectangular) magnitude)
(put 'angle '(rectangular) angle)
(put 'make-from-real-imag 'rectangular
(lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'rectangular
(lambda (r a) (tag (make-from-mag-ang r a))))
'done)
(define (install-polar-package)
;; internal procedures
(define (magnitude z) (car z))
(define (angle z) (cdr z))
(define (make-from-mag-ang r a) (cons r a))
(define (real-part z)
(mul (magnitude z) (cosine (angle z))))
(define (imag-part z)
(mul (magnitude z) (sine (angle z))))
(define (make-from-real-imag x y)
(cons (sqrt (add (square x) (square y)))
(arctan (div y x))))
;; interface to the rest of the system
(define (tag x) (attach-tag 'polar x))
(put 'real-part '(polar) real-part)
(put 'imag-part '(polar) imag-part)
(put 'magnitude '(polar) magnitude)
(put 'angle '(polar) angle)
(put 'make-from-real-imag 'polar
(lambda (x y) (tag (make-from-real-imag x y))))
(put 'make-from-mag-ang 'polar
(lambda (r a) (tag (make-from-mag-ang r a))))
'done)
(define (make-complex-from-real-imag x y)
((get 'make-from-real-imag 'complex) x y))
(define (make-complex-from-mag-ang r a)
((get 'make-from-mag-ang 'complex) r a))
(define (equ? x y)
(apply-generic 'equ? x y)
)
(define (exp x y) (apply-generic 'exp x y))
(define (add x y) (apply-generic 'add x y))
(define (sub x y) (apply-generic 'sub x y))
(define (mul x y) (apply-generic 'mul x y))
(define (div x y) (apply-generic 'div x y))
(define (=zero? x) (apply-generic '=zero? x))
(define (negate x) (apply-generic 'negate x))
(install-rectangular-package)
(install-polar-package)
(install-scheme-number-package)
(install-rational-package)
(install-int-package)
(install-complex-package)
(install-sparse-termlist-package)
(install-dense-termlist-package)
(install-polynomial-package)

Test/Sample Output:

Note that - my integer representation adds tag - integer and drop is dropping to int when ‘add is performed. Thus `(int 5)`

actually means `5`

.

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> (display (add (make-polynomial 'x (attach-tag 'sparse-termlist '((5 2) (3 2)))) (make-polynomial 'x (attach-tag 'sparse-termlist '((5 3) (3 6))))))
(polynomial x sparse-termlist (5 (int . 5)) (3 (int . 8)))
> (display (add (make-polynomial 'x (attach-tag 'dense-termlist '(1 2 3))) (make-polynomial 'x (attach-tag 'dense-termlist '(4 5 6)))))
(polynomial x dense-termlist (int . 5) (int . 7) (int . 9))
> (display (add (make-polynomial 'x (attach-tag 'dense-termlist '(1 2 3))) (make-polynomial 'x (attach-tag 'sparse-termlist '((2 4) (1 5) (0 6))))))
(polynomial x sparse-termlist (2 (int . 5)) (1 (int . 7)) (0 (int . 9)))
> (display (sub (make-polynomial 'x (attach-tag 'dense-termlist '(1 2 3))) (make-polynomial 'x (attach-tag 'dense-termlist '(4 5 6)))))
(polynomial x dense-termlist (int . -3) (int . -3) (int . -3))
> (display (sub (make-polynomial 'x (attach-tag 'dense-termlist '(1 2 3))) (make-polynomial 'x (attach-tag 'sparse-termlist '((2 4) (1 5) (0 6))))))
(polynomial x sparse-termlist (2 (int . -3)) (1 (int . -3)) (0 (int . -3)))
> (display (add (make-polynomial 'x (attach-tag 'sparse-termlist '((5 2) (3 2)))) (make-polynomial 'x (attach-tag 'sparse-termlist '((5 3) (3 6))))))
(polynomial x sparse-termlist (5 (int . 5)) (3 (int . 8)))
> (display (mul (make-polynomial 'x (attach-tag 'sparse-termlist '((1 1) (0 1)))) (make-polynomial 'x (attach-tag 'sparse-termlist '((1 1) (0 1))))))
(polynomial x sparse-termlist (2 (int . 1)) (1 (int . 2)) (0 (int . 1)))
> (display (mul (make-polynomial 'x (attach-tag 'dense-termlist '(1 1))) (make-polynomial 'x (attach-tag 'dense-termlist '(1 1)))))
(polynomial x dense-termlist (int . 1) (int . 2) (int . 1))
> (display (mul (make-polynomial 'x (attach-tag 'dense-termlist '(1 1))) (make-polynomial 'x (attach-tag 'sparse-termlist '((1 1) (0 1))))))
(polynomial x sparse-termlist (2 (int . 1)) (1 (int . 2)) (0 (int . 1)))