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HUV 5NPF5HUV lMM H$ 5O5 H$ ;;-Num P VUUe " ea mH$ 5PN5dinH$ lOO ag-HH@QD UJHHin UTRqr ` 3 ) Complex Number Arithmetic &UT UT` -p ;UR UT` 2 ˪(define (add-complex z1 z2) UBPUP UT` 4  (make-from-real-imag -paeUN UT` 5 ˪& (+ (real-part z1) (real-part z2)) zUL UT` 6 ng( (+ (imag-part z1) (imag-part z2)))) (UJ UT` 7 a) UH UT` 9 (define (sub-complex z1 z2) UF UT` : 5 (make-from-real-imag HUD UT` ; & (- (real-part z1) (real-part z2)) UB UT` < ( (- (imag-part z1) (imag-part z2)))) 5U@ UT` =   U> UT` > (define (mul-complex z1 z2) "U< UT` ?  (make-from-mag-ang 7U: UT` @ & (* (magnitude z1) (magnitude z2)) LU8 UT` A (+ (angle z1) (angle z2)))) eaaU6 UT` C  vU4 UT` D (define (div-complex z1 z2) U2 UT` E  (make-from-mag-ang U0 UT` F @& (/ (magnitude z1) (magnitude z2)) U. UT` G (- (angle z1) (angle z2)))) qrU, UT` H  3HH@RD HHlSQQ PUPHHISKaUNHHlRVLL  UTdJTa zVV5 HHJUT zz2HH<5 HUDV ` Y eaAlyssas representation <) ` -p UT` d ) (cons (sqrt (+ (square x) (square y))) 8U< UT` e  (atan y x))) HHJ VTHHlSYUU dJmWYYHHJnXW HH=Y ` i nt Tagged Data ) ` j UT T? ` l ep aRUT UT` m Nu'(define (attach-tag type-tag contents) romgUR UT` n s  (cons type-tag contents)) (d|UP UT` o )  rUN UT` p ˪(define (type-tag datum) UL UT` q UT (if (pair? datum) UTUJ UT` r in (car datum) UH UT` u 4 (error "Bad tagged datum - TYPE-TAG" datum))) UF UT` s rt UD UT` t ) (define (contents datum) aUB UT` v UT (if (pair? datum) UT$U@ UT` w in (cdr datum) 9U> UT` z ˪4 (error "Bad tagged datum - CONTENTS" datum))) U<HHJpYWHHlV\XX dJZ\\HHJ[Z HH\ ` x Complex Number Type Predicates ` i&UT UT` $  ;UR UT` | T(define (rectangular? z) PUP UT` } (d# (eq? (type-tag z) rectangular)) romeUN UT` % s  zUL UT`  te(define (polar? z) ` oUJ UT` ~ ˪ (eq? (type-tag z) polar)) uUH UT` b q THHJ\Zn HHlY_[[ d ddJ]srt__(dinHHJ^] f HHUT datum) _ z ` gg*Rectangular Representation with Type Tags ) `  Sch-Num UB UT` ar"(define (real-part-rectangular z) U@ UT` j ar (car (contents z))) #U> UT` "(define (imag-part-rectangular z) 8U< UT` k  (cdr (contents z))) MU: UT`  bU8 UT` #(define (magnitude-rectangular z) wU6 UT` . (sqrt (+ (square (real-part-rectangular z)) U4 UT` 1 (square (imag-part-rectangular z))))) U2 UT` gg(define (angle-rectangular z) U0 UT` " (atan (imag-part-rectangular z) U. UT` nt$ (real-part-rectangular z))) ngU, UT` r  e ` ٪ ZHHJ_]UTHHl\b^^  UTdK"`abbtth-HHK#a` HHs UF UTb ? ` ea$Polar representation with type tags -N&UT UT`  r;UR UT` rt;; Alyssas representation ` jPUP UT` \ en;; Polar = polar X RepPolar deUN UT` ec (define (make-from-mag-ang r a) zUL UT` ) " (attach-tag polar (cons r a))) UJ UT` (m"(define (make-from-real-imag x y) UH UT` qr (attach-tag polar -UF UT` U4+ (cons (sqrt (+ (square x) (square y))) rt-UD UT`  (atan y x)))) inUB UT` ar U@ UT` ;; magnitude: Polar -> Sch-Num z)  U> UT` ] nt0(define (magnitude-polar z) (car (contents z))) "U< UT` ,(define (angle-polar z) (cdr (contents z))) 7U: UT`  LU8 UT` (define (real-part-polar z) aU6 UT` 1 (* (magnitude-polar z) (cos (angle-polar z)))) vU4 UT` (define (imag-part-polar z) U2 UT` 1 (* (magnitude-polar z) (sin (angle-polar z)))) U0 UT`  HHK%b`eagHHl_eaa  redKUcl =eeUTHHKVdc ULHHctt))) UJe(m ` im Corresponding Generic Operators tt) ` UF T Sch-Num @{UN UT` ;;(define (real-part z) UL UT` ˪5 (cond ((rectangular? z) (real-part-rectangular z)) )UJ UT` ) ((polar? z) (real-part-polar z)) sUH UT` _ ˪6 (else (error "Unknown type - REAL-PART" z)))) ` ٪ UF UT` a ud!;; imag-part: Complex -> Sch-Num UD UT` (define (imag-part z) UB UT` ˪ (cond ((rectangular? z) $U@ UT` -p$ (imag-part-rectangular z)) 9U> UT` K%) ((polar? z) (imag-part-polar z)) NU< UT` 6 (else (error "Unknown type - IMAG-PART" z)))) cU: UT`  xU8 UT` UT!;; magnitude: Complex -> Sch-Num U6 UT` b (define (magnitude z) U4 UT`  (cond ((rectangular? z) U2 UT` $ (magnitude-rectangular z)) ttU0 UT` UF) ((polar? z) (magnitude-polar z)) aU. UT` UR6 (else (error "Unknown-type - MAGNITUDE" z)))) U, UT` @ N U* UT` (d;; angle: Complex -> Sch-Num  U( UT` c (((define (angle z) 5U& UT` z1 (cond ((rectangular? z) (angle-rectangular z)) -JU$ UT` % ((polar? z) (angle-polar z)) "_U" UT` L-2 (else (error "Unknown-type - ANGLE" z)))) HHKXecDUTHHlb~dd condPmf hhz)HHPngf ig-HHMUTlse (errhpe b UT$Polar Representation & Installation ;;) b x  S UTb  KX+ (cons (sqrt (+ (square x) (square y))) 8U< UTb   (atan y x))) MU: UTb   bU8 UTb  ) ;; interface to the rest of the system wU6 UTb  ) (define (tag x) (attach-tag polar x)) U4 UTb  e & (put real-part (polar) real-part) U2 UTb  pr& (put imag-part (polar) imag-part) U0 UTb  UT& (put magnitude (polar) magnitude) U. UTb  UT" (put angle (polar) angle) U, UTb UT# (put make-from-real-imag polar s 0U* UTb ! 4 (lambda (x y) (tag (make-from-real-imag x y))))  U( UTb " z! (put make-from-mag-ang polar U& UTb # -m2 (lambda (x y) (tag (make-from-mag-ang r a)))) 4U$ UTb $ ˪ done) IU" UTb % ma tHHPphf-rHHlkgg 6dPie kkl-agHHPji r(+HH)) k)) ` Generic Constructors ) ` e  t UT` 1 ng (make-sum UT"U< UT` 8  (make-product 7U: UT` I  (multiplier exp) LU8 UT` O j- (deriv (multiplicand exp) var)) aU6 UT` X ~ (make-product vU4 UT` ^  (multiplicand exp) U2 UT` c / (deriv (multiplier exp) var))))))  ` f D aU0 UT` d eb U. UT` g  U, UT` h  dHHK~| HHle}} dK*bl eHHK (keHHUT  (make  T ` k Generic Constructors T&UT UT` y  (;UR UT` dd4;; make-from-real-imag: Sch-Num, Sch-Num -> Complex PUP UT` p)"(define (make-from-real-imag x y) eUN UT` ge) (make-from-real-imag-rectangular x y)) TzUL UT`  UJ UT` du2;; make-from-mag-ang: Sch-Num, Sch-Num -> Complex UH UT` O (define (make-from-mag-ang r a) icUF UT` U6! (make-from-mag-ang-polar r a)) pUD UT` ˪ ^HHK2UTHHl~  dKb U,UTHHK HH  } ` +Layered Procedures with Generic Operations &UT UT`  ;UR UT` ,;; add-complex: Complex, Complex -> Complex PUP UT` ((define (add-complex z1 z2) eUN UT` Ge (make-from-real-imag UTzUL UT` UR& (+ (real-part z1) (real-part z2)) UJ UT` -( (+ (imag-part z1) (imag-part z2)))) (mUH UT` x UF UT` ge,;; sub-complex: Complex, Complex -> Complex ULUD UT` (define (sub-complex z1 z2) frUB UT` m, (make-from-real-imag UTU@ UT` in& (- (real-part z1) (real-part z2))  U> UT` fr( (- (imag-part z1) (imag-part z2)))) "U< UT`  7U: UT` ,;; mul-complex: Complex, Complex -> Complex LU8 UT` (define (mul-complex z1 z2) aU6 UT`  (make-from-mag-ang vU4 UT` & (* (magnitude z1) (magnitude z2)) U2 UT` (+ (angle z1) (angle z2)))) U0 UT`  U. UT` La,;; div-complex: Complex, Complex -> Complex UTU, UT` (define (div-complex z1 z2) omU* UT` pl (make-from-mag-ang TU( UT` in& (/ (magnitude z1) (magnitude z2))  U& UT` -r (- (angle z1) (angle z2)))) HHLTHHl dLmexleULHHL zz2HHm, UTU@ in ` { eaGeneric Interface &UT UT` (- m;UR UT` ) pa4(define (real-part z) (apply-generic real-part z)) PUP UT` * Co4(define (imag-part z) (apply-generic imag-part z)) ineUN UT` + z24(define (magnitude z) (apply-generic magnitude z)) UTzUL UT` , 0(define (angle z) (apply-generic angle z)) UJ UT` - )  gHHLTHHl  UTdLlmU*fr-mHHLm te HHLU& (angle  )) ` LApply-Generic &UT UT` ;; A simple version... ;UR UT` &(define (simple-apply-generic op arg) PUP UT` # (let ((type-tag (type-tag arg))) eUN UT` $ (let ((proc (get op type-tag))) zUL UT`  (if proc UJ UT` " (apply proc (list arg)) UH UT` m8 (error "No method for types - APPLY-GENERIC" UF UT` UP) (list op type-tag)))))) pUD UT` ar )UB UT` +4;; Version to support variable number of arguments: z)U@ UT` ,+(define (multiple-apply-generic op . args) ngl U> UT` ˪) (let ((type-tags (map type-tag args))) "U< UT` % (let ((proc (get op type-tags))) 7U: UT` UT (if proc LU8 UT`  (apply proc args) aU6 UT` 7 (error "No method for types - APPLY-GENERIC" U&vU4 UT` ) (list op type-tags)))))) U2 UT` y- eU0 UT` 1;; Convention: Generic system manages type tags. U. UT` & ap"(define (apply-generic op . args) U, UT` ' e-) (let ((type-tags (map type-tag args))) U* UT` ( (g% (let ((proc (get op type-tags))) U( UT` 3  (if proc  U& UT` 4 p; (apply proc  (map   contents args) ) ethU$ UT` 5 LY7 (error "No method for types - APPLY-GENERIC" op 3U" UT` 6 UD) (list op type-tags)))))) ;HU UT` 7 t  iHHLo ,HHl ` dM@) (l (HHMA UTHHMU8 (app ` *Rectangular Implementation & Installation ) ` ٪ UT` " (define (make-from-mag-ang r a) 8U< UT` M@( (cons (* r (cos a)) (* r (sin a)))) MU: UT`  bU8 UT` ) ;; interface to the rest of the system wU6 UT` / (define (tag x) (attach-tag rectangular x)) U4 UT` em, (put real-part (rectangular) real-part) U2 UT`  , (put imag-part (rectangular) imag-part) n.U0 UT`  , (put magnitude (rectangular) magnitude) UPU. 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