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< title > Zapiski in vaje #6 srečanja programerskega bralnega krožka SICP< / title >
< meta name = "author" content = "Jurij" / >
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< / style >
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< h1 class = "title" > Zapiski in vaje #6 srečanja programerskega bralnega krožka SICP< / h1 >
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< div id = "outline-container-org19a71b6" class = "outline-2" >
< h2 id = "org19a71b6" > Teme< / h2 >
< div class = "outline-text-2" id = "text-org19a71b6" >
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< / div >
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< div id = "outline-container-orgaca5b02" class = "outline-3" >
< h3 id = "orgaca5b02" > Grajenje abstrakcij s podatki< / h3 >
< div class = "outline-text-3" id = "text-orgaca5b02" >
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< p >
Prvo poglavje, v katerem smo operirali s preprostimi števili, drugo poglavje nadgrajuje s podatkovnimi struktura oz. kombiniranjem podatkovnih objektov v sestavljene podatkovne modele.
< / p >
< p >
Torej ustvarili bomo podatkovne abstrakcije in definirali funkcije ki lahko operirajo nad njimi.
Preprost primer je recimo racionalno število, ki ga sestavlja par števca in imenovalca.
< / p >
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< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > polovica< / span > < span style = "color: #b16286;" > (< / span > ustvari-rac 1 2< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< p >
Uporabimo funkcijo za najvecji skupni imenovlec, da poenostavimo recimo 6/3 v 2/1.
< / p >
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a
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< / div >
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< h2 id = "org8206e7f" > vaje< / h2 >
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< / div >
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< div id = "outline-container-org6ec3c99" class = "outline-3" >
< h3 id = "org6ec3c99" > 2.1 bolji ustvari-rac< / h3 >
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< h3 id = "org80d30fc" > 2.2 polovica daljice< / h3 >
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< h3 id = "orgf6d22ce" > 2.3 obseg in ploščina pravokotnik< / h3 >
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Najprej super simpl imeplemntacija - imamo samo dolžino in širino, ni res v koordinatnem sistemu. Plod lenobe, na katerega in na katero sem ponosen.
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< pre class = "src src-scheme" > < span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > Dolzina in sirina< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > ploscina-kvadra< / span > k< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > * < span style = "color: #8ec07c;" > (< / span > car k< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > cdr k< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > obseg-kvadra< / span > k< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > * 2 < span style = "color: #8ec07c;" > (< / span > + car k< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > cdr k< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > make-kvader< / span > cons< span style = "color: #458588;" > )< / span >
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Pa še primer v koordinatnem sistemu. Dejmo reč da je kvader vektor s širino; točka od in točka do daljice dolžine ter širina, ki se zgodi desno od daljice dolžine.
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< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > make-segment< / span > cons< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > x-point< / span > car< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > y-point< / span > cdr< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > print-point< / span > p< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > newline< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > display < span style = "color: #b8bb26;" > "("< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > display < span style = "color: #8ec07c;" > (< / span > x-point p< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > display < span style = "color: #b8bb26;" > ","< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > display < span style = "color: #8ec07c;" > (< / span > y-point p< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > display < span style = "color: #b8bb26;" > ")"< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > daljica< / span > pravokotnik< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > car pravokotnik< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > sirina< / span > pravokotnik< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > cdr pravokotnik< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > make-pravokotnik< / span > daljica sirina< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > cons daljica sirina< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > tocke-pravokotnika< / span > pravokotnik< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > print-point < span style = "color: #8ec07c;" > (< / span > start-segment < span style = "color: #d65d0e;" > (< / span > daljica pravokotnik< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > print-point < span style = "color: #8ec07c;" > (< / span > end-segment pravokotnik < span style = "color: #d65d0e;" > (< / span > daljica pravokotnik< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > print-point < span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > x-point < span style = "color: #458588;" > (< / span > daljica pravokotnik< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > TODO cetrta tocka< / span >
< span style = "color: #458588;" > )< / span >
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< h3 id = "org165756d" > 2.4 Proceduralna reprezantacija parov< / h3 >
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< pre class = "src src-scheme" > < span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > cons< / span > x y< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #8ec07c;" > (< / span > m< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > m x y< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > car< / span > z< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > z < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > p q< span style = "color: #d65d0e;" > )< / span > p< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > kaksen je cdr?< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > cdr< / span > z< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > z < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > p q< span style = "color: #d65d0e;" > )< / span > q< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > list
< span style = "color: #b16286;" > (< / span > cons 10 12< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > car < span style = "color: #8ec07c;" > (< / span > cons 10 12< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > cdr < span style = "color: #8ec07c;" > (< / span > cons 10 12< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< h3 id = "org265a0b2" > 2.5 aritmeticni par v stevilu< / h3 >
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< span style = "color: #b16286;" > (< / span > * < span style = "color: #8ec07c;" > (< / span > expt 2 a< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > expt 3 b< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > car< / span > p< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > if< / span > < span style = "color: #8ec07c;" > (< / span > = 0 < span style = "color: #d65d0e;" > (< / span > modulo p 2< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > + 1 < span style = "color: #d65d0e;" > (< / span > car < span style = "color: #458588;" > (< / span > / p 2< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
0< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > cdr< / span > p< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > if< / span > < span style = "color: #8ec07c;" > (< / span > = 0 < span style = "color: #d65d0e;" > (< / span > modulo p 3< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > + 1 < span style = "color: #d65d0e;" > (< / span > cdr < span style = "color: #458588;" > (< / span > / p 3< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
0< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > list
< span style = "color: #b16286;" > (< / span > cons 12 41< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > car < span style = "color: #8ec07c;" > (< / span > cons 12 41< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > cdr < span style = "color: #8ec07c;" > (< / span > cons 12 41< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< h3 id = "orgc00d6df" > 2.6 churchova števila< / h3 >
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< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > add-1< / span > n< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #8ec07c;" > (< / span > f< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > f < span style = "color: #458588;" > (< / span > < span style = "color: #b16286;" > (< / span > n f< span style = "color: #b16286;" > )< / span > x< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > one< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #8ec07c;" > (< / span > f< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > f < span style = "color: #458588;" > (< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > f< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #458588;" > (< / span > x< span style = "color: #458588;" > )< / span > x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > f< span style = "color: #b16286;" > )< / span > x< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > two< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #8ec07c;" > (< / span > f< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > f < span style = "color: #458588;" > (< / span > < span style = "color: #b16286;" > (< / span > one f< span style = "color: #b16286;" > )< / span > x< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > pokrajsano< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > one< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #8ec07c;" > (< / span > f< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > f x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > two< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #8ec07c;" > (< / span > f< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > f < span style = "color: #458588;" > (< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > f< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #458588;" > (< / span > x< span style = "color: #458588;" > )< / span > < span style = "color: #458588;" > (< / span > f x< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > f< span style = "color: #b16286;" > )< / span > x< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > @TODO hmm kaj se zgodi tu vmes koristnega za razumevanje?< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > two< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #8ec07c;" > (< / span > f< span style = "color: #8ec07c;" > )< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #fb4933;" > lambda< / span > < span style = "color: #d65d0e;" > (< / span > x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > f < span style = "color: #458588;" > (< / span > f x< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< div id = "outline-container-org7b1892d" class = "outline-3" >
< h3 id = "org7b1892d" > 2.7 Racunanje z intervali (z napako)< / h3 >
< div class = "outline-text-3" id = "text-org7b1892d" >
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< div class = "org-src-container" >
< pre class = "src src-scheme" > < span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > add-interval< / span > x y< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > make-interval < span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > lower-bound x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > lower-bound y< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > upper-bound x< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > upper-bound y< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > mul-interval< / span > x y< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > < span style = "color: #fb4933;" > let< / span > < span style = "color: #8ec07c;" > (< / span > < span style = "color: #d65d0e;" > (< / span > p1 < span style = "color: #458588;" > (< / span > * < span style = "color: #b16286;" > (< / span > lower-bound x< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > lower-bound y< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > p2 < span style = "color: #458588;" > (< / span > * < span style = "color: #b16286;" > (< / span > lower-bound x< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > upper-bound y< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > p3 < span style = "color: #458588;" > (< / span > * < span style = "color: #b16286;" > (< / span > upper-bound x< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > lower-bound y< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > p4 < span style = "color: #458588;" > (< / span > * < span style = "color: #b16286;" > (< / span > upper-bound x< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > upper-bound y< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > make-interval < span style = "color: #d65d0e;" > (< / span > min p1 p2 p3 p4< span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > max p1 p2 p3 p4< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > div-interval< / span > x y< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > mul-interval x
< span style = "color: #8ec07c;" > (< / span > make-interval < span style = "color: #d65d0e;" > (< / span > / 1.0 < span style = "color: #458588;" > (< / span > upper-bound y< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > / 1.0 < span style = "color: #458588;" > (< / span > lower-bound y< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > make-interval< / span > a b< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > cons a b< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > upper-bound< / span > cdr< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > lower-bound< / span > car< span style = "color: #458588;" > )< / span >
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< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > izpisi-interval< / span > a< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > string-append < span style = "color: #8ec07c;" > (< / span > lower-bound a< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b8bb26;" > "— "< / span > < span style = "color: #8ec07c;" > (< / span > upper-bound a< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< span style = "color: #458588;" > (< / span > list
< span style = "color: #b8bb26;" > "3— 4 + 5— 8"< / span >
< span style = "color: #b16286;" > (< / span > izpisi-interval
< span style = "color: #8ec07c;" > (< / span > add-interval
< span style = "color: #d65d0e;" > (< / span > make-interval 3 4< span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > make-interval 5 8< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b8bb26;" > "5— 6 × 8— 10"< / span >
< span style = "color: #b16286;" > (< / span > izpisi-interval
< span style = "color: #8ec07c;" > (< / span > mul-interval
< span style = "color: #d65d0e;" > (< / span > make-interval 5 6< span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > make-interval 8 10< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< h3 id = "orgdbb464f" > 2.8 odstevanje intervala< / h3 >
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Pri odštevanju intervala moramo pazit, da od zgornje meje prvega intervala odštejemo spodnjo mejo drugega!
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< pre class = "src src-scheme" > < span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > make-interval< / span > a b< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > cons a b< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > upper-bound< / span > cdr< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > lower-bound< / span > car< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > sub-interval< / span > a b< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > make-interval < span style = "color: #8ec07c;" > (< / span > - < span style = "color: #d65d0e;" > (< / span > lower-bound a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > upper-bound b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > - < span style = "color: #d65d0e;" > (< / span > upper-bound a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > lower-bound b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > list
< span style = "color: #b16286;" > (< / span > sub-interval < span style = "color: #8ec07c;" > (< / span > make-interval 10 12< span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > make-interval 3 7< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< h3 id = "orgb6310f8" > 2.9 srednja vrednost in napaka< / h3 >
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< p >
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Seštevanje je isto pri intervalu od-do kot srednja-vrednost in napaka. Odštevanje je podobno, le da napaki preprosto seštejemo (kar je malo bolj "intuitivno" kot pri intervalu, vsaj meni).
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< pre class = "src src-scheme" > < span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > "napaka" je "width" intervala< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > make-priblizek< / span > vrednost napaka< span style = "color: #b16286;" > )< / span > < span style = "color: #b16286;" > (< / span > cons vrednost napaka< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > vrednost< / span > car< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #fabd2f;" > napaka< / span > cdr< span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > add-priblizek< / span > a b< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > make-priblizek < span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > vrednost a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > vrednost b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > napaka a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > napaka b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > sub-priblizek< / span > a b< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > make-priblizek < span style = "color: #8ec07c;" > (< / span > - < span style = "color: #d65d0e;" > (< / span > vrednost a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > vrednost b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > napaka a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > napaka b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > mul-priblizek< / span > a b< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > make-priblizek < span style = "color: #8ec07c;" > (< / span > * < span style = "color: #d65d0e;" > (< / span > vrednost a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > vrednost b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
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< span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > * < span style = "color: #458588;" > (< / span > vrednost a< span style = "color: #458588;" > )< / span > < span style = "color: #458588;" > (< / span > napaka b< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > * < span style = "color: #458588;" > (< / span > vrednost b< span style = "color: #458588;" > )< / span > < span style = "color: #458588;" > (< / span > napaka a< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #458588;" > (< / span > < span style = "color: #fb4933;" > define< / span > < span style = "color: #b16286;" > (< / span > < span style = "color: #fabd2f;" > div-priblizek< / span > a b< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > make-priblizek < span style = "color: #8ec07c;" > (< / span > * < span style = "color: #d65d0e;" > (< / span > vrednost a< span style = "color: #d65d0e;" > )< / span > < span style = "color: #d65d0e;" > (< / span > vrednost b< span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > + < span style = "color: #d65d0e;" > (< / span > * < span style = "color: #458588;" > (< / span > vrednost a< span style = "color: #458588;" > )< / span > < span style = "color: #458588;" > (< / span > napaka b< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span >
< span style = "color: #d65d0e;" > (< / span > * < span style = "color: #458588;" > (< / span > vrednost b< span style = "color: #458588;" > )< / span > < span style = "color: #458588;" > (< / span > napaka a< span style = "color: #458588;" > )< / span > < span style = "color: #d65d0e;" > )< / span > < span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
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< span style = "color: #458588;" > (< / span > list
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< span style = "color: #b8bb26;" > "vsota in razlika sta preprosti"< / span >
< span style = "color: #b8bb26;" > "8± 3 + 4± 1 = 12± 4 (8— 16)"< / span >
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< span style = "color: #b16286;" > (< / span > add-priblizek < span style = "color: #8ec07c;" > (< / span > make-priblizek 8 3< span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > make-priblizek 4 1< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
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< span style = "color: #b8bb26;" > "8± 3 - 4± 1 = 4± 4 (6— 8)"< / span >
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< span style = "color: #b16286;" > (< / span > sub-priblizek < span style = "color: #8ec07c;" > (< / span > make-priblizek 8 3< span style = "color: #8ec07c;" > )< / span >
< span style = "color: #8ec07c;" > (< / span > make-priblizek 4 1< span style = "color: #8ec07c;" > )< / span > < span style = "color: #b16286;" > )< / span >
< span style = "color: #b8bb26;" > "pri mnozenju in deljenju pa je \"sirina\" (napaka) odvisna tudi od vrednosti"< / span > < span style = "color: #458588;" > )< / span >
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< span style = "color: #b8bb26;" > "8± 3 × 4± 1 = 35± 20 (8× 4 + 3× 1) ± (1× 8 + 3× 4) (15— 55)"< / span >
< span style = "color: #458588;" > (< / span > mul-priblizek < span style = "color: #b16286;" > (< / span > make-priblizek 8 3< span style = "color: #b16286;" > )< / span >
< span style = "color: #b16286;" > (< / span > make-priblizek 4 1< span style = "color: #b16286;" > )< / span > < span style = "color: #458588;" > )< / span >
< span style = "color: #b8bb26;" > "8± 3 ÷ 4± 1 = ?"< / span >
< span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > TODO< / span >
< span style = "color: #7c6f64;" > ;< / span > < span style = "color: #7c6f64;" > (div-priblizek (make-priblizek 8 3)< / span >
< span style = "color: #7c6f64;" > ; < / span > < span style = "color: #7c6f64;" > (make-priblizek 4 1))< / span >
< span style = "color: #7c6f64;" > ;; < / span > < span style = "color: #7c6f64;" > TODO napisi funkcije za deljenje< / span >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Jurij< / p >
2024-09-04 19:25:19 +02:00
< p class = "date" > Created: 2024-09-04 sre 19:25< / p >
2024-07-25 11:08:15 +02:00
< p class = "validation" > < a href = "https://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
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< / html >
