Removed references to the the graphics submodule due to the mysterious submodule error

This commit is contained in:
Jens Axel Søgaard 2012-06-20 23:02:24 +02:00
parent 0ee88d6310
commit 37bb90af0b
3 changed files with 253 additions and 260 deletions

View File

@ -1,5 +1,26 @@
#lang racket #lang racket
#;(module bracket-graphics racket
(require "../graphics/graphics.rkt")
(define-syntax (declare/provide-vars stx)
(syntax-case stx ()
[(_ id ...)
#'(begin
(define id 'id) ...
(provide id) ...)]))
(provide Graphics)
(declare/provide-vars
Blend Darker Hue Lighter
Circle Disk Line Point Rectangle
Text Thickness
; Colors
Red Blue Green Black White Yellow
; Options
ImageSize PlotRange))
;;; An ATOMIC EXPRESSION is an ;;; An ATOMIC EXPRESSION is an
; - number (integer, real, complex) ; - number (integer, real, complex)
; - reserved symbol (pi, e, i, inf, true, false) ; - reserved symbol (pi, e, i, inf, true, false)
@ -112,22 +133,22 @@
; This version prevents duplication of args. ; This version prevents duplication of args.
; But uses apply in place of #%app ; But uses apply in place of #%app
#;(define-syntax (sym-app stx) #;(define-syntax (sym-app stx)
(syntax-case stx () (syntax-case stx ()
[(_ op arg ...) [(_ op arg ...)
(quasisyntax/loc stx (quasisyntax/loc stx
(let ([o op] (let ([o op]
[as (λ () (list arg ...))]) [as (λ () (list arg ...))])
; TODO: 1. If o is Flat, then flattened nested expression with o. ; TODO: 1. If o is Flat, then flattened nested expression with o.
; TODO: 2. If o is Listable, then ... ; TODO: 2. If o is Listable, then ...
; TODO: 3. If o is Orderless then ... ; TODO: 3. If o is Orderless then ...
; TODO: 4. If o has associated rules ... ; TODO: 4. If o has associated rules ...
; TODO: ; TODO:
; REF: http://reference.wolfram.com/mathematica/tutorial/Evaluation.html ; REF: http://reference.wolfram.com/mathematica/tutorial/Evaluation.html
(if (procedure? o) (if (procedure? o)
#,(syntax/loc stx (apply o (as))) #,(syntax/loc stx (apply o (as)))
(if (holdable? o) (if (holdable? o)
(cons o '(arg ...)) (cons o '(arg ...))
(cons o (as))))))]))) (cons o (as))))))])))
(module expression-core racket (module expression-core racket
(require (submod ".." identifiers) (require (submod ".." identifiers)
@ -204,7 +225,7 @@
(when compound? (when compound?
(hash-set! recent-compound-expressions e #t)) (hash-set! recent-compound-expressions e #t))
compound?))) compound?)))
(define (construct operator operands) (define (construct operator operands)
(cons operator operands)) (cons operator operands))
@ -258,7 +279,7 @@
(submod ".." undefined) (submod ".." undefined)
(submod ".." identifiers)) (submod ".." identifiers))
(require (planet dherman/memoize:3:1)) (require (planet dherman/memoize:3:1))
(provide simplify (provide simplify
simplify-plus simplify-plus
simplify-minus simplify-minus
@ -323,7 +344,7 @@
[(1) (first vs)] [(1) (first vs)]
[(0) 0] [(0) 0]
[else (construct 'Plus vs)]))])])) [else (construct 'Plus vs)]))])]))
(define (simplify-plus-rec us) (define (simplify-plus-rec us)
; a list of terms is received, ; a list of terms is received,
; a list of simplified terms is returned. ; a list of simplified terms is returned.
@ -369,9 +390,9 @@
(λ (u2i) (λ (u2i)
(let ([us (simplify-plus-rec (cons u1 (list u2i)))]) (let ([us (simplify-plus-rec (cons u1 (list u2i)))])
; If length(us)>=2 wrap with Plus ; If length(us)>=2 wrap with Plus
(if (empty? (rest us)) (if (empty? (rest us))
(first us) (first us)
(construct 'Plus us)))) (construct 'Plus us))))
(operands u2)))] (operands u2)))]
[(before? u2 u1) (list u2 u1)] [(before? u2 u1) (list u2 u1)]
[else (list u1 u2)])] [else (list u1 u2)])]
@ -407,7 +428,7 @@
(cons q1 (merge-sums p (rest q))) (cons q1 (merge-sums p (rest q)))
(cons p1 (merge-sums (rest p) q)))] (cons p1 (merge-sums (rest p) q)))]
[else (error)])])) [else (error)])]))
(define/memo (simplify-times ops) (define/memo (simplify-times ops)
;(displayln (list 'simplify-times ops)) ;(displayln (list 'simplify-times ops))
; the operands os are simplified ; the operands os are simplified
@ -530,106 +551,106 @@
; See [Cohen] for the complete algorithm and explanation. ; See [Cohen] for the complete algorithm and explanation.
(define result (define result
(cond (cond
[(and (number? u) (number? v)) [(and (number? u) (number? v))
; straightforward for two real numbers, ; straightforward for two real numbers,
; but complex numbers must be handled too. ; but complex numbers must be handled too.
(if (= u v) (if (= u v)
#t #t
(if (real? u) (if (real? u)
(if (real? v) (< u v) v) (if (real? v) (< u v) v)
(if (real? v) (if (real? v)
v v
(if (= (imag-part u) (imag-part v)) (if (= (imag-part u) (imag-part v))
(< (real-part u) (real-part v)) (< (real-part u) (real-part v))
(< (imag-part u) (imag-part v))))))] (< (imag-part u) (imag-part v))))))]
; Number always come first ; Number always come first
[(number? u) #t] [(number? u) #t]
[(number? v) #f] [(number? v) #f]
; Symbols are sorted in alphabetical order ; Symbols are sorted in alphabetical order
[(and (symbol? u) (symbol? v)) [(and (symbol? u) (symbol? v))
(string<? (symbol->string u) (symbol->string v))] (string<? (symbol->string u) (symbol->string v))]
; For products and sums order on the last different ; For products and sums order on the last different
; factor or term. Thus x+y < y+z. ; factor or term. Thus x+y < y+z.
[(or (and (times-expression? u) (times-expression? v)) [(or (and (times-expression? u) (times-expression? v))
(and (plus-expression? u) (plus-expression? v))) (and (plus-expression? u) (plus-expression? v)))
(define first-non-equal (define first-non-equal
(for/first ([ui (in-list (reverse (operands u)))] (for/first ([ui (in-list (reverse (operands u)))]
[vi (in-list (reverse (operands v)))] [vi (in-list (reverse (operands v)))]
#:unless (equal? ui vi)) #:unless (equal? ui vi))
(list ui vi))) (list ui vi)))
(if first-non-equal (if first-non-equal
(apply before? first-non-equal) (apply before? first-non-equal)
(< (length (operands u)) (length (operands v))))] (< (length (operands u)) (length (operands v))))]
; When comparing a product with something else, use the last factor. ; When comparing a product with something else, use the last factor.
; Thus x*y < z and y < x*z. ; Thus x*y < z and y < x*z.
; Note: This is consistent with comparisons of two products since ; Note: This is consistent with comparisons of two products since
; x*y < 1*z and 1*y < x*z. ; x*y < 1*z and 1*y < x*z.
[(and (times-expression? u) [(and (times-expression? u)
(or ;(power-expression? v) (or ;(power-expression? v)
;(plus-expression? v) ;(plus-expression? v)
(symbolic-id? v) (symbolic-id? v)
(compound-expression? v))) (compound-expression? v)))
(let ([un (last-operand u)]) (let ([un (last-operand u)])
(or (equal? un v) (before? un v)))] (or (equal? un v) (before? un v)))]
[(and (times-expression? v) [(and (times-expression? v)
(or ;(power-expression? v) (or ;(power-expression? v)
;(plus-expression? v) ;(plus-expression? v)
(symbolic-id? u) (symbolic-id? u)
(compound-expression? u))) (compound-expression? u)))
(define vn (last-operand v)) (define vn (last-operand v))
(or (equal? vn u) (before? u vn))] (or (equal? vn u) (before? u vn))]
; Powers with smallest base are first. 2^z < 3^y ; Powers with smallest base are first. 2^z < 3^y
[(and (power-expression? u) (power-expression? v)) [(and (power-expression? u) (power-expression? v))
(if (equal? (base u) (base v)) (if (equal? (base u) (base v))
(before? (exponent u) (exponent v)) (before? (exponent u) (exponent v))
(before? (base u) (base v)))] (before? (base u) (base v)))]
; When comparing a product with something else, pretend ; When comparing a product with something else, pretend
; the else part is a power with exponent 1. ; the else part is a power with exponent 1.
; Thus x^2 > x. ; Thus x^2 > x.
[(and (power-expression? u) [(and (power-expression? u)
(or ; (plus-expression? v) (or ; (plus-expression? v)
(symbolic-id? v) (symbolic-id? v)
(compound-expression? v))) (compound-expression? v)))
(before? u (construct 'Power (list v 1)))] (before? u (construct 'Power (list v 1)))]
[(and (power-expression? v) [(and (power-expression? v)
(or ; (plus-expression? v) (or ; (plus-expression? v)
(symbolic-id? u) (symbolic-id? u)
(compound-expression? u))) (compound-expression? u)))
(before? (construct 'Power (list u 1)) v)] (before? (construct 'Power (list u 1)) v)]
; Same trick with sums. Thus x+(-1) < x (+0) ; Same trick with sums. Thus x+(-1) < x (+0)
[(and (plus-expression? u) [(and (plus-expression? u)
(or (symbolic-id? v) (or (symbolic-id? v)
(compound-expression? v))) (compound-expression? v)))
(before? u (construct 'Plus (list v)))] (before? u (construct 'Plus (list v)))]
[(and (plus-expression? v) [(and (plus-expression? v)
(or (symbolic-id? u) (or (symbolic-id? u)
(compound-expression? u))) (compound-expression? u)))
(before? (construct 'Plus (list u)) v)] (before? (construct 'Plus (list u)) v)]
; Here only function applications are left. ; Here only function applications are left.
; Sort after name. ; Sort after name.
[(and (compound-expression? u) (compound-expression? v)) [(and (compound-expression? u) (compound-expression? v))
(if (not (equal? (kind u) (kind v))) (if (not (equal? (kind u) (kind v)))
(before? (kind u) (kind v)) (before? (kind u) (kind v))
(let () (let ()
; If the names are equal, sort after the first ; If the names are equal, sort after the first
; non-equal operand. ; non-equal operand.
(define first-non-equal (define first-non-equal
(for/first ([ui (in-list (operands u))] (for/first ([ui (in-list (operands u))]
[vi (in-list (operands v))] [vi (in-list (operands v))]
#:unless (equal? ui vi)) #:unless (equal? ui vi))
(list ui vi))) (list ui vi)))
(if first-non-equal (if first-non-equal
(apply before? first-non-equal) (apply before? first-non-equal)
(< (length (operands u)) (length (operands v))))))] (< (length (operands u)) (length (operands v))))))]
[(compound-expression? u) [(compound-expression? u)
#f] #f]
[(compound-expression? v) [(compound-expression? v)
#t] #t]
[else [else
(error 'before? "Internal error: A case is missing, got ~a and ~a" u v)] (error 'before? "Internal error: A case is missing, got ~a and ~a" u v)]
; TODO : This isn't done ; TODO : This isn't done
; some rules are missing ... functions???? ; some rules are missing ... functions????
)) ))
;(displayln (format " => ~a" result)) ;(displayln (format " => ~a" result))
result result
) )
@ -743,35 +764,35 @@
(kind u) (kind u)
(map (λ (ui) (concurrent-substitute ui ts rs)) (map (λ (ui) (concurrent-substitute ui ts rs))
(operands u))))]))) (operands u))))])))
#;(module pattern-matching racket #;(module pattern-matching racket
(require (submod ".." expression)) (require (submod ".." expression))
(define (linear-form u x) (define (linear-form u x)
; u expression, x a symbol ; u expression, x a symbol
(if (eq? u x) (if (eq? u x)
(list 1 0) (list 1 0)
(case (kind u) (case (kind u)
[(symbol-id integer fraction real complex) [(symbol-id integer fraction real complex)
(list 0 u)] (list 0 u)]
[(Times) [(Times)
(if (free-of u x) (if (free-of u x)
(list 0 u) (list 0 u)
(let ([u/x (Quotient u x)]) (let ([u/x (Quotient u x)])
(if (Free-of u/x x) (if (Free-of u/x x)
(list u/x 0) (list u/x 0)
#f)))] #f)))]
[(Plus) [(Plus)
(let ([f (linear-form (operand u 1) x)]) (let ([f (linear-form (operand u 1) x)])
(and f (and f
(let ([r (linear-form (Minus u (operand u 1)))]) (let ([r (linear-form (Minus u (operand u 1)))])
(and r (and r
(list (+ (operand f 0) (operand r 0)) (list (+ (operand f 0) (operand r 0))
(+ (operand f 1) (operand r 1)))))))] (+ (operand f 1) (operand r 1)))))))]
[else [else
(and (free-of u x) (and (free-of u x)
(list 0 u))])))) (list 0 u))]))))
(module equation-expression racket (module equation-expression racket
(require (submod ".." expression)) (require (submod ".." expression))
@ -785,68 +806,50 @@
(values (map (curryr operand 0) (operands t=r-List)) (values (map (curryr operand 0) (operands t=r-List))
(map (curryr operand 1) (operands t=r-List))))) (map (curryr operand 1) (operands t=r-List)))))
(module bracket-graphics racket
(require "../graphics/graphics.rkt")
(define-syntax (declare/provide-vars stx)
(syntax-case stx ()
[(_ id ...)
#'(begin
(define id 'id) ...
(provide id) ...)]))
(provide Graphics)
(declare/provide-vars
Blend Darker Hue Lighter
Circle Disk Line Point Rectangle
Text Thickness
; Colors
Red Blue Green Black White Yellow
; Options
ImageSize PlotRange
))
(module bracket racket (module bracket racket
(require (submod ".." number-theory) (require (submod ".." number-theory)
(submod ".." expression) (submod ".." expression)
(submod ".." undefined) (submod ".." undefined)
(submod ".." equation-expression) (submod ".." equation-expression)
(submod ".." bracket-graphics)) ;(submod ".." bracket-graphics)
)
(provide ; (all-from-out (submod ".." symbolic-application)) (provide ; (all-from-out (submod ".." symbolic-application))
(rename-out [free-of Free-of] (rename-out [free-of Free-of]
[base Base] [base Base]
[const Const] [const Const]
[term Term] [term Term]
[exponent Exponent] [exponent Exponent]
[before? Before?] [before? Before?]
[kind Kind]) [kind Kind])
(all-from-out (submod ".." bracket-graphics)) ;(all-from-out (submod ".." bracket-graphics))
Operand Operand
Operands Operands
Hold Hold
Complete-sub-expressions Complete-sub-expressions
Substitute Substitute
Sequential-substitute Sequential-substitute
Concurrent-substitute Concurrent-substitute
Cons Cons
List List
List-ref List-ref
Plus Minus Times Quotient Power Plus Minus Times Quotient Power
Equal Equal
Expand Expand
Set Member? Set Member?
Variables Variables
Map Map
Apply Apply
Append Append
AppendStar AppendStar
Sin Cos Tan Sqrt Sin Cos Tan Sqrt
Solve-quadratic Solve-quadratic
Solve-linear Solve-linear
List->Set List->Set
Define Define
Range Range
Plot) Plot)
;;; ;;;
;;; INVARIANT ;;; INVARIANT
@ -888,7 +891,7 @@
(define (Cons u1 u2) (define (Cons u1 u2)
(construct 'List (cons u1 (List->list u2)))) (construct 'List (cons u1 (List->list u2))))
(define (Set . us) (define (Set . us)
(construct 'Set (set->list (list->set us)))) (construct 'Set (set->list (list->set us))))
@ -1108,12 +1111,12 @@
(define (List? u) (define (List? u)
(and (list? u) (and (list? u)
(eq? (Kind u) 'List))) (eq? (Kind u) 'List)))
(define-listable (Sqr u) (define-listable (Sqr u)
(cond (cond
[(real? u) (sqr u u)] [(real? u) (sqr u u)]
[else (Power u 2)])) [else (Power u 2)]))
(define-syntax (define-real-function stx) (define-syntax (define-real-function stx)
(syntax-case stx () (syntax-case stx ()
[(_ new old) [(_ new old)
@ -1141,7 +1144,7 @@
(define-real-function Ceiling ceiling) (define-real-function Ceiling ceiling)
(define-real-function Truncate truncate) (define-real-function Truncate truncate)
(define-real-function Sgn sgn) (define-real-function Sgn sgn)
(define (Solve-quadratic a b c) (define (Solve-quadratic a b c)
; return List of all solutions to ax^2+bx+c=0 ; return List of all solutions to ax^2+bx+c=0
(define d (Minus (Power b 2) (Times 4 a c))) (define d (Minus (Power b 2) (Times 4 a c)))
@ -1192,7 +1195,7 @@
(define (N u) (define (N u)
; TODO: Improve this ; TODO: Improve this
(eval u ns)) (eval u ns))
(define (Plot f range [options '(List)]) (define (Plot f range [options '(List)])
; TODO: Implement options ; TODO: Implement options
(displayln (list f range)) (displayln (list f range))
@ -1206,23 +1209,23 @@
(λ (x) (N (Substitute f (Equal var x))))) (λ (x) (N (Substitute f (Equal var x)))))
x-min x-max y-min y-max excluded?)] x-min x-max y-min y-max excluded?)]
[else (error)])) [else (error)]))
#;(and (real? x-min) (real? x-max) (real? y-min) (real? y-max) #;(and (real? x-min) (real? x-max) (real? y-min) (real? y-max)
(< x-min x-max) (< y-min y-max)) (< x-min x-max) (< y-min y-max))
; (define (Monomial-gpe u v) ; (define (Monomial-gpe u v)
; (define s (if (eq? (Kind v) 'set) (list v) v)) ; (define s (if (eq? (Kind v) 'set) (list v) v))
; (cond ; (cond
; [(Member? u (operands s)) #t] ; [(Member? u (operands s)) #t]
; [else ; [else
; (if(power-expression? u) ; (if(power-expression? u)
; (define base (Operand u 0)) ; (define base (Operand u 0))
; (define exponent (Operand u 1)) ; (define exponent (Operand u 1))
; (if (and (Member? base s) ; (if (and (Member? base s)
; (eq? (Kind exponent) 'integer) ; (eq? (Kind exponent) 'integer)
; (> exponent 1)) ; (> exponent 1))
) )
(module test racket (module test racket
(require (submod ".." symbolic-application) (require (submod ".." symbolic-application)

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@ -36,7 +36,8 @@
(strip-context (strip-context
#'(module anything bracket-lang #'(module anything bracket-lang
(require (submod bracket.rkt bracket) (require (submod bracket.rkt bracket)
(submod bracket.rkt symbolic-application)) (submod bracket.rkt symbolic-application)
#;(submod bracket.rkt bracket-graphics))
(define-syntax (#%infix stx) (define-syntax (#%infix stx)
(syntax-case stx () [(_ expr) #'expr])) (syntax-case stx () [(_ expr) #'expr]))
; This lists the operators used by the parser. ; This lists the operators used by the parser.

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@ -50,7 +50,7 @@
1 0 32 #"(lib \"text-snipclass.ss\" \"xml\")\0" 1 0 32 #"(lib \"text-snipclass.ss\" \"xml\")\0"
1 0 15 #"test-case-box%\0" 1 0 15 #"test-case-box%\0"
2 0 1 6 #"wxloc\0" 2 0 1 6 #"wxloc\0"
0 0 63 0 1 #"\0" 0 0 65 0 1 #"\0"
0 75 1 #"\0" 0 75 1 #"\0"
0 12 90 -1 90 -1 3 -1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 255 255 255 1 -1 0 9 0 12 90 -1 90 -1 3 -1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 255 255 255 1 -1 0 9
#"Standard\0" #"Standard\0"
@ -236,7 +236,13 @@
-1 -1 2 1 #"\0" -1 -1 2 1 #"\0"
0 71 1 #"\0" 0 71 1 #"\0"
1.0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 1.0 1.0 1.0 0 100 0 0 0 0 -1 1.0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 1.0 1.0 1.0 0 100 0 0 0 0 -1
-1 0 4352 0 26 3 12 #"#lang racket" -1 4 1 #"\0"
0 -1 1 #"\0"
1.0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1.0 1.0 1.0 1.0 1.0 1.0 0 0 0 0 0 0
-1 -1 45 1 #"\0"
0 -1 1 #"\0"
1.0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1.0 1.0 1.0 1.0 1.0 1.0 0 0 0 0 0 0
-1 -1 0 4335 0 26 3 12 #"#lang racket"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 1 #"(" 0 0 22 3 1 #"("
0 0 14 3 7 #"require" 0 0 14 3 7 #"require"
@ -2361,8 +2367,7 @@
0 0 22 3 1 #" " 0 0 22 3 1 #" "
0 0 14 3 1 #"r" 0 0 14 3 1 #"r"
0 0 22 3 3 #")) " 0 0 22 3 3 #")) "
0 0 17 3 10 #"; relative" 0 0 17 3 34 #"; relative to hor. range "
0 0 17 3 24 #" to hor. range "
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 13 #" (" 0 0 22 3 13 #" ("
0 0 15 3 12 #"parameterize" 0 0 15 3 12 #"parameterize"
@ -2394,8 +2399,7 @@
0 0 22 3 1 #" " 0 0 22 3 1 #" "
0 0 14 3 1 #"r" 0 0 14 3 1 #"r"
0 0 22 3 3 #")) " 0 0 22 3 3 #")) "
0 0 17 3 10 #"; relative" 0 0 17 3 34 #"; relative to hor. range "
0 0 17 3 24 #" to hor. range "
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 15 #" (" 0 0 22 3 15 #" ("
0 0 15 3 12 #"parameterize" 0 0 15 3 12 #"parameterize"
@ -3218,8 +3222,7 @@
0 0 14 3 5 #"Style" 0 0 14 3 5 #"Style"
0 0 22 3 1 #" " 0 0 22 3 1 #" "
0 0 19 3 1 #"\"" 0 0 19 3 1 #"\""
0 0 19 3 7 #"Unknown" 0 0 19 3 16 #"Unknown spec ~a\""
0 0 19 3 9 #" spec ~a\""
0 0 22 3 2 #" (" 0 0 22 3 2 #" ("
0 0 14 3 5 #"first" 0 0 14 3 5 #"first"
0 0 22 3 1 #" " 0 0 22 3 1 #" "
@ -3242,8 +3245,7 @@
0 0 22 3 1 #" " 0 0 22 3 1 #" "
0 0 19 3 1 #"\"" 0 0 19 3 1 #"\""
0 0 19 3 8 #"Internal" 0 0 19 3 8 #"Internal"
0 0 19 3 1 #" " 0 0 19 3 12 #" error: ~a \""
0 0 19 3 11 #"error: ~a \""
0 0 22 3 1 #" " 0 0 22 3 1 #" "
0 0 14 3 1 #"p" 0 0 14 3 1 #"p"
0 0 22 3 7 #")])])))" 0 0 22 3 7 #")])])))"
@ -4019,8 +4021,7 @@
0 0 17 3 2 #") " 0 0 17 3 2 #") "
0 0 17 3 1 #"," 0 0 17 3 1 #","
0 0 17 3 1 #"(" 0 0 17 3 1 #"("
0 0 17 3 1 #"/" 0 0 17 3 14 #"/ x (* 2 pi)))"
0 0 17 3 13 #" x (* 2 pi)))"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
@ -4033,8 +4034,7 @@
0 0 17 3 1 #" " 0 0 17 3 1 #" "
0 0 17 3 1 #"1" 0 0 17 3 1 #"1"
0 0 17 3 2 #" (" 0 0 17 3 2 #" ("
0 0 17 3 1 #"/" 0 0 17 3 15 #"/ x (* 2 pi))))"
0 0 17 3 14 #" x (* 2 pi))))"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 50 #"; (Rotate (Rectangle) ,x)))" 0 0 17 3 50 #"; (Rotate (Rectangle) ,x)))"
@ -4047,16 +4047,14 @@
0 0 17 3 1 #"0" 0 0 17 3 1 #"0"
0 0 17 3 2 #" (" 0 0 17 3 2 #" ("
0 0 17 3 1 #"*" 0 0 17 3 1 #"*"
0 0 17 3 1 #" " 0 0 17 3 20 #" 4 pi) (* 2/24 pi)))"
0 0 17 3 19 #"4 pi) (* 2/24 pi)))"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
0 0 17 3 3 #" " 0 0 17 3 3 #" "
0 0 17 3 1 #"'" 0 0 17 3 1 #"'"
0 0 17 3 2 #"((" 0 0 17 3 2 #"(("
0 0 17 3 5 #"Range" 0 0 17 3 24 #"Range ((-2 2) (-2 2)))))"
0 0 17 3 19 #" ((-2 2) (-2 2)))))"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
@ -4265,8 +4263,7 @@
0 0 17 3 3 #"0.0" 0 0 17 3 3 #"0.0"
0 0 17 3 1 #"," 0 0 17 3 1 #","
0 0 17 3 1 #" " 0 0 17 3 1 #" "
0 0 17 3 3 #"1.0" 0 0 17 3 33 #"1.0]>; given: -0.0416666666666663"
0 0 17 3 30 #"]>; given: -0.0416666666666663"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
@ -4386,8 +4383,7 @@
0 0 17 3 1 #"," 0 0 17 3 1 #","
0 0 17 3 2 #" {" 0 0 17 3 2 #" {"
0 0 17 3 1 #"x" 0 0 17 3 1 #"x"
0 0 17 3 2 #", " 0 0 17 3 10 #", 0, 10}]]"
0 0 17 3 8 #"0, 10}]]"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 2 #"; " 0 0 17 3 2 #"; "
@ -5086,8 +5082,7 @@
0 0 17 3 1 #";" 0 0 17 3 1 #";"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 16 #";Graphics[Table["
0 0 17 3 15 #"Graphics[Table["
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
@ -5099,8 +5094,7 @@
0 0 17 3 1 #"0" 0 0 17 3 1 #"0"
0 0 17 3 1 #"," 0 0 17 3 1 #","
0 0 17 3 1 #" " 0 0 17 3 1 #" "
0 0 17 3 3 #"0.5" 0 0 17 3 28 #"0.5]}], ; black, opacity 50%"
0 0 17 3 25 #"]}], ; black, opacity 50%"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
@ -5117,8 +5111,7 @@
0 0 17 3 1 #" " 0 0 17 3 1 #" "
0 0 17 3 1 #"1" 0 0 17 3 1 #"1"
0 0 17 3 1 #"," 0 0 17 3 1 #","
0 0 17 3 1 #" " 0 0 17 3 7 #" 0.6], "
0 0 17 3 6 #"0.6], "
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
@ -5143,8 +5136,7 @@
0 0 17 3 1 #"," 0 0 17 3 1 #","
0 0 17 3 2 #" (" 0 0 17 3 2 #" ("
0 0 17 3 3 #"8-r" 0 0 17 3 3 #"8-r"
0 0 17 3 1 #")" 0 0 17 3 7 #")/3]}, "
0 0 17 3 6 #"/3]}, "
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
@ -5154,8 +5146,7 @@
#" {" #" {"
) 0 0 17 3 1 #"r" ) 0 0 17 3 1 #"r"
0 0 17 3 1 #"," 0 0 17 3 1 #","
0 0 17 3 1 #" " 0 0 17 3 5 #" 6}, "
0 0 17 3 4 #"6}, "
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 17 3 1 #";" 0 0 17 3 1 #";"
@ -5163,8 +5154,7 @@
( (
#" " #" "
#" {" #" {"
) 0 0 17 3 1 #"q" ) 0 0 17 3 8 #"q, 12}]]"
0 0 17 3 7 #", 12}]]"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 22 3 2 #" " 0 0 22 3 2 #" "
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
@ -5443,7 +5433,6 @@
0 0 17 3 1 #" " 0 0 17 3 1 #" "
0 0 17 3 1 #"0" 0 0 17 3 1 #"0"
0 0 17 3 1 #" " 0 0 17 3 1 #" "
0 0 17 3 1 #"0" 0 0 17 3 7 #"0) 5)))"
0 0 17 3 6 #") 5)))"
0 0 22 29 1 #"\n" 0 0 22 29 1 #"\n"
0 0 0 0