Теорема о квадрате

Жегалин Михаил/Konkatenatsia.rkt

@@ -0,0 +1,7 @@
+(define (concat li1 li2)
+    (if (empty? li2)
+        li1
+        (concat (append li1 (list (car li2))) (cdr li2))
+    )
+)
+(writeln (concat (list 1 2 3) (list 3 4 5)))

Жегалин Михаил/README.md

@@ -0,0 +1,8 @@
+# Конкатенация
+## Ссылка на видеоразбор
+https://youtu.be/UCdiG5nTiFY
+## Код из книги
+    #let rec append l1 l2 = 
+    match l1 with
+    [] -> l2
+    | (h::t) -> h::(append t l2);;

Ковтун Богдан/Kovtun Bogdan.rkt

@@ -0,0 +1,29 @@
+
+#lang racket/base
+(define (coordinations x1 y1 x2 y2 x3 y3 x4 y4 x5 y5)
+(define (square x) (* x x))
+(if (equal? (* (- x1 x2) (- y2 y3)) (* (- y1 y2) (- x2 x3))) 
+(displayln "Points 1, 2 and 3 lie on a common line.") 
+(displayln "Points 1, 2 and 3 do not lie on a common line."))
+(if (equal? (* (- x1 x2) (- y3 y4)) (* (- y1 y2) (- x3 x4))) 
+(displayln "Lines (1,2) and (3,4) are parallel.") 
+(displayln "Lines (1,2) and (3,4) are not parallel."))
+(if (equal? (+ (* (- x1 x2) (- x3 x4)) (* (- y1 y2) (- y3 y4))) 0 ) 
+(displayln "Lines (1,2) and (3,4) are perpendicular.") 
+(displayln "Lines (1,2) and (3,4) are not perpendicular."))
+(if (equal? (+ (square(- x1 x2)) (square(- y1 y2))) (+ (square(- x3 x4)) (square(- y3 y4)))) 
+(displayln "Lines (1,2) and (3,4) have the same length.") 
+(displayln "Lines (1,2) and (3,4) do not have the same length.."))
+(if (and (equal? (* 2 x1) (+ x2 x3)) (equal? (* 2 y1) (+ y2 y3)))
+(displayln "Point 1 is the midpoint of line (2,3).") 
+(displayln "Point 1 is not the midpoint of line (2,3)."))
+(if (and (equal? (* (- x1 x2) (- y2 y3)) (* (- y1 y2) (- x2 x3)) ) 
+(equal? (* (- x1 x4) (- y4 y5)) (* (- y1 y4) (- x4 x5)) ) )
+(displayln "Lines (2,3) and (4,5) meet at point 1.") 
+(displayln "Lines (2,3) and (4,5) do not intersect at point 1."))
+(if (and (equal? x1 x2) (equal? y1 y2))
+(displayln "Points 1 and 2 are the same.") 
+(displayln "Points 1 and 2 are not the same."))
+
+)
+(coordinations 0 1 0 0 0 1 1 1 2 2)

Ковтун Богдан/README.md

@@ -0,0 +1,32 @@
+# Перевод геометрических свойств в координаты
+## Ссылка на видеоразбор
+https://youtu.be/Nu43zpDrWuM
+## Код из книги
+    let coordinations =
+    ["collinear", (** Points 1, 2 and 3 lie on a common line **)
+    <<(1_x - 2_x) * (2_y - 3_y) = (1_y - 2_y) * (2_x - 3_x)>>;
+    "parallel", (** Lines (1,2) and (3,4) are parallel **)
+    <<(1_x - 2_x) * (3_y - 4_y) = (1_y - 2_y) * (3_x - 4_x)>>;
+    "perpendicular", (** Lines (1,2) and (3,4) are perpendicular **)
+    <<(1_x - 2_x) * (3_x - 4_x) + (1_y - 2_y) * (3_y - 4_y) = 0>>;
+    "lengths_eq", (** Lines (1,2) and (3,4) have the same length **)
+    <<(1_x - 2_x)^2 + (1_y - 2_y)^2 = (3_x - 4_x)^2 + (3_y - 4_y)^2>>;
+    "is_midpoint", (** Point 1 is the midpoint of line (2,3) **)
+    <<2 * 1_x = 2_x + 3_x /\ 2 * 1_y = 2_y + 3_y>>;
+    "is_intersection", (** Lines (2,3) and (4,5) meet at point 1 **)
+    <<(1_x - 2_x) * (2_y - 3_y) = (1_y - 2_y) * (2_x - 3_x) /\
+     (1_x - 4_x) * (4_y - 5_y) = (1_y - 4_y) * (4_x - 5_x)>>;
+    "=", (** Points 1 and 2 are the same **)
+    <<(1_x = 2_x) /\ (1_y = 2_y)>>];;
+
+    let coordinate = onatoms
+    (fun (R(a,args)) ->
+    let xtms,ytms = unzip
+     (map (fun (Var v) -> Var(v^"_x"),Var(v^"_y")) args) in
+    let xs = map (fun n -> string_of_int n^"_x") (1--length args)
+    and ys = map (fun n -> string_of_int n^"_y") (1--length args) in
+    subst (fpf (xs @ ys) (xtms @ ytms)) (assoc a coordinations));;
+
+    START_INTERACTIVE;;
+    coordinate <<collinear(a,b,c) ==> collinear(b,a,c)>>;;
+    END_INTERACTIVE;;

Костин Андрей/README.md

@@ -0,0 +1,8 @@
+# Вычисление степени
+## Ссылка на видеоразбор
+https://youtu.be/4LgMiXXWyE4
+## Код из книги
+    #let rec exp x n =
+        if n = 0 then 1
+        else x * exp x (n - 1);;
+        

Костин Андрей/power.rkt

@@ -0,0 +1,4 @@
+#lang racket
+(define (power n m)
+  (if (= m 0) 1
+      (* n (power n (- m 1)))))

Латин Ярослав/1ch.fs

@@ -0,0 +1,33 @@
+// For more information see https://aka.ms/fsharp-console-apps
+
+
+let mutable y1 = 1
+let _ = y1 <- y1*2 in
+let _ = y1 <- y1+1 in
+let _ = y1 <- y1+1 in
+
+printf "y1 = %A\n"y1
+
+let mutable x1 = 1
+let _ = x1 <- x1+1 in
+let _ = x1 <- x1*2 in
+let _ = x1 <- x1+1 in
+
+printf "x1 = %A\n"x1
+
+let mutable y = 1
+y <- y * 2
+y <- y + 1
+y <- y + 1
+
+
+printf "y = %A\n"y
+
+let mutable x = 1
+x <- x + 1
+x <- x * 2
+x <- x + 1
+
+
+printf "x = %A\n"x
+

Латин Ярослав/2ch.fs

@@ -0,0 +1,16 @@
+// For more information see https://aka.ms/fsharp-console-apps
+module kolok
+
+let mutable x = []
+
+let mutable refx = ref x
+
+let _ = refx <- ref [2]
+//let _ = refx <- ref [true]
+
+
+printf "%O\n" refx
+printf "%A\n" refx
+
+
+

Латин Ярослав/README.md

@@ -0,0 +1,16 @@
+# Последовательность вычислений и Работа с системой типов
+## Ссылка на видеоразбор
+
+## Код из книги
+Ярик Латин, [5/10/22 4:31 PM]
+let _ = x := !x + 1 in
+let _ = x := !x + 1 in
+let _ = x := !x + 1 in
+let _ = x := !x + 1 in
+();;
+
+Ярик Латин, [5/10/22 4:31 PM]
+x := !x + 1;
+x := !x + 1;
+x := !x + 1;
+x := !x + 1;;

Носов Иван/README.md

@@ -0,0 +1,29 @@
+# Дифференцирование 
+## Ссылка на видеоразбор
+https://youtu.be/Kh0shn9UW6Y
+## Код из книги
+    #let rec differentiate x tm = match tm with
+    Var y -> if y = x then Const "1" else Const "0"
+    | Const c -> Const "0"
+    | Fn("-",[t]) -> Fn("-",[differentiate x t])
+    | Fn("+",[t1;t2]) -> Fn("+",[differentiate x t1;
+    differentiate x t2])
+    | Fn("-",[t1;t2]) -> Fn("-",[differentiate x t1;
+    differentiate x t2])
+    |    Fn("*",[t1;t2]) ->
+    Fn("+",[Fn("*",[differentiate x t1; t2]);
+    Fn("*",[t1; differentiate x t2])])
+    | Fn("inv",[t]) -> chain x t
+    (Fn("-",[Fn("inv",[Fn("^",[t;Const "2"])])]))
+    | Fn("^",[t;n]) -> chain x t
+    (Fn("*",[n; Fn("^",[t; Fn("-",[n; Const "1"])])]))
+    | Fn("exp",[t]) -> chain x t tm
+    | Fn("ln",[t]) -> chain x t (Fn("inv",[t]))
+    | Fn("sin",[t]) -> chain x t (Fn("cos",[t]))
+    | Fn("cos",[t]) -> chain x t
+    (Fn("-",[Fn("sin",[t])]))
+    | Fn("/",[t1;t2]) -> differentiate x
+    (Fn("*",[t1; Fn("inv",[t2])]))
+    | Fn("tan",[t]) -> differentiate x
+    (Fn("/",[Fn("sin",[t]); Fn("cos",[t])]))
+    and chain x t u = Fn("*",[differentiate x t; u]);;

Носов Иван/proizvodnaya.rkt

@@ -0,0 +1,113 @@
+#lang racket
+(define (deriv exp var)
+  (cond ((number? exp) 0)
+        ((variable? exp)
+         (if (same-variable? exp var) 1 0))
+        
+        ((sum? exp)
+         (make-sum (deriv (addend exp) var)
+                   (deriv (augend exp) var)))
+        
+        ((dif? exp)
+         (make-dif (deriv (addend exp) var)
+                   (deriv (augend exp) var)))
+        
+        ((product? exp)
+         (make-sum
+          (make-product (multiplier exp)
+                        (deriv (multipicand exp) var))
+          (make-product (deriv (multiplier exp) var)
+                        (multipicand exp))))
+
+        ((exponentiation? exp)
+         (make-product
+          (make-product (exponent exp)
+                        (make-exponentiation (base exp) (- (exponent exp) 1)))
+          (deriv (base exp)
+                 var)))
+        
+        ((sinus? exp)
+         (make-product
+          (deriv (base exp)
+                 var)(make-cos (base exp))))
+        
+        ((cosinus? exp)
+         (make-product
+          (deriv (base exp)var)(make-sin (base exp))))
+
+        ((ex? exp)
+         (make-product
+          (deriv (base exp)
+                 var)(make-exp (base exp))))
+         
+
+        (else
+         error "unknow expression type -- DERIV" exp)))
+
+(define (ex? x)
+  (and (pair? x) (eq? 'exp (car x))))
+
+(define (make-exp a0)(list 'exp a0))
+
+(define (sinus? x)
+  (and (pair? x) (eq? 'sin (car x) )))
+
+(define (make-cos a0)(list 'cos a0))
+
+(define (cosinus? x)
+  (and (pair? x) (eq? 'cos (car x) )))
+
+(define (make-sin a0)(list '-sin a0))
+
+(define (=number? exp num)
+  (and (number? exp) (= exp num)))
+
+(define (multipicand p) (caddr p))
+
+(define (variable? x) (symbol? x))
+
+(define (same-variable? v0 v1)
+  (and (variable? v0) (variable? v1) (eq? v0 v1)))
+
+(define (make-sum a0 a1)
+  (cond ((and (number? a0) (number? a1)) (+ a0 a1))
+        (else (list '+ a0 a1))))
+
+(define (sum? x)
+  (and (pair? x) (eq? (car x) '+)))
+
+(define (dif? x)
+  (and (pair? x) (eq? (car x) '-)))
+
+(define (make-dif a0 a1)
+  (cond ((and (number? a0) (number? a1)) (- a0 a1))
+        (else (list '- a0 a1))))
+
+(define (addend s) (cadr s))
+
+(define (augend s) (caddr s))
+
+(define (make-product m0 m1)
+  (cond ((or (=number? m0 0) (=number? m1 0)) 0)
+        ((=number? m0 1) m1)
+        ((=number? m1 1) m0)
+        ((and (number? m0) (number? m1)) (* m0 m1))
+        (else (list '* m0 m1))))
+
+(define (product? x)
+  (and (pair? x) (eq? (car x) '*)))
+
+(define (multiplier p) (cadr p))
+
+(define (make-exponentiation x n)
+  (cond ((= n 0) 1)
+        ((= n 1) x)
+        (else (list '** x n))))
+
+(define (exponentiation? x)
+  (and (pair? x) (eq? (car x) '**)))
+
+(define (base s) (cadr s))
+
+(define (exponent s) (caddr s))
+

Павлова Наташа/README.md

@@ -0,0 +1,3 @@
+# Лемма 7.6
+## Ссылка на видеоразбор
+https://youtu.be/8mOFRUgdmZU

Павлова Наташа/lemma_7.6.rkt

@@ -0,0 +1,22 @@
+#lang racket
+
+(define (rev lst)
+  (if (null? lst);ф-я принимает пустой список
+      lst;возвращает пустой список
+      (if (= 1 (length lst));ф-я принимает список из 1 элемента
+          lst; возвращает  список из 1 элемента
+          ;в списке можно выделить голову и хвост
+          (append (rev (cdr lst)); запускаем rev для хвоста (cdr - хвост)
+                      (list(car lst));возвращаем голову (car - голова)
+           )
+      )
+  )
+)
+
+(writeln(rev(rev '(1 2 3 4))))
+
+
+
+
+
+

Погребицкий Евгений/README.md

@@ -0,0 +1,24 @@
+# Теорема Симсона
+## Ссылка на видеоразбор
+https://youtu.be/_ewjiWIH0VY
+## Код из книги
+	START_INTERACTIVE;;
+	let simson =
+	 <<lengths_eq(o,a,o,b) /\
+  	 lengths_eq(o,a,o,c) /\
+  	 lengths_eq(o,a,o,d) /\
+  	 collinear(e,b,c) /\
+  	 collinear(f,a,c) /\
+  	 collinear(g,a,b) /\
+  	 perpendicular(b,c,d,e) /\
+  	 perpendicular(a,c,d,f) /\
+  	 perpendicular(a,b,d,g)
+  	 ==> collinear(e,f,g)>>;;
+
+	let vars =
+ 	["g_y"; "g_x"; "f_y"; "f_x"; "e_y"; "e_x"; "d_y"; "d_x"; "c_y"; "c_x";
+  	"b_y"; "b_x"; "o_x"]
+	and zeros = ["a_x"; "a_y"; "o_y"];;
+
+	wu simson vars zeros;;
+

Погребицкий Евгений/simson.rkt

@@ -0,0 +1,38 @@
+#lang racket/base
+
+(define (square x) (* x x))
+
+(define (lengths_eq x1 y1 x2 y2 x3 y3)
+(if (equal? (+ (square(- x1 x2)) (square(- y1 y2))) (+ (square(- x3 x1)) (square(- y3 y1)))) 
+#t #f
+))
+
+(define (collinear x1 y1 x2 y2 x3 y3)
+(if (equal? (* (- x1 x2) (- y2 y3)) (* (- y1 y2) (- x2 x3))) 
+#t #f
+))
+
+(define (perpendicular x1 y1 x2 y2 x3 y3 x4 y4)
+(if (equal? (+ (* (- x1 x2) (- x3 x4)) (* (- y1 y2) (- y3 y4))) 0 ) 
+#t #f
+))
+
+
+
+(define (simson o_x o_y a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y f_x f_y g_x g_y)
+(if (and 
+    (lengths_eq o_x o_y a_x a_y b_x b_y) 
+    (lengths_eq o_x o_y a_x a_y c_x c_y) 
+    (lengths_eq o_x o_y a_x a_y d_x d_y) 
+    (collinear e_x e_y b_x b_y c_x c_y)
+    (collinear f_x f_y a_x a_y c_x c_y)
+    (collinear g_x g_y a_x a_y b_x b_y)
+    (perpendicular b_x b_y c_x c_y d_x d_y e_x e_y)
+    (perpendicular a_x a_y c_x c_y d_x d_y f_x f_y)
+    (perpendicular a_x a_y b_x b_y d_x d_y g_x g_y))
+    
+    (begin (displayln "3 Points lie on one line.") (collinear e_x e_y f_x f_y g_x g_y)
+    ) (displayln "3 Points do not lie on one line.")
+))
+
+(simson 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 )

Сивочуб Алексей/README.md

@@ -0,0 +1,18 @@
+# Теорема о квадрате
+## Ссылка на видеоразбор
+https://youtu.be/0Yp5sgddlko
+## Код из сайта
+    START_INTERACTIVE;;
+    let coordinations =
+    ["perpendicular", (** Lines (1,2) and (3,4) are perpendicular **)
+    <<(1_x - 2_x) * (3_x - 4_x) + (1_y - 2_y) * (3_y - 4_y) = 0>>;
+    "lengths_eq", (** Lines (1,2) and (3,4) have the same length **)
+    <<(1_x - 2_x)^2 + (1_y - 2_y)^2 = (3_x - 4_x)^2 + (3_y - 4_y)^2>>;
+    "is_midpoint", (** Point 1 is the midpoint of line (2,3) **)
+    <<2 * 1_x = 2_x + 3_x /\ 2 * 1_y = 2_y + 3_y>>];;
+    #Square theorem
+
+    (grobner_decide ** originate)
+    <<is_midpoint(m,a,c) /\ perpendicular(a,c,m,b)
+    ==> lengths_eq(a,b,b,c)>>;;
+    END_INTERACTIVE;

Сивочуб Алексей/square.rkt

@@ -0,0 +1,35 @@
+#lang racket/base
+
+(define (square x) (* x x))
+
+(define (lengths_eq x1 y1 x2 y2 x3 y3 x4 y4)
+(if (equal? (+ (square(- x1 x2)) (square(- y1 y2))) 
+(+ (square(- x3 x4)) (square(- y3 y4)))) 
+(displayln "Lines (1,2) and (3,4) have the same length.") 
+(displayln "Lines (1,2) and (3,4) do not have the same length.")))
+
+(define (perpendicular x1 y1 x2 y2 x3 y3 x4 y4)
+(if (equal? (+ (* (- x1 x2) (- x3 x4)) (* (- y1 y2) (- y3 y4))) 0 ) 
+#t #f
+))
+
+(define (is_midpoint x1 y1 x2 y2 x3 y3)
+(if (and (equal? (* 2 x1) (+ x2 x3)) (equal? (* 2 y1) (+ y2 y3)))
+(displayln "Point 1 is the midpoint of line (2,3).")
+(displayln "Point 1 is not the midpoint of line (2,3).")
+))
+
+
+(define (grobner_decide_mid a_x a_y b_x b_y c_x c_y d_x d_y m_x m_y)
+(if (and (is_midpoint m_x m_y a_x a_y c_x c_y) 
+    (perpendicular a_x a_y c_x c_y m_x m_y b_x b_y))
+    (begin 
+  (lengths_eq a_x a_y b_x b_y b_x b_y c_x c_y) 
+  (displayln "This is a square.") 
+  )
+  (displayln "This is not a square.") 
+))
+
+
+
+(grobner_decide_mid 0 0 0 2 2 2 2 0 1 1)