Add more examples

.gitignore

@@ -1,51 +1,52 @@
-# ---> VisualStudioCode
-.vscode/*
-!.vscode/settings.json
-!.vscode/tasks.json
-!.vscode/launch.json
-!.vscode/extensions.json
+# Created by https://www.gitignore.io/api/macos,scheme,jetbrains+all,visualstudiocode
+# Edit at https://www.gitignore.io/?templates=macos,scheme,jetbrains+all,visualstudiocode
 
-# ---> Scheme
-*.ss~
-*.ss#*
-.#*.ss
-
-*.scm~
-*.scm#*
-.#*.scm
-
-# ---> JetBrains
-# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio and Webstorm
+### JetBrains+all ###
+# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio and WebStorm
 # Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839
 
-# User-specific stuff:
+# User-specific stuff
 .idea/**/workspace.xml
 .idea/**/tasks.xml
-.idea/dictionaries
+.idea/**/usage.statistics.xml
+.idea/**/dictionaries
+.idea/**/shelf
 
-# Sensitive or high-churn files:
+# Generated files
+.idea/**/contentModel.xml
+
+# Sensitive or high-churn files
 .idea/**/dataSources/
 .idea/**/dataSources.ids
-.idea/**/dataSources.xml
 .idea/**/dataSources.local.xml
 .idea/**/sqlDataSources.xml
 .idea/**/dynamic.xml
 .idea/**/uiDesigner.xml
+.idea/**/dbnavigator.xml
 
-# Gradle:
+# Gradle
 .idea/**/gradle.xml
 .idea/**/libraries
 
-# Mongo Explorer plugin:
+# Gradle and Maven with auto-import
+# When using Gradle or Maven with auto-import, you should exclude module files,
+# since they will be recreated, and may cause churn.  Uncomment if using
+# auto-import.
+# .idea/modules.xml
+# .idea/*.iml
+# .idea/modules
+
+# CMake
+cmake-build-*/
+
+# Mongo Explorer plugin
 .idea/**/mongoSettings.xml
 
-## File-based project format:
+# File-based project format
 *.iws
 
-## Plugin-specific files:
-
 # IntelliJ
-/out/
+out/
 
 # mpeltonen/sbt-idea plugin
 .idea_modules/
@@ -62,15 +63,37 @@ crashlytics.properties
 crashlytics-build.properties
 fabric.properties
 
-# ---> macOS
-*.DS_Store
+# Editor-based Rest Client
+.idea/httpRequests
+
+# Android studio 3.1+ serialized cache file
+.idea/caches/build_file_checksums.ser
+
+### JetBrains+all Patch ###
+# Ignores the whole .idea folder and all .iml files
+# See https://github.com/joeblau/gitignore.io/issues/186 and https://github.com/joeblau/gitignore.io/issues/360
+
+.idea/
+
+# Reason: https://github.com/joeblau/gitignore.io/issues/186#issuecomment-249601023
+
+*.iml
+modules.xml
+.idea/misc.xml
+*.ipr
+
+# Sonarlint plugin
+ .idea/sonarlint
+
+### macOS ###
+# General
+.DS_Store
 .AppleDouble
 .LSOverride
 
 # Icon must end with two \r
 Icon
 
-
 # Thumbnails
 ._*
 
@@ -90,3 +113,24 @@ Network Trash Folder
 Temporary Items
 .apdisk
 
+### Scheme ###
+*.ss~
+*.ss#*
+.#*.ss
+
+*.scm~
+*.scm#*
+.#*.scm
+
+### VisualStudioCode ###
+.vscode/*
+!.vscode/settings.json
+!.vscode/tasks.json
+!.vscode/launch.json
+!.vscode/extensions.json
+
+### VisualStudioCode Patch ###
+# Ignore all local history of files
+.history
+
+# End of https://www.gitignore.io/api/macos,scheme,jetbrains+all,visualstudiocode

lib.scm

@@ -1,6 +1,11 @@
-(define (sqrt x)
+#lang sicp
 (define (average x y) (/ (+ x y) 2))
 (define (square x) (* x x))
+(define (cube x) (* x x x))
+(define (% a b)
+  (remainder a b))
+
+(define (sqrt x)
   (define (good-enough? guess)
     (< (abs (- (square guess) x)) 0.00001))
   (define (improve guess)
@@ -21,7 +26,6 @@
         (fact-iter (* counter product)
                    (+ counter 1)
                    max-count)))
-
   (fact-iter 1 1 n))
 
 
@@ -64,7 +68,6 @@
            (+ (cc amount (- kinds-of-coins 1))
               (cc (- amount (first-denomination kinds-of-coins))
                   kinds-of-coins)))))
-  
   (cc amount 5))
 
 
@@ -74,3 +77,52 @@
        (ptri (- n 1))
        (+ (* (ptri (- n 2)) 2)
           (* (ptri (- n 3)) 3)))))
+
+
+(define (p x) (- (* 3 x) (* 4 (cube x))))
+(define (sine angle)
+  (if (not (> (abs angle) 0.1))
+      angle
+      (p (sine (/ angle 3.0)))))
+
+;(define (expt b n)
+;  (if (= n 0) 1 (* b (expt b (- n 1)))))
+
+(define (expt b n) (expt-iter b n 1))
+(define (expt-iter b counter product)
+  (if (= counter 0)
+      product
+      (expt-iter b
+                 (- counter 1)
+                 (* b product))))
+
+(define (fast-exp b n)
+  (cond ((= n 0)
+         1)
+        ((even? n)
+         (square (fast-exp b (/ n 2))))
+        (else
+         (* b (fast-exp b (- n 1))))))
+
+(define (gcd a b)
+  (if (= b 0)
+      a
+      (gcd b (% a b))))
+
+(define (smallest-divisor n)
+  (find-divisor n 2))
+
+(define (find-divisor n test-divisor)
+  (cond ((> (square test-divisor) n)
+         n)
+        ((divides? test-divisor n)
+         test-divisor)
+        (else (find-divisor
+               n
+               (+ test-divisor 1)))))
+
+(define (divides? a b)
+  (= (% b a) 0))
+
+(define (prime? n)
+  (= n (smallest-divisor n)))