finished newton polynom

.idea/.gitignore

@@ -0,0 +1,8 @@
+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml

.idea/Python-Math-Algorithms.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="jdk" jdkName="Python 3.11" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>

.idea/inspectionProfiles/profiles_settings.xml

@@ -0,0 +1,6 @@
+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.11" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/Python-Math-Algorithms.iml" filepath="$PROJECT_DIR$/.idea/Python-Math-Algorithms.iml" />
+    </modules>
+  </component>
+</project>

.idea/vcs.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="" vcs="Git" />
+  </component>
+</project>

newton_polynom/__init__.py

@@ -14,27 +14,32 @@
 # Licensed under the GPLv2 License, Version 2.0 (the "License");
 # Copyright (c) Sven Vogel
 
-def combine(p0, p1):
-    return (p1[1] - p1[0]) / (p0[1] - p0[0])
-
-
-def combine_n(*points):
-    k = len(points) - 1
+def combine_n(points):
+    k = len(points)
 
     if k == 1:
-        return combine(points[0], points[1])
+        return points[0][1]
+    elif k == 2:
+        return (points[1][1] - points[0][1]) / (points[1][0] - points[0][0])
     else:
-        return (combine_n(points[1:k]) - combine_n(points[0:(k - 1)])) / (points[k][0] - points[0][0])
+        return (combine_n(points[1:k]) - combine_n(points[0:(k - 1)])) / (points[k - 1][0] - points[0][0])
 
 
-def newton_polynom(*points):
-    for x in range(len(points)):
+# returns a polynom that will intersect all supplied points as long as
+# the number of points is bigger than 1
+def newton_polynom(points):
+    for x in range(1, len(points)):
 
-        print(combine_n(points[0:x]))
+        if x == 1:
+            print(points[0][1], end=' + ')
+        else:
+            print(end=' + ')
+
+        print(combine_n(points[0:(x + 1)]), end='')
 
         for y in range(x):
-            print(format(" * (x - %s)", points[y][0]))
+            print(" * (x - {value:.2f})".format(value=points[y][0]), end='')
 
 
 def test():
-    newton_polynom([1, 2], [3, 4], [9, -5])
+    newton_polynom([[-1, 5], [2, -1], [3, -1], [4, 5], [8, 9]])