From 201931050a82b533453295c7ac5eb2ce63878d5b Mon Sep 17 00:00:00 2001
From: teridax <sven.vogel123@web.de>
Date: Tue, 25 Apr 2023 16:27:32 +0200
Subject: [PATCH] finished newton polynom

---
 .idea/.gitignore                              |  8 +++++
 .idea/Python-Math-Algorithms.iml              |  8 +++++
 .../inspectionProfiles/profiles_settings.xml  |  6 ++++
 .idea/misc.xml                                |  4 +++
 .idea/modules.xml                             |  8 +++++
 .idea/vcs.xml                                 |  6 ++++
 newton_polynom/__init__.py                    | 31 +++++++++++--------
 7 files changed, 58 insertions(+), 13 deletions(-)
 create mode 100644 .idea/.gitignore
 create mode 100644 .idea/Python-Math-Algorithms.iml
 create mode 100644 .idea/inspectionProfiles/profiles_settings.xml
 create mode 100644 .idea/misc.xml
 create mode 100644 .idea/modules.xml
 create mode 100644 .idea/vcs.xml

diff --git a/.idea/.gitignore b/.idea/.gitignore
new file mode 100644
index 0000000..13566b8
--- /dev/null
+++ b/.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
diff --git a/.idea/Python-Math-Algorithms.iml b/.idea/Python-Math-Algorithms.iml
new file mode 100644
index 0000000..909438d
--- /dev/null
+++ b/.idea/Python-Math-Algorithms.iml
@@ -0,0 +1,8 @@
+<?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>
\ No newline at end of file
diff --git a/.idea/inspectionProfiles/profiles_settings.xml b/.idea/inspectionProfiles/profiles_settings.xml
new file mode 100644
index 0000000..105ce2d
--- /dev/null
+++ b/.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>
\ No newline at end of file
diff --git a/.idea/misc.xml b/.idea/misc.xml
new file mode 100644
index 0000000..a971a2c
--- /dev/null
+++ b/.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>
\ No newline at end of file
diff --git a/.idea/modules.xml b/.idea/modules.xml
new file mode 100644
index 0000000..c1955aa
--- /dev/null
+++ b/.idea/modules.xml
@@ -0,0 +1,8 @@
+<?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>
\ No newline at end of file
diff --git a/.idea/vcs.xml b/.idea/vcs.xml
new file mode 100644
index 0000000..35eb1dd
--- /dev/null
+++ b/.idea/vcs.xml
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="" vcs="Git" />
+  </component>
+</project>
\ No newline at end of file
diff --git a/newton_polynom/__init__.py b/newton_polynom/__init__.py
index f71e814..6620b2b 100644
--- a/newton_polynom/__init__.py
+++ b/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]])