New linear algebra algorithm (#1122)

* Added new algorithm which takes points as an input and outputs a polynom connecting them

* Rename Python-Polynom-for-points.py to python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Add doctests and run thru psf/black

linear_algebra/src/python-polynom-for-points.py

@@ -0,0 +1,130 @@
+def points_to_polynomial(coordinates):
+    """
+    coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
+    number of points you want to use
+
+    >>> print(points_to_polynomial([]))
+    The program cannot work out a fitting polynomial.
+    >>> print(points_to_polynomial([[]]))
+    The program cannot work out a fitting polynomial.
+    >>> print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
+    f(x)=x^2*0.0+x^1*-0.0+x^0*0.0
+    >>> print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
+    f(x)=x^2*0.0+x^1*-0.0+x^0*1.0
+    >>> print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
+    f(x)=x^2*0.0+x^1*-0.0+x^0*3.0
+    >>> print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
+    f(x)=x^2*0.0+x^1*1.0+x^0*0.0
+    >>> print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
+    f(x)=x^2*1.0+x^1*-0.0+x^0*0.0
+    >>> print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
+    f(x)=x^2*1.0+x^1*-0.0+x^0*2.0
+    >>> print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
+    f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0
+    >>> print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
+    f(x)=x^2*5.0+x^1*-18.0+x^0*18.0
+    """
+    try:
+        check = 1
+        more_check = 0
+        d = coordinates[0][0]
+        for j in range(len(coordinates)):
+            if j == 0:
+                continue
+            if d == coordinates[j][0]:
+                more_check += 1
+                solved = "x=" + str(coordinates[j][0])
+                if more_check == len(coordinates) - 1:
+                    check = 2
+                    break
+                elif more_check > 0 and more_check != len(coordinates) - 1:
+                    check = 3
+                else:
+                    check = 1
+
+        if len(coordinates) == 1 and coordinates[0][0] == 0:
+            check = 2
+            solved = "x=0"
+    except Exception:
+        check = 3
+
+    x = len(coordinates)
+
+    if check == 1:
+        count_of_line = 0
+        matrix = []
+        # put the x and x to the power values in a matrix
+        while count_of_line < x:
+            count_in_line = 0
+            a = coordinates[count_of_line][0]
+            count_line = []
+            while count_in_line < x:
+                count_line.append(a ** (x - (count_in_line + 1)))
+                count_in_line += 1
+            matrix.append(count_line)
+            count_of_line += 1
+
+        count_of_line = 0
+        # put the y values into a vector
+        vector = []
+        while count_of_line < x:
+            count_in_line = 0
+            vector.append(coordinates[count_of_line][1])
+            count_of_line += 1
+
+        count = 0
+
+        while count < x:
+            zahlen = 0
+            while zahlen < x:
+                if count == zahlen:
+                    zahlen += 1
+                if zahlen == x:
+                    break
+                bruch = (matrix[zahlen][count]) / (matrix[count][count])
+                for counting_columns, item in enumerate(matrix[count]):
+                    # manipulating all the values in the matrix
+                    matrix[zahlen][counting_columns] -= item * bruch
+                # manipulating the values in the vector
+                vector[zahlen] -= vector[count] * bruch
+                zahlen += 1
+            count += 1
+
+        count = 0
+        # make solutions
+        solution = []
+        while count < x:
+            solution.append(vector[count] / matrix[count][count])
+            count += 1
+
+        count = 0
+        solved = "f(x)="
+
+        while count < x:
+            remove_e = str(solution[count]).split("E")
+            if len(remove_e) > 1:
+                solution[count] = remove_e[0] + "*10^" + remove_e[1]
+            solved += "x^" + str(x - (count + 1)) + "*" + str(solution[count])
+            if count + 1 != x:
+                solved += "+"
+            count += 1
+
+        return solved
+
+    elif check == 2:
+        return solved
+    else:
+        return "The program cannot work out a fitting polynomial."
+
+
+if __name__ == "__main__":
+    print(points_to_polynomial([]))
+    print(points_to_polynomial([[]]))
+    print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
+    print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
+    print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
+    print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
+    print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
+    print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
+    print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
+    print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))