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