polynom_for_points.py

defpoints_to_polynomial(coordinates: list[list[int]]) ->str:
"""
 coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
 number of points you want to use

 >>> points_to_polynomial([])
 Traceback (most recent call last):
 ...
 ValueError: The program cannot work out a fitting polynomial.
 >>> points_to_polynomial([[]])
 Traceback (most recent call last):
 ...
 ValueError: The program cannot work out a fitting polynomial.
 >>> points_to_polynomial([[1, 0], [2, 0], [3, 0]])
 'f(x)=x^2*0.0+x^1*-0.0+x^0*0.0'
 >>> points_to_polynomial([[1, 1], [2, 1], [3, 1]])
 'f(x)=x^2*0.0+x^1*-0.0+x^0*1.0'
 >>> points_to_polynomial([[1, 3], [2, 3], [3, 3]])
 'f(x)=x^2*0.0+x^1*-0.0+x^0*3.0'
 >>> points_to_polynomial([[1, 1], [2, 2], [3, 3]])
 'f(x)=x^2*0.0+x^1*1.0+x^0*0.0'
 >>> points_to_polynomial([[1, 1], [2, 4], [3, 9]])
 'f(x)=x^2*1.0+x^1*-0.0+x^0*0.0'
 >>> points_to_polynomial([[1, 3], [2, 6], [3, 11]])
 'f(x)=x^2*1.0+x^1*-0.0+x^0*2.0'
 >>> points_to_polynomial([[1, -3], [2, -6], [3, -11]])
 'f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0'
 >>> points_to_polynomial([[1, 5], [2, 2], [3, 9]])
 'f(x)=x^2*5.0+x^1*-18.0+x^0*18.0'
 >>> points_to_polynomial([[1, 1], [1, 2], [1, 3]])
 'x=1'
 >>> points_to_polynomial([[1, 1], [2, 2], [2, 2]])
 Traceback (most recent call last):
 ...
 ValueError: The program cannot work out a fitting polynomial.
 """
iflen(coordinates) ==0ornotall(len(pair) ==2forpairincoordinates):
raiseValueError("The program cannot work out a fitting polynomial.")

iflen({tuple(pair) forpairincoordinates}) !=len(coordinates):
raiseValueError("The program cannot work out a fitting polynomial.")

set_x= {xforx, _incoordinates}
iflen(set_x) ==1:
returnf"x={coordinates[0][0]}"

iflen(set_x) !=len(coordinates):
raiseValueError("The program cannot work out a fitting polynomial.")

x=len(coordinates)

# put the x and x to the power values in a matrix
matrix: list[list[float]] = [
 [
coordinates[count_of_line][0] ** (x- (count_in_line+1))
forcount_in_lineinrange(x)
 ]
forcount_of_lineinrange(x)
 ]

# put the y values into a vector
vector: list[float] = [coordinates[count_of_line][1] forcount_of_lineinrange(x)]

forcountinrange(x):
fornumberinrange(x):
ifcount==number:
continue
fraction=matrix[number][count] /matrix[count][count]
forcounting_columns, iteminenumerate(matrix[count]):
# manipulating all the values in the matrix
matrix[number][counting_columns] -=item*fraction
# manipulating the values in the vector
vector[number] -=vector[count] *fraction

# make solutions
solution: list[str] = [
str(vector[count] /matrix[count][count]) forcountinrange(x)
 ]

solved="f(x)="

forcountinrange(x):
remove_e: list[str] =solution[count].split("E")
iflen(remove_e) >1:
solution[count] =f"{remove_e[0]}*10^{remove_e[1]}"
solved+=f"x^{x- (count+1)}*{solution[count]}"
ifcount+1!=x:
solved+="+"

returnsolved


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]]))