human
Newton 's Divided Difference Interpolation Formula | Function to find the product term.
Function for calculating divided difference table.
Function for applying Newton 's  divided difference formula .
Function for displaying divided difference table.
number of inputs given.
y [ ] [ ] is used for divided difference table where y [ ] [ 0 ] is used for input.
calculating divided difference table.
displaying divided difference table.
value to be interpolated.
printing the value"
How can the above be solved in Python?
 Write me a code to newton 's Divided Difference Interpolation Formula and the other steps required?
assistant
#Here is code to newton 's Divided Difference Interpolation Formula and the other steps required.
 def proterm ( i , value , x ) :
	pro = 1 ;
	for j in range ( i ) :
		pro = pro * ( value - x [ j ] ) ;
	return pro ;
def dividedDiffTable ( x , y , n ) :
	for i in range ( 1 , n ) :
		for j in range ( n - i ) :
			y [ j ] [ i ] = ( ( y [ j ] [ i - 1 ] - y [ j + 1 ] [ i - 1 ] ) / ( x [ j ] - x [ i + j ] ) ) ;
	return y ;
def applyFormula ( value , x , y , n ) :
	sum = y [ 0 ] [ 0 ] ;
	for i in range ( 1 , n ) :
		sum = sum + ( proterm ( i , value , x ) * y [ 0 ] [ i ] ) ;
	return sum ;
def printDiffTable ( y , n ) :
	for i in range ( n ) :
		for j in range ( n - i ) :
			print ( round ( y [ i ] [ j ] , 4 ) , " 	 " , end = " ▁ " ) ;
		print ( " " ) ;
n = 4 ;
y = [ [ 0 for i in range ( 10 ) ] for j in range ( 10 ) ] ;
x = [ 5 , 6 , 9 , 11 ] ;
y [ 0 ] [ 0 ] = 12 ;
y [ 1 ] [ 0 ] = 13 ;
y [ 2 ] [ 0 ] = 14 ;
y [ 3 ] [ 0 ] = 16 ;
y = dividedDiffTable ( x , y , n ) ;
printDiffTable ( y , n ) ;
value = 7 ;
print ( " Value at " , ▁ value , ▁ " is " , round ( applyFormula ( value , x , y , n ) , 2 ) )