numpy.poly1d() in Python
The numpy.poly1d() function helps to define a polynomial function. It makes it easy to apply “natural operations” on polynomials.
Syntax: numpy.poly1d(arr, root, var)
Parameters :
arr : [array_like] The polynomial coefficients are given in decreasing order of powers. If the second parameter (root) is set to True then array values are the roots of the polynomial equation.root : [bool, optional] True means polynomial roots. Default is False.
var : variable like x, y, z that we need in polynomial [default is x].Arguments :
c : Polynomial coefficient.
coef : Polynomial coefficient.
coefficients : Polynomial coefficient.
order : Order or degree of polynomial.
o : Order or degree of polynomial.
r : Polynomial root.
roots : Polynomial root.Return: Polynomial and the operation applied
For example: poly1d(3, 2, 6) = 3x2 + 2x + 6
poly1d([1, 2, 3], True) = (x-1)(x-2)(x-3) = x3 – 6x2 + 11x -6
Code 1 : Explaining poly1d() and its argument
# Python code explaining# numpy.poly1d() # importing librariesimport numpy as np # Constructing polynomialp1 = np.poly1d([1, 2])p2 = np.poly1d([4, 9, 5, 4]) print ("P1 : ", p1)print ("\n p2 : \n", p2) # Solve for x = 2print ("\n\np1 at x = 2 : ", p1(2))print ("p2 at x = 2 : ", p2(2)) # Finding Rootsprint ("\n\nRoots of P1 : ", p1.r)print ("Roots of P2 : ", p2.r) # Finding Coefficientsprint ("\n\nCoefficients of P1 : ", p1.c)print ("Coefficients of P2 : ", p2.coeffs) # Finding Orderprint ("\n\nOrder / Degree of P1 : ", p1.o)print ("Order / Degree of P2 : ", p2.order) |
Output :
P1 :
1 x + 2
p2 :
3 2
4 x + 9 x + 5 x + 4
p1 at x = 2 : 4
p2 at x = 2 : 82
Roots of P1 : [-2.]
Roots of P2 : [-1.86738371+0.j -0.19130814+0.70633545j -0.19130814-0.70633545j]
Coefficients of P1 : [1 2]
Coefficients of P2 : [4 9 5 4]
Order / Degree of P1 : 1
Order / Degree of P2 : 3
Code 2 : Basic mathematical operation on polynomial
# Python code explaining# numpy.poly1d() # importing librariesimport numpy as np # Constructing polynomialp1 = np.poly1d([1, 2])p2 = np.poly1d([4, 9, 5, 4]) print ("P1 : ", p1)print ("\n p2 : \n", p2) print ("\n\np1 ^ 2 : \n", p1**2)print ("p2 ^ 2 : \n", np.square(p2)) p3 = np.poly1d([1, 2], variable = 'y')print ("\n\np3 : ", p3) print ("\n\np1 * p2 : \n", p1 * p2)print ("\nMultiplying two polynimials : \n", np.poly1d([1, -1]) * np.poly1d([1, -2])) |
Output :
P1 :
1 x + 2
p2 :
3 2
4 x + 9 x + 5 x + 4
p1 ^ 2 :
2
1 x + 4 x + 4
p2 ^ 2 :
[16 81 25 16]
p3 :
1 y + 2
p1 * p2 :
4 3 2
4 x + 17 x + 23 x + 14 x + 8
Multiplying two polynimials :
2
1 x - 3 x + 2
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