numpy.poly1d — NumPy v1.13 Manual (original) (raw)

class numpy. poly1d(c_or_r, r=False, variable=None)[source]¶

A one-dimensional polynomial class.

A convenience class, used to encapsulate “natural” operations on polynomials so that said operations may take on their customary form in code (see Examples).

Parameters:

c_or_r : array_like The polynomial’s coefficients, in decreasing powers, or if the value of the second parameter is True, the polynomial’s roots (values where the polynomial evaluates to 0). For example,poly1d([1, 2, 3]) returns an object that represents, whereas poly1d([1, 2, 3], True) returns one that represents . r : bool, optional If True, c_or_r specifies the polynomial’s roots; the default is False. variable : str, optional Changes the variable used when printing p from x to variable(see Examples).

Examples

Construct the polynomial :

p = np.poly1d([1, 2, 3]) print(np.poly1d(p)) 2 1 x + 2 x + 3

Evaluate the polynomial at :

Find the roots:

p.r array([-1.+1.41421356j, -1.-1.41421356j]) p(p.r) array([ -4.44089210e-16+0.j, -4.44089210e-16+0.j])

These numbers in the previous line represent (0, 0) to machine precision

Show the coefficients:

Display the order (the leading zero-coefficients are removed):

Show the coefficient of the k-th power in the polynomial (which is equivalent to p.c[-(i+1)]):

Polynomials can be added, subtracted, multiplied, and divided (returns quotient and remainder):

p * p poly1d([ 1, 4, 10, 12, 9])

(p**3 + 4) / p (poly1d([ 1., 4., 10., 12., 9.]), poly1d([ 4.]))

asarray(p) gives the coefficient array, so polynomials can be used in all functions that accept arrays:

p**2 # square of polynomial poly1d([ 1, 4, 10, 12, 9])

np.square(p) # square of individual coefficients array([1, 4, 9])

The variable used in the string representation of p can be modified, using the variable parameter:

p = np.poly1d([1,2,3], variable='z') print(p) 2 1 z + 2 z + 3

Construct a polynomial from its roots:

np.poly1d([1, 2], True) poly1d([ 1, -3, 2])

This is the same polynomial as obtained by:

np.poly1d([1, -1]) * np.poly1d([1, -2]) poly1d([ 1, -3, 2])

Attributes

Methods