numpy.poly1d¶

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

A one-dimensional polynomial class.

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

Parameters:

c_or_r:array_like The polynomial’s coefficients, in decreasing powers, or ifthe value of the second parameter is True, the polynomial’sroots (values where the polynomial evaluates to 0). For example,poly1d([1,2,3]) returns an object that representsx^2 + 2x + 3, whereaspoly1d([1,2,3],True) returnsone that represents(x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6. r:bool, optional If True,c_or_r specifies the polynomial’s roots; the defaultis False. variable:str, optional Changes the variable used when printingp fromx tovariable(see Examples).

Examples

Construct the polynomialx^2 + 2x + 3:

>>>p=np.poly1d([1,2,3])>>>print(np.poly1d(p))   21 x + 2 x + 3

Evaluate the polynomial atx = 0.5:

>>>p(0.5)4.25

Find the roots:

>>>p.rarray([-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:

>>>p.carray([1, 2, 3])

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

>>>p.order2

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

>>>p[1]2

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

>>>p*ppoly1d([ 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 beused in all functions that accept arrays:

>>>p**2# square of polynomialpoly1d([ 1,  4, 10, 12,  9])

>>>np.square(p)# square of individual coefficientsarray([1, 4, 9])

The variable used in the string representation ofp can be modified,using thevariable parameter:

>>>p=np.poly1d([1,2,3],variable='z')>>>print(p)   21 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:

c A copy of the polynomial coefficients coef A copy of the polynomial coefficients coefficients A copy of the polynomial coefficients coeffs A copy of the polynomial coefficients o The order or degree of the polynomial order The order or degree of the polynomial r The roots of the polynomial, where self(x) == 0 roots The roots of the polynomial, where self(x) == 0 variable The name of the polynomial variable

Methods

__call__(val)
deriv([m])	Return a derivative of this polynomial.
integ([m, k])	Return an antiderivative (indefinite integral) of this polynomial.