### Navigation

- index
- modules |
- next |
- previous |
- NumPy v1.3 Manual (DRAFT) »
- NumPy Reference »
- Routines »
- Polynomials »

# numpy.poly1d

class `numpy.``poly1d`(c_or_r, r=0, variable=None)

  A one-dimensional polynomial class.

  Parameters: | c_or_r : array_like Polynomial coefficients, in decreasing powers. For example, `(1, 2, 3)` implies . If r is set to True, these coefficients specify the polynomial roots (values where the polynomial evaluate to 0) instead. r : bool, optional If True, c_or_r gives the polynomial roots. Default is False.

  Examples

  Construct the polynomial :

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

  Evaluate the polynomial:

      >>> p(0.5)
      4.25

  Find the roots:

      >>> p.r
      array([-1.+1.41421356j, -1.-1.41421356j])

  Show the coefficients:

      >>> p.c
      array([1, 2, 3])

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

      >>> p.order
      2

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

      >>> p[1]
      2

  Polynomials can be added, substracted, multplied 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])

### Navigation

- index
- modules |
- next |
- previous |
- NumPy v1.3 Manual (DRAFT) »
- NumPy Reference »
- Routines »
- Polynomials »