`numpy:polyint`

source: /dev/numpy/build-install/usr/lib/python3.14/site-packages/numpy/lib/_polynomial_impl.py:267

Signature

def polyint(p, m = 1, k = None)

Summary

Return an antiderivative (indefinite integral) of a polynomial.

Extended Summary

The returned order m antiderivative P of polynomial p satisfies $\frac{d ^{m}}{d x ^{m}} P (x) = p (x)$ and is defined up to m - 1 integration constants k. The constants determine the low-order polynomial part

\frac{k _{m - 1}}{0 !} x^{0} + \dots + \frac{k _{0}}{( m - 1 )!} x^{m - 1}

of P so that $P^{(j)} (0) = k_{m - j - 1}$ .

Parameters

p : array_like or poly1d

Polynomial to integrate. A sequence is interpreted as polynomial coefficients, see poly1d.

m : int, optional

Order of the antiderivative. (Default: 1)

k : list of `m` scalars or scalar, optional

Integration constants. They are given in the order of integration: those corresponding to highest-order terms come first.

If None (default), all constants are assumed to be zero. If m = 1, a single scalar can be given instead of a list.

Examples

The defining property of the antiderivative:

import numpy as np

✓

p = np.poly1d([1,1,1])
P = np.polyint(p)

✓

P
np.polyder(P) == p

✗

np.True_

The integration constants default to zero, but can be specified:

P = np.polyint(p, 3)

✓

P(0)
np.polyder(P)(0)
np.polyder(P, 2)(0)

✗

np.float64(0.0)

P = np.polyint(p, 3, k=[6,5,3])

✓

✗

poly1d([0.01666667, 0.04166667, 0.16666667, 3.        , 5.        , 3.        ])

Note that 3 = 6 / 2!, and that the constants are given in the order of integrations. Constant of the highest-order polynomial term comes first:

np.polyder(P, 2)(0)
np.polyder(P, 1)(0)
P(0)

✗

np.float64(3.0)

Aliases

numpy.polyint

Signature

Summary

Extended Summary

Parameters

Examples

See also

Aliases