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numpy.polyint(p, m=1, k=None)
[source] -
Return an antiderivative (indefinite integral) of a polynomial.
The returned order
m
antiderivativeP
of polynomialp
satisfies and is defined up tom - 1
integration constantsk
. The constants determine the low-order polynomial partof
P
so that .Parameters: p : array_like or poly1d
Polynomial to differentiate. 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, optionalIntegration 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. Ifm = 1
, a single scalar can be given instead of a list.See also
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polyder
- derivative of a polynomial
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poly1d.integ
- equivalent method
Examples
The defining property of the antiderivative:
>>> p = np.poly1d([1,1,1]) >>> P = np.polyint(p) >>> P poly1d([ 0.33333333, 0.5 , 1. , 0. ]) >>> np.polyder(P) == p True
The integration constants default to zero, but can be specified:
>>> P = np.polyint(p, 3) >>> P(0) 0.0 >>> np.polyder(P)(0) 0.0 >>> np.polyder(P, 2)(0) 0.0 >>> P = np.polyint(p, 3, k=[6,5,3]) >>> P 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) 6.0 >>> np.polyder(P, 1)(0) 5.0 >>> P(0) 3.0
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numpy.polyint()
2017-01-10 18:16:32
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