polyint

Arguments

P, Q

arrays (from scalars to hypermatrices) of polynomials with real or complex coefficients, of same size.

Const

Set of real or complex constants of integration. length(Const) sets the number of consecutive integrations to perform. By default, 0 is used. Const can be one of the following:

• a scalar: then only the first antiderivatives are computed, and all use the same Const value.
• an array of size size(P): then only the first antiderivatives are computed, with the respective Const(i) for Q(i).
• a list that can mix scalars, arrays of size size(P), or undefined elements. Then Const(i) is used for the i^th antiderivatives. Undefined elements are equivalent to 0.

Description

polyint(..) computes the first or any n^th antiderivative of each polynomial of the input array.

Examples

Single integration (first order):

s = %s;
P = [-2, s ; s^2-3, s-2*s^3]
polyint(P)
polyint(P, 1)
polyint(P, [1 2 ; 3 4])

--> P = [-2, s ; s^2-3, s-2*s^3]
 P  =
  -2      s
  -3 +s²  s -2s³

--> polyint(P)
 ans  =
  -2s               0.5s²
  -3s +0.3333333s³  0.5s² -0.5s⁴

--> polyint(P, 1)
 ans  =
  1 -2s               1 +0.5s²
  1 -3s +0.3333333s³  1 +0.5s² -0.5s⁴

--> polyint(P, [1 2 ; 3 4])
 ans  =
  1 -2s               2 +0.5s²
  3 -3s +0.3333333s³  4 +0.5s² -0.5s⁴

Multiple integrations:

s = %s;
polyint(1-3*s, list(-1,1))
P = [3 ; 1-s ; 6*s^2-2]
polyint(P, list(2, [-2 1 0]))
polyint(P, list(, [-2 1 0]))

k = list(); k(5) = 0;
polyint(1+0*s, k)
1 / factorial(5)

--> polyint(1-3*s, list(-1,1))
 ans  =
  1 -s +0.5s² -0.5s³

--> P = [3 ; 1-s ; 6*s^2-2]
 P  =
  3
  1 -s
  -2 +6s²

--> polyint(P, list(2, [-2 1 0]))
 ans  =
  -2 +2s +1.5s²
  1 +2s +0.5s² -0.1666667s³
  2s -s² +0.5s⁴

--> polyint(P, list(, [-2 1 0]))
 ans  =
  -2 +1.5s²
  1 +0.5s² -0.1666667s³
  -s² +0.5s⁴


--> k = list(); k(5) = 0;
--> polyint(1+0*s, k)
 ans  =
  0.0083333s⁵

--> 1 / factorial(5)
 ans  =
   0.0083333

See also

• derivat — derivative of polynomials or of rationals

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