28.4 Derivatives / Integrals / Transforms ¶

Octave comes with functions for computing the derivative and the integral of a polynomial. The functions polyder and polyint both return new polynomials describing the result. As an example we’ll compute the definite integral of p(x) = x^2 + 1 from 0 to 3.

c = [1, 0, 1];
integral = polyint (c);
area = polyval (integral, 3) - polyval (integral, 0)
⇒ 12

: k = polyder (p) ¶

: k = polyder (a, b) ¶

: [q, d] = polyder (b, a) ¶

Return the coefficients of the derivative of the polynomial whose coefficients are given by the vector p.

If a pair of polynomials is given, return the derivative of the product a*b.

If two inputs and two outputs are given, return the derivative of the polynomial quotient b/a. The quotient numerator is in q and the denominator in d.

See also: polyint, polyval, polyreduce.

: q = polyint (p) ¶

: q = polyint (p, k) ¶

Return the coefficients of the integral of the polynomial whose coefficients are represented by the vector p.

The variable k is the constant of integration, which by default is set to zero.

See also: polyder, polyval.

: g = polyaffine (f, mu) ¶

Return the coefficients of the polynomial vector f after an affine transformation.

If f is the vector representing the polynomial f(x), then g = polyaffine (f, mu) is the vector representing:

g(x) = f( (x - mu(1)) / mu(2) )

See also: polyval, polyfit.