The command rgf_norm(Fz, z) puts the generating function in normal form, expands the numerator and denominator, and factors the low order coefficient from the denominator.

If the optional 'factored' argument is used, the function factor is applied to the denominator.

The algebraic extensions ext may be a single extension, an expression sequence of extensions, or a set of extensions to be used when factoring the denominator.

The command with(genfunc,rgf_norm) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{genfunc}\right)\:$

$\mathrm{rgf\_norm}\left(\frac{1}{2-3z+z^2}\,z\right)$

$\frac{1}{2\left(\frac{1}{2}{z}^2-\frac{3}{2}z+1\right)}$

$\mathrm{rgf\_norm}\left(\frac{1}{2-3z+z^2}\,z\,'\mathrm{factored}'\right)$

$\frac{1}{2\left(1-z\right)\left(-\frac{z}{2}+1\right)}$

$\mathrm{rgf\_norm}\left(\frac{1}{5-z^2}\,z\,'\mathrm{factored}'\left(\mathrm{sqrt}\left(5\right)\right)\right)$

$\frac{1}{5\left(1-\frac{\sqrt{5}z}{5}\right)\left(1+\frac{\sqrt{5}z}{5}\right)}$