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genfunc

 rgf_norm
 normalize a rational generating function

 Calling Sequence rgf_norm(Fz, z) rgf_norm(Fz, z, 'factored') rgf_norm(Fz, z, 'factored'(ext))

Parameters

 Fz - rational generating function z - name, generating function variable ext - (optional) algebraic extensions for factor

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{genfunc}\right):$
 > $\mathrm{rgf_norm}\left(\frac{1}{2-3z+{z}^{2}},z\right)$
 $\frac{{1}}{{2}{}\left(\frac{{1}}{{2}}{}{{z}}^{{2}}{-}\frac{{3}}{{2}}{}{z}{+}{1}\right)}$ (1)
 > $\mathrm{rgf_norm}\left(\frac{1}{2-3z+{z}^{2}},z,'\mathrm{factored}'\right)$
 $\frac{{1}}{{2}{}\left({-}{z}{+}{1}\right){}\left({-}\frac{{1}}{{2}}{}{z}{+}{1}\right)}$ (2)
 > $\mathrm{rgf_norm}\left(\frac{1}{5-{z}^{2}},z,'\mathrm{factored}'\left(\sqrt{5}\right)\right)$
 $\frac{{1}}{{5}{}\left({1}{-}\frac{{1}}{{5}}{}{z}{}\sqrt{{5}}\right){}\left({1}{+}\frac{{1}}{{5}}{}{z}{}\sqrt{{5}}\right)}$ (3)