The algfuntoalgeq(expr, y(z)) command returns a polynomial in y and z that has expr as a root. The polynomial is not necessarily minimal.

If ini is specified, it is assigned a set of initial conditions for the polynomial to specify which branch is indicated (if possible).

If typ is specified as 'rational', the coefficients of the polynomial are of type rational or type name. This is particularly useful for finding a polynomial for an algebraic number.  The default is 'rational'.

If typ is specified as 'algebraic' the coefficients are algebraic numbers. This option can be used with algebraicsubs.

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

$\mathrm{algfuntoalgeq}\left(a\mathrm{RootOf}\left({\mathrm{\_Z}}^5+1\right)x^{\frac{2}{3}}\,y\left(x\right)\right)$

$a^{15}{x}^{10}+y^{15}$

$\mathrm{algfuntoalgeq}\left(a\mathrm{RootOf}\left({\mathrm{\_Z}}^5+1\right)x^{\frac{2}{3}}\,y\left(x\right)\,'\mathrm{algebraic}'\right)$

${\mathrm{RootOf}\left({\mathrm{\_Z}}^5+1\right)}^3{a}^3{x}^2-y^3$

$\mathrm{algfuntoalgeq}\left(5^{\frac{1}{3}}+37^{\frac{2}{3}}\,y\left(x\right)\right)$

$y^9-3984y^6+5112147y^3-2342039552$

$\mathrm{algfuntoalgeq}\left(1+\mathrm{RootOf}\left({\mathrm{\_Z}}^3+1\right)x\,y\left(x\right)\,\mathrm{ini}\right)$

$-x^3-y^3+3y^2-3y+1$

$\mathrm{ini}$

$\left\{y\left(0\right)=1\,\mathrm{D}\left(y\right)\left(0\right)=\mathrm{RootOf}\left({\mathrm{\_Z}}^3+1\right)\,{\mathrm{D}}^{\left(2\right)}\left(y\right)\left(0\right)=0\right\}$