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The listtoalgeq(l, y(x), [typelist]) command computes a polynomial equation in y and x satisfied by the generating function y(x) of the expressions in l. The generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes .

The seriestoalgeq(s, y(x), [typelist]) command computes a polynomial equation in y and x satisfied by the generating function y(x) of the expressions in s. The generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes .

If typelist contains more than one element, these types are considered in the order that they are listed.

If typelist is not specified, the default typelist, 'ogf','egf', is used. The function returns a list whose first element is the polynomial in y(x) and x that was found. The second element is the generating function type to which the first element corresponds.

In the implementation, the maximal degree of y is 6 and the maximum degree of the coefficients is 3. You can change these degree specifications by modifying the variables gfun['maxdegeqn'] and gfun['maxdegcoeff'] .

If sufficiently many terms are specified and no solution is found, then the generating function does not satisfy any algebraic equation of degree less than or equal to gfun['maxdegeqn'] with coefficients of degree less than or equal to gfun['maxdegcoeff'].

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

$l≔\left[1\,1\,2\,5\,14\,42\,132\,429\,1430\,4862\,16796\,58786\right]\:$

$\mathrm{listtoalgeq}\left(l\,y\left(x\right)\right)$

$\left[-1+y\left(x\right)-x{y\left(x\right)}^2\,\mathrm{ogf}\right]$

$s≔\mathrm{series}\left(1-\mathrm{sqrt}\left(1-4x\right)\,x\,9\right)$

$s≔2x+2x^2+4x^3+10x^4+28x^5+84x^6+264x^7+858x^8+O\left(x^9\right)$

$\mathrm{seriestoalgeq}\left(s\,y\left(x\right)\right)$

$\left[4x-2y\left(x\right)+{y\left(x\right)}^2\,\mathrm{ogf}\right]$