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genpoly computes the unique polynomial $a\left(x\right)$ over $\mathbb{Z}\left[x\right]$ from the integer n with coefficients less than $\frac{b}{2}$ in magnitude such that $\mathrm{subs}\left(x=b\,a\left(x\right)\right)=n$.

This is directly related to b-adic expansion of an integer. If the base-b representation of the integer n is $c_0+c_{1}b+\cdots +c_k{b}^k$ where $c_i$ are integers modulo b (using symmetric representation) then the polynomial generated is $c_0+c_{1}x+\cdots +c_k{x}^k$.

If n is a polynomial with integer coefficients then each integer coefficient is expanded into a polynomial. This polynomial, n, must be in fully expanded form.

The genpoly command is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe .

$\mathrm{genpoly}\left(11\,5\,x\right)$

$1+2x$

$\mathrm{genpoly}\left(11y^2-13y+21\,5\,x\right)$

$\left(1+2x\right)y^2+\left(-x^2+2x+2\right)y+x^2-x+1$