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The Roots function is a placeholder for representing the roots of the univariate polynomial a. The roots are returned as a list of pairs of the form $\[\[r_1,m_1\],...,\[r_n,m_n\]\]$ where $r_k$ is a root and $m_k$ its multiplicity, that is, ${\left(x-r_k\right)}^{m_k}$ divides a.

The call Roots(a) mod n computes the roots of the polynomial a modulo n.

The call Roots(a,K) mod p computes the roots over the finite field defined by K an algebraic extension of the integers mod p where K is a RootOf.

The call modp1(Roots(a), p) computes the roots of the polynomial a in the $\mathrm{modp1}$ representation modulo the prime integer p.

$\mathrm{Roots}\left(x^3-x\right)\mathbf{mod}6$

$\left[\left[0\,1\right]\,\left[1\,1\right]\,\left[2\,1\right]\,\left[3\,1\right]\,\left[4\,1\right]\,\left[5\,1\right]\right]$

$\mathrm{Roots}\left(x^3-1\right)\mathbf{mod}2$

$\left[\left[1\,1\right]\right]$

$\mathrm{alias}\left(\mathrm{\alpha }=\mathrm{RootOf}\left(x^2+x+1\right)\right)\:$

$\mathrm{Roots}\left(x^3-1\,\mathrm{\alpha }\right)\mathbf{mod}2$

$\left[\left[1\,1\right]\,\left[\mathrm{\alpha }+1\,1\right]\,\left[\mathrm{\alpha }\,1\right]\right]$