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The Indep function is a placeholder for representing the independence-checking of a RootOf or of a set of RootOfs. It is used in conjunction with evala.

The call evala(Indep(S, 'r')) returns true if the RootOfs in S are independent, or false otherwise. In case relations are found, the name r is assigned the set of relations.

RootOfs representing algebraic numbers (or functions) are said to be independent if the polynomial defining a RootOfR is irreducible over the field generated by the RootOfs which do not contain R.

$\mathrm{alias}\left(\mathrm{r1}=\mathrm{RootOf}\left(x^2-1\right)\right)\:$

$\mathrm{evala}\left(\mathrm{Indep}\left(\mathrm{r1}\,'r'\right)\right)$

$\mathrm{false}$

$r$

$\left\{\mathrm{r1}=\mathrm{-1}\,\mathrm{r1}=1\right\}$

$\mathrm{alias}\left(\mathrm{sqrt2}=\mathrm{RootOf}\left(x^2-2\right)\,\mathrm{sqrt3}=\mathrm{RootOf}\left(x^2-3\right)\,\mathrm{sqrt6}=\mathrm{RootOf}\left(x^2-6\right)\right)\:$

$\mathrm{evala}\left(\mathrm{Indep}\left(\left\{\mathrm{sqrt2}\,\mathrm{sqrt3}\,\mathrm{sqrt6}\right\}\,'r'\right)\right)$

$\mathrm{false}$

$r$

$\left\{\mathrm{sqrt6}=\mathrm{sqrt3}\mathrm{sqrt2}\,\mathrm{sqrt6}=-\mathrm{sqrt3}\mathrm{sqrt2}\right\}$