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Indep

inert independence checking

 Calling Sequence Indep(S, 'r')

Parameters

 S - RootOf or set of RootOfs r - (optional) name

Description

 • 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 RootOf R is irreducible over the field generated by the RootOfs which do not contain R.

Examples

 > $\mathrm{alias}\left(\mathrm{r1}=\mathrm{RootOf}\left({x}^{2}-1\right)\right):$
 > $\mathrm{evala}\left(\mathrm{Indep}\left(\mathrm{r1},'r'\right)\right)$
 ${\mathrm{false}}$ (1)
 > $r$
 $\left\{{\mathrm{r1}}{=}{-1}{,}{\mathrm{r1}}{=}{1}\right\}$ (2)
 > $\mathrm{alias}\left(\mathrm{sqrt2}=\mathrm{RootOf}\left({x}^{2}-2\right),\mathrm{sqrt3}=\mathrm{RootOf}\left({x}^{2}-3\right),\mathrm{sqrt6}=\mathrm{RootOf}\left({x}^{2}-6\right)\right):$
 > $\mathrm{evala}\left(\mathrm{Indep}\left(\left\{\mathrm{sqrt2},\mathrm{sqrt3},\mathrm{sqrt6}\right\},'r'\right)\right)$
 ${\mathrm{false}}$ (3)
 > $r$
 $\left\{{\mathrm{sqrt6}}{=}{\mathrm{sqrt3}}{}{\mathrm{sqrt2}}{,}{\mathrm{sqrt6}}{=}{-}{\mathrm{sqrt3}}{}{\mathrm{sqrt2}}\right\}$ (4)