Primitive - Maple Programming Help

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Primitive

test whether a polynomial is primitive mod p

 Calling Sequence Primitive(a) mod p

Parameters

 a - univariate polynomial p - prime integer

Description

 • The Primitive(a) mod p command returns true if the univariate polynomial a over the integers mod p is "primitive", and false otherwise.
 • If $a$ is an irreducible polynomial in ${ℤ}_{p}\left[x\right]$ of degree $k$, then it is primitive if $x$ is a primitive element in the finite field${ℤ}_{p}\left[x\right]/\left(a\right)$ Thus, ${x}^{i}$, for $i=1..{p}^{k}-1$ is the set of all non-zero elements in the field.

Examples

 > $\mathrm{Primitive}\left({x}^{4}+x+1\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}2$
 ${\mathrm{true}}$ (1)
 > $\mathrm{Primitive}\left({x}^{4}+{x}^{3}+{x}^{2}+x+1\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}2$
 ${\mathrm{false}}$ (2)