 GaloisGroup - Maple Help

GroupTheory

 GaloisGroup Calling Sequence GaloisGroup( p, x ) Parameters

 p - : polynom : an irreducible polynomial in x over the rationals, or over Q(t1,t2,...,tk), for some indeterminates t1,...,tk. x - : name : an indeterminate Description

 • The GaloisGroup command returns the Galois group of a polynomial p over the field $ℚ$ of rational numbers, or over the rational function field, $ℚ\left({t}_{1},{t}_{1},\dots ,{t}_{k}\right)$ as a permutation group.  Since the polynomial p is required to be irreducible, the resulting permutation group is transitive.
 • The degree of p may be at most 9 in the univariate case, and at most 8 in the multivariate case. Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{GaloisGroup}\left({x}^{5}-x+1,x\right)$
 ${G}{≔}{\mathrm{Gal}}{}\left({{x}}^{{5}}{-}{x}{+}{1}{,}{x}\right)$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${120}$ (2)
 > $\mathrm{IsTransitive}\left(G\right)$
 ${\mathrm{true}}$ (3) Compatibility

 • The GroupTheory[GaloisGroup] command was introduced in Maple 17.