GaloisGroup( p, x )
: polynom : an irreducible polynomial in x over the rationals, or over Q(t1,t2,...,tk), for some indeterminates t1,...,tk.
: name : an indeterminate
The GaloisGroup command returns the Galois group of a polynomial p over the field ℚ of rational numbers, or over the rational function field, ℚt1,t1,…,tk 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.
G ≔ GaloisGroup⁡x5−x+1,x
The GroupTheory[GaloisGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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