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GroupTheory

  

GaloisGroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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  of rational numbers, or over the rational function field, t1,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.

Examples

withGroupTheory:

GGaloisGroupx5x+1,x

G:=Galx5x+1,x

(1)

GroupOrderG

120

(2)

IsTransitiveG

true

(3)

Compatibility

• 

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

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

galois

GroupTheory[GroupOrder]

GroupTheory[IsTransitive]

GroupTheory[PermutationGroup]

 


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