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 KASH3 Reference Manual
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Function

IsNormal ( elt-fld^fin x, fld^fin E ) -> elt-alg^boo

Description

True iff the element x of the finite field F generates a normal basis over the subfield E of F, i.e. the conjugates of x w.r.t. E (x, x^q, ..., x^(q^(n - 1)) where q is the cardinality of E and n the degree of F over E) form a basis for F over E.

Examples

x_gf5 := FiniteField(5);; x_3 := Element(x_gf5,3);; IsNormal(x_3,x_gf5);
x_gf25 := FiniteField(25);; x_5 := Element(x_gf25,5);; IsNormal(x_5,x_gf25);
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