ExistsRealQ[ineqs, {x_1, x_2, ...}] tests whether there exist real values of the x_i for which the inequalities and equations ineqs are satisfied.
ForAllRealQ[ineqs, {x_1, x_2, ...}] tests whether for all real values of the x_i the inequalities and equations ineqs are satisfied.
ImpliesQ[expr_1, expr_2] tests whether the expression expr_1 implies expr_2.
ImpliesRealQ[ineqs_1, ineqs_2] tests whether the inequalities and equations ineqs_1 imply the ineqs_2 for all real values of all variables.
ExtensionDegree[f] gives the degree of the extension of the field f over its base field.
FieldIrreducible[f, s] gives the irreducible polynomial in the symbol s associated with the field f.
FromElementCode[f, code] gives the field element of f associated with code, a non-negative integer less than the field size of f.
FunctionOfCode[g] is a setting for the option FormatType that specifies the format g[c] for an element, where c is the integer code for the element.
FunctionOfCoefficients[g] is a setting for the option FormatType that specifies the format g[c_0, c_1, ...] for an element, where c_0, c_1, ... are the coefficients in the ...
PerfectPowerQ[e, n] gives True if e is a perfect n\[Null]^th power in its field, and False otherwise.