FindInstance[expr, vars] finds an instance of vars that makes the statement expr be True. FindInstance[expr, vars, dom] finds an instance over the domain dom. Common choices ...
RealExponent[x] gives log_10 (|x|).RealExponent[x, b] gives log_b (|x|).
GF
(Finite Fields Package Symbol) GF[p, d] gives the Galois field that is a degree d extension of the prime field of p elements.GF[q] gives the Galois field with q elements, for q a prime power.GF[p, ilist] ...
AlgebraicNumberTrace[a] gives the trace of the algebraic number a.
Contexts[] gives a list of all contexts. Contexts["string"] gives a list of the contexts that match the string.
Positive[x] gives True if x is a positive number.
RootSum
(Built-in Mathematica Symbol) RootSum[f, form] represents the sum of form[x] for all x that satisfy the polynomial equation f[x] == 0.
Cancel
(Built-in Mathematica Symbol) Cancel[expr] cancels out common factors in the numerator and denominator of expr.
LogicalExpand[expr] expands out logical combinations of equations, inequalities, and other functions.
Reals
(Built-in Mathematica Symbol) Reals represents the domain of real numbers, as in x \[Element] Reals.