Appendix E: Notation

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	the set of nonnegative integers 0,1,2,3,...
	the set of positive integers 1,2,3,...
	the set of integers...,−2,−1,0,1,2,3,...
	the residue class ring modulo n over the integers (Chapter 5)
ā	the residue class a + n in
a ≈ b	a approximately equal to b
a b	a less than and approximately equal to b
a ← b	assignment of b to a
|a|	absolute value of a
a | b	a divides b without remainder
a ∤ b	a does not divide b
a ≡ b mod n	a is congruent to b modulo n, that is, n | (a − b)
a ≢ b mod n	a is not congruent to b modulo n, that is, n ∤ (a − b)
gcd(a, b)	greatest common divisor of a and b (Section 10.1)
lcm(a, b)	least common multiple of a and b (Section 10.1)
φ(n)	Euler phi function (Section 10.2)
O( )	"Big-Oh." For two real-valued functions f and g with g(x) ≥ 0 one writes f = O(g) and says "f is big-Oh of g" if there exists a constant C such that f (x) ≤ Cg(x) for all x sufficiently large.
	Jacobi symbol (Section 10.4.1)
⌊x⌋	greatest integer less than or equal to x
⌈x⌉	least integer greater than or equal to x
P	the set of computational problems that can be solved in polynomial time
NP	the set of computational problems that can be solved nondeterministically in polynomial time
logbx	logarithm of x to the base b
B	B = 216, the base for the representation of objectsof type CLINT
MAXb	maximal number of digits for a CLINT object to base B
MAX2	maximal number of digits for a CLINT object to base 2
Nmax	largest natural number that can be represented by a CLINT object

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