Programs by Type

      

Carmichael function car(m)	car [m]
Chinese Remainder Theorem	crt [a1 m1 a2 m2]
convert decimal to rational	d2r [x]
convert rational to decimal	r2d [a q]
determinant modulo m	detmodm
discrete logarithm base g of a modulo p	ind [g a p]
factor n
by trial division	factor [n]
by p - 1 method	p-1 [n [a]]
by rho method	rho [n [c]]
find next prime	getnextp [x]
greatest common divisor	gcd [b c]
index base g of a modulo p	ind [g a p]
Jacobi symbol (P/Q)	jacobi [P Q]
Lucas functions Un, Vn modulo m	lucas [n [a b] m]
multiply residue classes modulo m	mult [a b m]
order of a modulo m	order [a m [c]]
phi function	phi [n]
pi(x)	pi [x]
power ak modulo m	power [a k m]
primitive root of prime p	primroot [p [a]]
prove primality of p	provep [p]
reduce ax2 + bxy + cy2	reduce a b c
represent n as a sum of s k-th powers	sumspwrs [n s k]
roots of
ax = b (mod m)	lincon [a b m]
f(x) = 0 (mod pj)	hensel
P(x) = 0 (mod m)	polysolv
x2 = a (mod p)	sqrtmodp [a p]
Ax = b in integers	simlinde
square root modulo p	sqrtmodp [a p]
strong pseudoprime test of m base a	spsp [[a] m]

Chinese Remainder Theorem	crtdem
determinants modulo m	detdem
discrete logarithm base g of a modulo p	inddem [g a p]
Euclidean algorithm	eualgdelm [b c]
factorization
by p - 1 method	p-1dem
by rho method	rhodem [n]
greatest common divisors	fastgcd, slowgcd
(see also Euclidean algorithm)
heapsort algorithm	hsortdem
index base g of a modulo p	inddem [g a p]
Jacobi symbol (P/Q)	jacobdem [P Q]
linear congruence ax = b (mod m)	lncndem [a b m]
Lucas functions	lucasdem [n [a b] m]
multiplication of residue classes	multdem1, multdem2, multdem3
order of a modulo m	orderdem [a m [c]]
powering algorithm	pwrdem1a [a k m]
	pwrdem1b [a k m]
	pwrdem2 [a k m]
RSA encryption	rsa, rsapars
square root modulo p	sqrtdem [a p]
strong pseudoprime test of m base a	spspdem[[a] m]

arithmetic functions	arfcntab
base conversions for integers	basestab
binary quadratic forms
reduced forms	qformtab
forms equivalent to f(x,y)	reduce
binomial coefficients modulo m	pascalst
class numbers	clanotab
congruential arithmetic	cngartab
discrete logarithms	indtab
factorials modulo m	fctrltab
Farey fractions	fareytab, fractab
greatest common divisors	gcdtab
indices	indtab
intersection of arithmetic progressions	intaptab
Jacobi symbols	jacobtab
least prime factor	factab
linear combinations	lncomtab
Lucas functions	lucastab
Pascal's triangle modulo m	pascalst
order of a modulo m	ordertab
powers of a modulo m	powertab
representations as sums of powers	sumspwrs, wrngtab
roots of
f(x) = 0 (mod pj)	hensel
P(x) = 0 (mod m)	polysolv