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 |