add, subtract, multiply a and b | a+b, a-b, a*b |
integer quotient when a is divided by b | a\b |
integer remainder when a is divided by b (i.e. a mod b) | a%b |
a raised to the power b (see powermod below) | a^b |
assign a the value b | a=b |
compare a to b | a<b, a>b, a<=b, a!=b a==b |
a `and' b, a `or' b, `not' a | a &&b, a||b, !a |
convert a to an element of Z_{n} | Mod(a,n) |
convert an element x of Z_{n} to an integer (see note) | lift(x) |
binary expansion of a | binary(a) |
n^{th} bit of a | bittest(a,n) |
random integer between 0 and n-1 | random(n) |
highest power of p dividing a | valuation(a,p) |
greatest common divisor of a and b | gcd(a,b) and bezout(a,b) |
chinese remainder theorem applied to x and y (note) | chinese(x,y) |
φ(n) | eulerphi(n) |
factor the integer a | factorint(a) |
is p a prime integer? | isprime(p) |
first prime larger or smaller than a | nextprime(a), precprime(a) |
n^{th} prime number | prime(n) |
discrete log of x to the base g (note) | znlog(x,g) |
multiplicative order of x in Z_{n} | znorder(x) |
find a primitive root modulo p | znprimroot(p) |
Legendre symbol of a over b | kronecker(a,b) |
define an elliptic curve E | E=ellinit([0,0,0,a,b]) |
add/subtract z and w on elliptic curve E | elladd(E,z,w) ellsub(E,z,w) |
multiply z by k on elliptic curve E | ellpow(E,z,k) |
quit gp | \q or quit |