Name

Function

inverse(z)

returns 1/z

pow(a, b)

exponentiation a^b

abs(z)

absolute value

real(z)

real part

imag(z)

imaginary part

csgn(z)

complex sign (returns an int)

step(x)

step function (returns an numeric)

numer(z)

numerator of rational or complex rational number

denom(z)

denominator of rational or complex rational number

sqrt(z)

square root

isqrt(n)

integer square root

sin(z)

sine

cos(z)

cosine

tan(z)

tangent

asin(z)

inverse sine

acos(z)

inverse cosine

atan(z)

inverse tangent

atan(y, x)

inverse tangent with two arguments

sinh(z)

hyperbolic sine

cosh(z)

hyperbolic cosine

tanh(z)

hyperbolic tangent

asinh(z)

inverse hyperbolic sine

acosh(z)

inverse hyperbolic cosine

atanh(z)

inverse hyperbolic tangent

exp(z)

exponential function

log(z)

natural logarithm

Li2(z)

dilogarithm

zeta(z)

Riemann's zeta function

tgamma(z)

gamma function

lgamma(z)

logarithm of gamma function

psi(z)

psi (digamma) function

psi(n, z)

derivatives of psi function (polygamma functions)

factorial(n)

factorial function n!

doublefactorial(n)

double factorial function n!!

binomial(n, k)

binomial coefficients

bernoulli(n)

Bernoulli numbers

fibonacci(n)

Fibonacci numbers

mod(a, b)

modulus in positive representation (in the range [0, abs(b)-1] with the sign of b, or zero)

smod(a, b)

modulus in symmetric representation (in the range [-iquo(abs(b)-1, 2), iquo(abs(b), 2)])

irem(a, b)

integer remainder (has the sign of a, or is zero)

irem(a, b, q)

integer remainder and quotient, irem(a, b, q) == a-q*b

iquo(a, b)

integer quotient

iquo(a, b, r)

integer quotient and remainder, r == a-iquo(a, b)*b

gcd(a, b)

greatest common divisor

lcm(a, b)

least common multiple