Mathematics

Module math

Elementary mathematical functions.

e

Euler's number 2.71828...

pi

3.14159...

nan

Not a number.

inf

Infinity.

floor(x)

Round down. Returns floating point numbers.

ceil(x)

Round up. Returns floating point numbers.

sqrt(x)

Square root of x.

exp(x)

Exponential function.

log2(x)

Logarithm to base 2.

ln(x)

Logarithm to base e.

lg(x)

Logarithm to base 10.

lg(x,b)

Logarithm to base b.

sin(x), cos(x), tan(x)

Sine, cosine and tangent.

asin(x), acos(x), atan(x)

Arc sine, arc cosine and arc tangent.

sinh(x), cosh(x), tanh(x)

Hyperbolic sine, hyperbolic cosine and hyperbolic tangent.

asinh(x), acosh(x), atanh(x)

Inverse functions of the hyperbolic functions.

fac(x)

Factorial function. Returns floating point numbers.

gamma(x)

Gamma function.

lgamma(x)

Return ln(abs(gamma(x))).

sgngamma(x)

Return sgn(gamma(x)).

erf(x)

Error function.

hypot(x1,...,xn)

Return sqrt(x1^2+...+xn^2).

atan2(y,x)

Return the phase angle of the coordinate vector [x,y].

expm1(x)

Return exp(x)-1.

ln1p(x)

Return ln(1+x).

isfinite(x)

Return true if x is not infinite and not a NaN.

isnan(x)

Return true if x is a NaN.

isinf(x)

Return true if x is infinite.

frexp(x)

Take x==m*2^n and return [m,n]. The type of m is float, the type of n is int.

ldexp(m,n)

Return m*2^n.

Module cmath

Elementary mathematical functions that can take or return complex numbers.

re(z)

Real part of z.

im(z)

Imaginary part of z.

conj(z)

Complex conjugate.

sqrt(z)

Square root.

exp(z)

Exponential function.

ln(z)

Natural logarithm.

sin(z), cos(z), tan(z)

Sine, cosine and tangent.

sinh(z), cosh(z), tanh(z)

Hyperbolic sine, hyperbolic cosine and hyperbolic tangent.

asinh(z), acosh(z), atanh(z)

Inverse functions of the hyperbolic functions.

gamma(z)

Gamma function.

Module math.rational

Rat

Rational numbers data type.

rat(n,d)

Rational number n/d.

r.n

Numerator.

r.d

Denominator.

Module math.nt

Number theory.

base(n,b)

Transform the number n into positional notation by base b. The result is in little endian (least significant digit first).

base(n,b).rev()

Big endian (least significant digit last) of the positional notation above.

isprime(n)

Deterministic primality test.

isprime(n,e)

Probalistic primality test with false positive probability of less than 1/(4^e).

gcd(a,b)

Greatest common divisor of a and b.

lcm(a,b)

Least common multiple of a and b.

lcm(a)

Least common multiple of the numbers in the iterable a.

factor(n)

Prime factorization of n.

divisors(n)

The list of divisors of n.

phi(n)

Euler's totient function.

lambda(n)

Carmichael function.

Module math.cf

Combinatorical functions.

fac(n)

Factorial function.

rf(n,k)

Raising factorial.

ff(n,k)

Falling factorial.

bc(n,k)

Binomial coefficient.

mc([k1,...,kn])

Multinomial coefficient.

stirling1(n,k)

Stirling number of the first kind.

stirling2(n,k)

Stirling number of the second kind.

euler1(n,k)

Eulerian number.

euler2(n,k)

Eulerien number of the second order.

bell(n)

Bell numbers.

pf(n)

Partition function.

pf(n,k)

Number of partitions of n into exactly k parts.

permutations(a)

Permutations of the list a.

combinations(k,s)

Combinations of set/list/string s into sets of k elements.

partitions(n,k)

Partitions of n into k parts.

Module math.la

vector(a1,...,an)

Return a coordinate vector.

matrix([a11,...,a1n],...,[am1,...,amn])

Return a matrix.

array(N,data)

Return a coordinate tensor of order N. Note that:

array(1,a) = vector.apply(a),
array(2,a) = matrix.apply(a).

diag(a1,...,an)

Return a diagonal matrix.

scalar(a)

Return a scalar matrix.

a.T

Transposed matrix.

a.H

Conjugate transpose.

a.conj

Conjugated complex matrix.

a.tr

Trace.

a.diag

Main diagonal as a coordinate vector.

a.shape

Shape of the array.

a.copy

Shallow copy of the array.

a.list

Convert the array into a list.

a.map(f)

Return (f(a[i,j])).

a[k]

Component of a vector (k=0 upto n-1). Row of a matrix.