AbsoluteValue (x)

Aliases: abs

Absolute value of a number and if x is a complex value the modulus of x. I.e. this the distance of x to the origin. This is equivalent to |x|.

See Wikipedia, Planetmath (absolute value), Planetmath (modulus), Mathworld (absolute value) or Mathworld (complex modulus) for more information.

Chop (x)

Replace very small number with zero.

ComplexConjugate (z)

Aliases: conj Conj

Calculates the complex conjugate of the complex number z. If z is a vector or matrix, all its elements are conjugated.

See Wikipedia for more information.

Denominator (x)

Get the denominator of a rational number.

See Wikipedia for more information.

FractionalPart (x)

Return the fractional part of a number.

See Wikipedia for more information.

Im (z)

Aliases: ImaginaryPart

Get the imaginary part of a complex number. For example Re(3+4i) yields 4.

See Wikipedia for more information.

IntegerQuotient (m,n)

Division without remainder.

IsComplex (num)

Check if argument is a complex (non-real) number. Do note that we really mean nonreal number. That is, IsComplex(3) yields false, while IsComplex(3-1i) yields true.

IsComplexRational (num)

Check if argument is a possibly complex rational number. That is, if both real and imaginary parts are given as rational numbers. Of course rational simply means "not stored as a floating point number."

IsFloat (num)

Check if argument is a real floating point number (non-complex).

IsGaussInteger (num)

Aliases: IsComplexInteger

Check if argument is a possibly complex integer. That is a complex integer is a number of the form n+1i*m where n and m are integers.

IsInteger (num)

Check if argument is an integer (non-complex).

IsNonNegativeInteger (num)

Check if argument is a non-negative real integer. That is, either a positive integer or zero.

IsPositiveInteger (num)

Aliases: IsNaturalNumber

Check if argument is a positive real integer. Note that we accept the convention that 0 is not a natural number.

IsRational (num)

Check if argument is a rational number (non-complex). Of course rational simply means "not stored as a floating point number."

IsReal (num)

Check if argument is a real number.

Numerator (x)

Get the numerator of a rational number.

See Wikipedia for more information.

Re (z)

Aliases: RealPart

Get the real part of a complex number. For example Re(3+4i) yields 3.

See Wikipedia for more information.

Sign (x)

Aliases: sign

Return the sign of a number. That is returns -1 if value is negative, 0 if value is zero and 1 if value is positive. If x is a complex value then Sign returns the direction or 0.

ceil (x)

Aliases: Ceiling

Get the lowest integer more than or equal to n. Examples:

genius> ceil(1.1)
= 2
genius> ceil(-1.1)
= -1

Note that you should be careful and notice that floating point numbers are stored in binary and so may not be what you expect. For example ceil(420/4.2) returns 101 instead of the expected 100. This is because 4.2 is actually very slightly less than 4.2. Use rational representation 42/10 if you want exact arithmetic.

exp (x)

The exponential function. This is the function e^x where e is the base of the natural logarithm.

See Wikipedia or Planetmath or Mathworld for more information.

float (x)

Make number a floating point value. That is returns the floating point representation of the number x.

floor (x)

Aliases: Floor

Get the highest integer less than or equal to n.

ln (x)

The natural logarithm, the logarithm to base e.

See Wikipedia or Planetmath or Mathworld for more information.

log (x)

log (x,b)

Logarithm of x base b (calls DiscreteLog if in modulo mode), if base is not given, e is used.

log10 (x)

Logarithm of x base 10.

log2 (x)

Aliases: lg

Logarithm of x base 2.

max (a,args...)

Aliases: Max Maximum

Returns the maximum of arguments or matrix.

min (a,args...)

Aliases: Min Minimum

Returns the minimum of arguments or matrix.

rand (size...)

Generate random float in the range [0,1). If size is given then a matrix (if two numbers are specified) or vector (if one number is specified) of the given size returned.

randint (max,size...)

Generate random integer in the range [0,max). If size is given then a matrix (if two numbers are specified) or vector (if one number is specified) of the given size returned. For example,

genius> randint(4)
= 3
genius> randint(4,2)
=
[0      1]
genius> randint(4,2,3)
=
[2      2       1
 0      0       3]

round (x)

Aliases: Round

Round a number.

sqrt (x)

Aliases: SquareRoot

The square root. When operating modulo some integer will return either a null or a vector of the square roots. Examples:

genius> sqrt(2)
= 1.41421356237
genius> sqrt(-1)
= 1i
genius> sqrt(4) mod 7
=
[2      5]
genius> 2*2 mod 7
= 4

See Wikipedia or Planetmath for more information.

trunc (x)

Aliases: Truncate IntegerPart

Truncate number to an integer (return the integer part).