Numeric

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.

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.

See Wikipedia for more information.

IntegerQuotient (m,n)

Division without remainder.

IsComplex (num)

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

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 floating point number (non-complex).

IsGaussInteger (num)

Aliases: IsComplexInteger

Check if argument is a possibly complex integer.

IsInteger (num)

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

IsNonNegativeInteger (num)

Check if argument is a non-negative real integer.

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.

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 an 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.

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 Planetmath for more information.

trunc (x)

Aliases: Truncate IntegerPart

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