AbsoluteValue (x)
Aliases: abs
Absolute value of a number and if x is
a complex value the modulus of x.
See Planetmath (absolute value), Planetmath (modulus), Mathworld (absolute value) or Mathworld (complex modulus) for more information.
Chop (x)
Replace very small number with zero
ComplexConjugate (M)
Aliases: conj Conj
Calculates the conjugate
Denominator (x)
Get the denominator of a rational number
FractionalPart (x)
Return the fractional part of a number
Im (z)
Aliases: ImaginaryPart
Get the imaginary part of a complex number
IntegerQuotient (m,n)
Division w/o remainder
IsComplex (num)
Check if argument is a complex (non-real) number
IsComplexRational (num)
Check if argument is a possibly complex rational 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
IsGaussianInteger (z)
Check if argument is a gaussian 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)
IsReal (num)
Check if argument is a real number
Numerator (x)
Get the numerator of a rational number
Re (z)
Aliases: RealPart
Get the real part of a complex number
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
exp (x)
The exponential function. This is the function
e^x where e
is the base of the natural
logarithm.
See 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,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)