- AbsoluteValue
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
Chop (x)

Replace very small number with zero.

- ComplexConjugate
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
Denominator (x)

Get the denominator of a rational number.

See Wikipedia for more information.

- FractionalPart
FractionalPart (x)

Return the fractional part of a number.

See Wikipedia for more information.

- Im
Im (z)

Aliases:

`ImaginaryPart`

Get the imaginary part of a complex number. For example

yields 4.`Re(3+4i)`

See Wikipedia for more information.

- IntegerQuotient
IntegerQuotient (m,n)

Division without remainder.

- IsComplex
IsComplex (num)

Check if argument is a complex (non-real) number. Do note that we really mean nonreal number. That is,

yields false, while`IsComplex(3)`

yields true.`IsComplex(3-1i)`

- IsComplexRational
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
IsFloat (num)

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

- IsGaussInteger
IsGaussInteger (num)

Aliases:

`IsComplexInteger`

Check if argument is a possibly complex integer. That is a complex integer is a number of the form

where`n+1i*m`

`n`

and`m`

are integers.- IsInteger
IsInteger (num)

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

- IsNonNegativeInteger
IsNonNegativeInteger (num)

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

- IsPositiveInteger
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
IsRational (num)

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

- IsReal
IsReal (num)

Check if argument is a real number.

- Numerator
Numerator (x)

Get the numerator of a rational number.

See Wikipedia for more information.

- Re
Re (z)

Aliases:

`RealPart`

Get the real part of a complex number. For example

yields 3.`Re(3+4i)`

See Wikipedia for more information.

- Sign
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
ceil (x)

Aliases:

`Ceiling`

Get the lowest integer more than or equal to

`n`

. Examples:`genius>`

= 2`ceil(1.1)`

`genius>`

= -1`ceil(-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

returns 101 instead of the expected 100. This is because 4.2 is actually very slightly less than 4.2. Use rational representation`ceil(420/4.2)`

if you want exact arithmetic.`42/10`

- exp
exp (x)

The exponential function. This is the function

where`e^x`

`e`

is the base of the natural logarithm.See Wikipedia or Planetmath or Mathworld for more information.

- float
float (x)

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

`x`

.- floor
floor (x)

Aliases:

`Floor`

Get the highest integer less than or equal to

`n`

.- ln
ln (x)

The natural logarithm, the logarithm to base

`e`

.See Wikipedia or Planetmath or Mathworld for more information.

- log
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
log10 (x)

Logarithm of

`x`

base 10.- log2
log2 (x)

Aliases:

`lg`

Logarithm of

`x`

base 2.- max
max (a,args...)

Aliases:

`Max`

`Maximum`

Returns the maximum of arguments or matrix.

- min
min (a,args...)

Aliases:

`Min`

`Minimum`

Returns the minimum of arguments or matrix.

- rand
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
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>`

= 3`randint(4)`

`genius>`

= [0 1]`randint(4,2)`

`genius>`

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

- round
round (x)

Aliases:

`Round`

Round a number.

- sqrt
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>`

= 1.41421356237`sqrt(2)`

`genius>`

= 1i`sqrt(-1)`

`genius>`

= [2 5]`sqrt(4) mod 7`

`genius>`

= 4`2*2 mod 7`

See Wikipedia or Planetmath for more information.

- trunc
trunc (x)

Aliases:

`Truncate`

`IntegerPart`

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