Complex(3o) OCaml library Complex(3o)NAME
Complex - Complex numbers.
Module
Module Complex
Documentation
Module Complex
: sig end
Complex numbers.
This module provides arithmetic operations on complex numbers. Complex numbers are represented by their real and imaginary parts (carte-
sian representation). Each part is represented by a double-precision floating-point number (type float ).
type t = {
re : float ;
im : float ;
}
The type of complex numbers. re is the real part and im the imaginary part.
val zero : t
The complex number 0 .
val one : t
The complex number 1 .
val i : t
The complex number i .
val neg : t -> t
Unary negation.
val conj : t -> t
Conjugate: given the complex x + i.y , returns x - i.y .
val add : t -> t -> t
Addition
val sub : t -> t -> t
Subtraction
val mul : t -> t -> t
Multiplication
val inv : t -> t
Multiplicative inverse ( 1/z ).
val div : t -> t -> t
Division
val sqrt : t -> t
Square root. The result x + i.y is such that x > 0 or x = 0 and y >= 0 . This function has a discontinuity along the negative real axis.
val norm2 : t -> float
Norm squared: given x + i.y , returns x^2 + y^2 .
val norm : t -> float
Norm: given x + i.y , returns sqrt(x^2 + y^2) .
val arg : t -> float
Argument. The argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through
zero and the number. This angle ranges from -pi to pi . This function has a discontinuity along the negative real axis.
val polar : float -> float -> t
polar norm arg returns the complex having norm norm and argument arg .
val exp : t -> t
Exponentiation. exp z returns e to the z power.
val log : t -> t
Natural logarithm (in base e ).
val pow : t -> t -> t
Power function. pow z1 z2 returns z1 to the z2 power.
OCamldoc 2012-06-26 Complex(3o)
Check Out this Related Man Page
Num(3o) OCaml library Num(3o)NAME
Num - Operation on arbitrary-precision numbers.
Module
Module Num
Documentation
Module Num
: sig end
Operation on arbitrary-precision numbers.
Numbers (type num ) are arbitrary-precision rational numbers, plus the special elements 1/0 (infinity) and 0/0 (undefined).
type num =
| Int of int
| Big_int of Big_int.big_int
| Ratio of Ratio.ratio
The type of numbers.
=== Arithmetic operations ===
val (+/) : num -> num -> num
Same as Num.add_num .
val add_num : num -> num -> num
Addition
val minus_num : num -> num
Unary negation.
val (-/) : num -> num -> num
Same as Num.sub_num .
val sub_num : num -> num -> num
Subtraction
val ( */ ) : num -> num -> num
Same as Num.mult_num .
val mult_num : num -> num -> num
Multiplication
val square_num : num -> num
Squaring
val (//) : num -> num -> num
Same as Num.div_num .
val div_num : num -> num -> num
Division
val quo_num : num -> num -> num
Euclidean division: quotient.
val mod_num : num -> num -> num
Euclidean division: remainder.
val ( **/ ) : num -> num -> num
Same as Num.power_num .
val power_num : num -> num -> num
Exponentiation
val abs_num : num -> num
Absolute value.
val succ_num : num -> num
succ n is n+1
val pred_num : num -> num
pred n is n-1
val incr_num : num Pervasives.ref -> unit
incr r is r:=!r+1 , where r is a reference to a number.
val decr_num : num Pervasives.ref -> unit
decr r is r:=!r-1 , where r is a reference to a number.
val is_integer_num : num -> bool
Test if a number is an integer
=== The four following functions approximate a number by an integer : ===
val integer_num : num -> num
integer_num n returns the integer closest to n . In case of ties, rounds towards zero.
val floor_num : num -> num
floor_num n returns the largest integer smaller or equal to n .
val round_num : num -> num
round_num n returns the integer closest to n . In case of ties, rounds off zero.
val ceiling_num : num -> num
ceiling_num n returns the smallest integer bigger or equal to n .
val sign_num : num -> int
Return -1 , 0 or 1 according to the sign of the argument.
=== Comparisons between numbers ===
val (=/) : num -> num -> bool
val (</) : num -> num -> bool
val (>/) : num -> num -> bool
val (<=/) : num -> num -> bool
val (>=/) : num -> num -> bool
val (<>/) : num -> num -> bool
val eq_num : num -> num -> bool
val lt_num : num -> num -> bool
val le_num : num -> num -> bool
val gt_num : num -> num -> bool
val ge_num : num -> num -> bool
val compare_num : num -> num -> int
Return -1 , 0 or 1 if the first argument is less than, equal to, or greater than the second argument.
val max_num : num -> num -> num
Return the greater of the two arguments.
val min_num : num -> num -> num
Return the smaller of the two arguments.
=== Coercions with strings ===
val string_of_num : num -> string
Convert a number to a string, using fractional notation.
val approx_num_fix : int -> num -> string
See Num.approx_num_exp .
val approx_num_exp : int -> num -> string
Approximate a number by a decimal. The first argument is the required precision. The second argument is the number to approximate.
Num.approx_num_fix uses decimal notation; the first argument is the number of digits after the decimal point. approx_num_exp uses scien-
tific (exponential) notation; the first argument is the number of digits in the mantissa.
val num_of_string : string -> num
Convert a string to a number.
=== Coercions between numerical types ===
val int_of_num : num -> int
val num_of_int : int -> num
val nat_of_num : num -> Nat.nat
val num_of_nat : Nat.nat -> num
val num_of_big_int : Big_int.big_int -> num
val big_int_of_num : num -> Big_int.big_int
val ratio_of_num : num -> Ratio.ratio
val num_of_ratio : Ratio.ratio -> num
val float_of_num : num -> float
OCamldoc 2012-06-26 Num(3o)