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{Complex|_numbers}



CLASS {Complex|_numbers}
,
OPERATORS, TESTED(99):



 Class to work with complex numbers in very near to its natural mathimatical
 form (e.i. such type variables can be used in expressions like usual numeric
 operands, and combined with usual mathimatical operations like +, -, *, /).
 But functions using operations with complex operands, should be marked with
 the modifiers OPERATORS({Complex}).





IMPORT : 
{Mathematics}
 .











STRUCTURE 
{complex|_number}

      REAL Re|al_part

      REAL Im|aginable
 .






 The complex number instance type.










FUNCTION 
To_complex|_from_REAL_or_INT

(

     REAL 
X|_parameter
)
 ==> {complex} 






 Getting a complex number from a real or integer.










FUNCTION 
Complex|_from_Re_Im

(

     REAL 
Re|al_part
, 

     REAL 
Im|agine_part
)
 ==> {complex} 






 Creating a complex number from a real and imagine parts represented by REAL
 numbers.










FUNCTION 
Complement|_to_complex

(

     {complex} 
X|_original_value
)
 ==> {complex} 






 Complementary value for a complex number: Re' = Re, Im' = -Im










FUNCTION 
Cmod|ule_of_complex_number

(

     {complex} 
X|_argument
)
 ==> REAL 






 A module of a complex number (a square root from a sum of squares of
 components).










FUNCTION 
Carg|ument_of_complex

(

     {complex} 
X|_parameter
)
 ==> REAL 






 An argument of a complex number (in radians).










FUNCTION 
I|_imagine_one

 ==> {complex} 






 Imagine one (mathematical i). It is possible to write: 5 + 3 * I to represent
 the number 5+3i, for example.










FUNCTION 
C_from_mod_arg

(

     REAL 
R|_module
, 

     REAL 
Arg|ument
)
 ==> {complex} 






 Creating a complex number from its module and argument.










FUNCTION 
Csame|_complex_number

(

     {complex} 
A|_argument
, 

     {complex} 
B|_argument
)
 ==> BOOL 






 Comparing two complex numbers for an equality. Returns TRUE if these are very
 near.






----------------------------------------------------------------------- '+'






OPERATOR {complex} + {complex}
 ==> {complex} 






 Adding two complex numbers.







OPERATOR {complex} + REAL
 ==> {complex} 
 , OPERATORS






 Adding a complex and a real (or integer still it can be converted to a real
 implicitly) number.







OPERATOR REAL + {complex}
 ==> {complex} 
 , OPERATORS






 Addign a real and a complex numbers.






----------------------------------------------------------------------- '-'






OPERATOR - {complex}
 ==> {complex} 






 Negate of a complex number.







OPERATOR {complex} - {complex}
 ==> {complex} 
 , OPERATORS






 Subtracting one complex number from another complex number.







OPERATOR {complex} - REAL
 ==> {complex} 
 , OPERATORS






 Subtracting a real number from a complex number.







OPERATOR REAL - {complex}
 ==> {complex} 
 , OPERATORS






 Subtracting a complex number from a real number.






----------------------------------------------------------------------- '*'






OPERATOR {complex} * {complex}
 ==> {complex} 






 Multiplying of two complex numbers.







OPERATOR {complex} * REAL
 ==> {complex} 
 , OPERATORS






 Multiplying of a complex and a real numbers.







OPERATOR REAL * {complex}
 ==> {complex} 
 , OPERATORS






 Multiplying of a real and a complex numberrs.










FUNCTION 
Cmul_i|_multimply_by_i

(

     {complex} 
X|_parameter
)
 ==> {complex} 






 Multiplying a complex value by i (imaginary one).






----------------------------------------------------------------------- '/'






OPERATOR {complex} / REAL
 ==> {complex} 
 , OPERATORS






 Dividing a complex number by a real divider.







OPERATOR {complex} / {complex}
 ==> {complex} 
 , OPERATORS






 Dividing one complex number by another complex number.







OPERATOR REAL / {complex}
 ==> {complex} 
 , OPERATORS






 Dividing a real number by a complex divider.






------------------------------------------------------------ 'exponent, ln'









FUNCTION 
Cexp|onent

(
{complex} 
X|_base_of_exponent
)
 ==> {complex} 






 Exponent function for a complex argument.










FUNCTION 
Cln|atural_logarithm

(
{complex} 
X|_parameter
)
 ==> {complex} 






 A natural logaritm of a complex argument.






------------------------------------------------------------- 'power, sqrt'









FUNCTION 
Cpow|er|_complex_by_real

(

     {complex} 
X|_base_to_power
, 

     INT,REAL,{complex} 
E|xponent
)
 ==> {complex} 
 , OPERATORS






 Power of a complex number (with a real or a complex exponent).










FUNCTION 
Csqrt|_square_root_of_complex

(

     {complex} 
X|_root_value
)
 ==> {complex} 






 Square root from a complex number.






------------------------------------------------------------ 'trigonometry'









FUNCTION 
Ccos|inus_trigonometric

(

     {complex} 
X|_radians
)
 ==> {complex} 
 , OPERATORS






 Trigonometric cosinus of a complex number argument.










FUNCTION 
Csin|us_trigonometric

(

     {complex} 
X|_radians
)
 ==> {complex} 
 , OPERATORS






 Trigonometric sinus of a complex number argument.










FUNCTION 
Ccosh|iperbolic

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Hyperbolic cosinus of a complex number argument.










FUNCTION 
Csinh|iperbolic

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Hyperbolic sinus of a complex number argument.










FUNCTION 
Carcsin|us_trigonometric

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Trigonometric arcsinus of a complex number argument.










FUNCTION 
Carccos|inus_trigonometric

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Trigonometric arccosinus of a complex number argument.










FUNCTION 
Carctan|gens_trigonometetric

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Trigonometric arctangens of a complex number argument.










FUNCTION 
Carccotan|gens_trigonometetric

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Trigonometric arccotangens of a complex number argument.










FUNCTION 
Carcsinh

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Hyperbolic arcsinus of a complex number argument.










FUNCTION 
Carccosh

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Hyperbolic arccosinus of a complex number argument.










FUNCTION 
Carcth|iperbolic

(

     {complex} 
X|_parameter
)
 ==> {complex} 
 , OPERATORS






 Hyperbolic arctangens of a complex number argument.






------------------------------------------------------------------ 'to STR'









FUNCTION 
Cstr|ing_from_complex_number

(

     {complex} 
X|_complex_number
)
 ==> STR 






 Representing a complex number as a string like "5+3.1415926535799i".










FUN 
S_complex

(
{complex} 
X|_parameter
)
 ==> STR 






 Same as above.





END