Classes
struct	Complex
	Internal structure. You should not call it directly, use API instead ! More...

Functions
	std_cAdd (c1, c2)
	Add two complex numbers. More...

	std_cAddNew (c1, c2)
	Add two complex numbers. The return is a new complex number. More...

	std_cArg (c, flag)
	Get the argument of a complex number. More...

	std_cCmp (c1, c2)
	Compare two complex numbers. More...

	std_cConjugate (c)
	Create the conjugate of a complex number. More...

	std_cDiv (c1, c2)
	Divide two complex numbers. More...

	std_cDivNew (c1, c2)
	Divide two complex numbers. The return is a new complex number. More...

	std_cEuler (f)
	Exponentiation by the Euler's formula : \(e^{f*i}\) where i is the imaginary unit ( \(i² = -1\)) and f is a real number (here, f is a floatting point number). More...

	std_cFromS (szC)
	Create a new Complex from a literal string (such as \(a + bi\)) More...

	std_cGet (c)
	Get a complex number. More...

	std_cGetImg (c)
	Get the imaginary part of a complex number. More...

	std_cGetReal (c)
	Get the real part of a complex number. More...

	std_cInv (c)
	Returns the inverse of a complex number. More...

	std_cInvNew (c)
	Returns the inverse of a complex number. This is a new complex number. More...

	std_cIsZero (c)
	Check if a complex number is 0. More...

	std_cLog (c)
	The natural logarithm (base 'e') of a complex number. More...

	std_cLogNew (c)
	Returns the first solution of the natural logarithm (base 'e') of a complex number. The return is a new complex number. More...

	std_cMod (c)
	Get the modulus (phasis) of a complex number. More...

	std_cMul (c1, c2)
	Multiply two complex numbers. More...

	std_cMulNew (c1, c2)
	Multiply two complex numbers. The return is a new complex number. More...

	std_cNew (fReal, fImg)
	Create a new Complex. More...

	std_cPow (c, i)
	The power of a complex number by an integer. More...

	std_cPowNew (c, i)
	The power of a complex number by an integer The return is a new complex number. More...

	std_cRootn (c, i)
	Returns the first solution of the n-th root of a complex number. More...

	std_cRootnAll (c, i)
	Returns all n-th roots of a complex number. More...

	std_cRootnK (c, i, k)
	Returns a particular soultion of the n-th root of a complex number. More...

	std_cRootnNew (c, i)
	Returns the first solution of the n-th root of a complex number. The return is a new complex number. More...

	std_cSet (c, fReal, fImg)
	Set a complex number. More...

	std_cSetImg (c, fImg)
	Set the imaginary part of a complex number. More...

	std_cSetReal (c, fReal)
	Set the real part of a complex number. More...

	std_cSqr (c)
	The square of a complex number. More...

	std_cSqrNew (c)
	Square of a complex number. The return is a new complex number. More...

	std_cSqrt (c)
	Square root of a complex number. More...

	std_cSqrtNew (c)
	Square root of a complex number. The return is two new complex numbers. More...

	std_cSub (c1, c2)
	Substract two complex numbers. More...

	std_cSubNew (c1, c2)
	Substract two complex numbers. The return is a new complex number. More...

	std_cToS (c)
	Get a complex number to a literal string (like \(a+bi\)) More...

	std_cZero ()
	Create a new zero (0) Complex : \(0+0i\). More...

Detailed Description

Package to load : lib/std/complex.pkg

Dependancies :

none

Function Documentation

std_cNew	(	fReal	,
		fImg
	)

Create a new Complex.

Prototype: fun [F F] Complex

Parameters

F	: the real part
F	: the imaginary part

Returns: Complex : the new complex number

std_cFromS ( szC )

Create a new Complex from a literal string (such as \(a + bi\))

Prototype: fun [S] Complex

Parameters

S	: a literal complex string.

Returns: Complex : the new complex number

std_cZero ( )

Create a new zero (0) Complex : \(0+0i\).

Prototype: fun [] Complex

Returns: Complex : the new complex number

std_cIsZero ( c )

Check if a complex number is 0.

Prototype: fun [Complex] I

Returns: I : 1 if 0

std_cSetReal	(	c	,
		fReal
	)

Set the real part of a complex number.

Prototype: fun [Complex F] Complex

Parameters

Complex	: a complex number.
F	: the new real part.

Returns: Complex : the same complex number structure

std_cSetImg	(	c	,
		fImg
	)

Set the imaginary part of a complex number.

Prototype: fun [Complex F] Complex

Parameters

Complex	: a complex number.
F	: the new imaginary part.

Returns: Complex : the same complex number structure

std_cSet	(	c	,
		fReal	,
		fImg
	)

Set a complex number.

Prototype: fun [Complex F F] Complex

Parameters

Complex	: a complex number.
F	: the new real part.
F	: the new imaginary part.

Returns: Complex : the same complex number structure

std_cGetReal ( c )

Get the real part of a complex number.

Prototype: fun [Complex] F

Parameters

Complex : a complex number.

Returns: F : the real part

std_cGetImg ( c )

Get the imaginary part of a complex number.

Prototype: fun [Complex] F

Parameters

Complex : a complex number.

Returns: F : the imaginary part

std_cGet ( c )

Get a complex number.

Prototype: fun [Complex] [F F]

Parameters

Complex : a complex number.

Returns: [F F] : the real part and the imaginary part

std_cToS ( c )

Get a complex number to a literal string (like \(a+bi\))

Prototype: fun [Complex] S

Parameters

Complex : a complex number.

Returns: S : the literal string

std_cConjugate ( c )

Create the conjugate of a complex number.

The conjugate of \(a+bi\) is \(a-bi\).

Prototype: fun [Complex] Complex

Parameters

Complex : a complex number.

Returns: Complex : its conjugate (a new Complex number)

std_cMod ( c )

Get the modulus (phasis) of a complex number.

The modulus of \(a+bi\) is \(|a-bi| = \sqrt{(a²+b²)}\)

Prototype: fun [Complex] F

Parameters

Complex : a complex number.

Returns: F : its modulus

std_cArg	(	c	,
		flag
	)

Get the argument of a complex number.

The argument (or phasis) of \(a+bi\) is \(\arctan {b / a}\).

Prototype: fun [Complex I] F

Parameters

Complex	: a complex number.
I	: a flag. In the case where a and b are equals at 0 (zero), this function returns 0 if this flag is 0 or nil if this flag has another value. Indeed, in mathematics, this value is undefined but the many language, like C, returns 0 instead of a 'NaN' (Not a Number).

Returns: F : its argument, in radians (see above)

std_cAdd	(	c1	,
		c2
	)

Add two complex numbers.

Prototype: fun [Complex Complex] [F F]

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: [F F] : the result (real part and imaginary part)

See also: std_cAddNew

std_cAddNew	(	c1	,
		c2
	)

Add two complex numbers. The return is a new complex number.

Prototype: fun [Complex Complex] Complex

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: Complex : a new Complex number

See also: std_cAdd

std_cSub	(	c1	,
		c2
	)

Substract two complex numbers.

Prototype: fun [Complex Complex] [F F]

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: [F F] : the result (real part and imaginary part)

See also: std_cSubNew

std_cSubNew	(	c1	,
		c2
	)

Substract two complex numbers. The return is a new complex number.

Prototype: fun [Complex Complex] Complex

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: Complex : a new Complex number

See also: std_cSub

std_cMul	(	c1	,
		c2
	)

Multiply two complex numbers.

Prototype: fun [Complex Complex] [F F]

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: [F F] : the result (real part and imaginary part)

See also: std_cMulNew

std_cMulNew	(	c1	,
		c2
	)

Multiply two complex numbers. The return is a new complex number.

Prototype: fun [Complex Complex] Complex

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: Complex : a new Complex number

See also: std_cMul

std_cDiv	(	c1	,
		c2
	)

Divide two complex numbers.

Prototype: fun [Complex Complex] [F F]

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: [F F] : the result (real part and imaginary part)

See also: std_cDivNew

std_cDivNew	(	c1	,
		c2
	)

Divide two complex numbers. The return is a new complex number.

Prototype: fun [Complex Complex] Complex

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: Complex : a new Complex number

See also: std_cDiv

std_cInv ( c )

Returns the inverse of a complex number.

Prototype: fun [Complex] [F F]

Parameters

Complex : a complex number.

Returns: [F F] : the result (real part and imaginary part), nil if error

See also: std_cInvNew; std_cPow (n = -1)

std_cInvNew ( c )

Returns the inverse of a complex number. This is a new complex number.

Prototype: fun [Complex] Complex

Parameters

Complex : a complex number.

Returns: Complex : a new Complex number or nil if error

See also: std_cInv; std_cPowNew (n = -1)

std_cSqr ( c )

The square of a complex number.

Prototype: fun [Complex] [F F]

Parameters

Complex : a complex number.

Returns: [F F] : the result (real part and imaginary part)

See also: std_cSqrNew

std_cSqrNew ( c )

Square of a complex number. The return is a new complex number.

Prototype: fun [Complex] Complex

Parameters

Complex : a complex number.

Returns: Complex : a new Complex number

See also: std_cSqr

std_cSqrt ( c )

Square root of a complex number.

Prototype: fun [Complex] [[F F] [F F]]

Parameters

Complex : a complex number.

Returns: [[F F] [F F]] : the result (two complex numbers with their real part and imaginary part)

See also: std_cSqrtNew

std_cSqrtNew ( c )

Square root of a complex number. The return is two new complex numbers.

Prototype: fun [Complex] [Complex Complex]

Parameters

Complex : a complex number.

Returns: [Complex Complex] : two new Complex number

See also: std_cSqrt

std_cPow	(	c	,
		i
	)

The power of a complex number by an integer.

Prototype: fun [Complex I] [F F]

Parameters

Complex	: a complex number.
I	: an integer

Returns: [F F] : the result (real part and imaginary part)

See also: std_cPowNew

std_cPowNew	(	c	,
		i
	)

The power of a complex number by an integer The return is a new complex number.

Prototype: fun [Complex I] Complex

Parameters

Complex	: a complex number.
I	: an integer

Returns: Complex : a new Complex number

See also: std_cPow

std_cRootn	(	c	,
		i
	)

Returns the first solution of the n-th root of a complex number.

Prototype: fun [Complex I] [F F]

Parameters

Complex	: a complex number.
I	: an integer

Returns: [F F] : the simplier result (real part and imaginary part)

Remarks: In fact, the n-th root of a complex number is 'multi valued'.

See also: std_cRootnNew; std_cRootnK for a particular value; std_cRootnAll for all values

std_cRootnNew	(	c	,
		i
	)

Returns the first solution of the n-th root of a complex number. The return is a new complex number.

Prototype: fun [Complex I] Complex

Parameters

Complex	: a complex number.
I	: an integer

Returns: Complex : a new Complex number (only the first value is returned here).

See also: std_cRootn; std_cRootnK; std_cRootnAll

std_cRootnAll	(	c	,
		i
	)

Returns all n-th roots of a complex number.

The part real is :

(the n-th root of modulus) * cosine ((the argument + 2*k*Pi) / n)

\(\sqrt[n]{(a²+b²)} * \cos {((\arctan {b / a} + 2*k*\Pi)/n)}\)

The imaginary part is :

(the n-th root of modulus) * sine ((the argument + 2*k*Pi) / n)

\(\sqrt[n]{(a²+b²)} * \sin {((\arctan {b / a} + 2*k*\Pi)/n)}\)

where 'k' is an integer, with \(0 <= k < n\).

Prototype: fun [Complex I] [[I F F] r1]

Parameters

Complex	: a complex number.
I	: an integer (the 'n_th')

Returns: [[I F F] r1] : a list of all values. The first item of each tuple is the indice 'k'. The size of the list is 'n'.

See also: std_cRootn for 'k' = 0; std_cRootnNew for 'k' = 0; std_cRootnK for a given 'k'

std_cRootnK	(	c	,
		i	,
		k
	)

Returns a particular soultion of the n-th root of a complex number.

Prototype: fun [Complex I I] [F F]

Parameters

Complex	: a complex number.
I	: an integer, the 'n'-th root
I	: k : a particular solution (see std_cRootnAll for more details) k must be positive or nul and strictly lower than n (else, nil is returned)

Returns: [F F] : the result (real part and imaginary part)

See also: std_cRootnNew for 'k' = 0; std_cRootn for 'k' = 0; std_cRootnAll for all 'k'

std_cLog ( c )

The natural logarithm (base 'e') of a complex number.

Prototype: fun [Complex] [F F]

Parameters

Complex : a complex number.

Returns: [F F] : the result (real part and imaginary part)

Remarks: Cosine and sine being periodic functions, the natural logarithm of a complex number is also periodic. So, only the simple value is returned here, i.E. when 'k' = 0. To obtain all values, it need to apply this formula :

the real part is : log of modulus : \(\ln {\sqrt{(a²+b²)}}\)

the imaginary part is : the argument + 2*k*Pi : \(\arctan {b / a}+ 2*k*\Pi\)

where 'k' is an integer (in \(\mathbb{Z}\))

If you want a particular result, add \(2k\Pi\) to the returned imaginary part.

std_cLogNew ( c )

Returns the first solution of the natural logarithm (base 'e') of a complex number. The return is a new complex number.

Prototype: fun [Complex] Complex

Parameters

Complex : a complex number.

Returns: Complex : a new Complex number (only the first value is returned here).

See also: std_cLog for 'k' = 0 (see std_cLog for more details)

std_cEuler ( f )

Exponentiation by the Euler's formula : \(e^{f*i}\) where i is the imaginary unit ( \(i² = -1\)) and f is a real number (here, f is a floatting point number).

e power fi = cos f + i sin f

\(e^{f*i} = \cos {f} + i*\sin{f}\)

Prototype: fun [F] [F F]

Parameters

F	: a floating point number.

Returns: [F F] : the result (real part and imaginary part)

std_cCmp	(	c1	,
		c2
	)

Compare two complex numbers.

Prototype: fun [Complex Complex] I

Parameters

Complex	: a complex number.
Complex	: a second complex number.

Returns: Complex : 1 if equals

Remarks: It is not possible to define an order between two complex number. So, only the equality can be defined and here 1 is returned in this case.

Classes

Functions

Detailed Description

Function Documentation