Fraction Complex Functions

Functions for rational complex numbers. More...

Functions
dc_complex_frac	dc_frac_from_ints (int64_t real_num, int64_t real_den, int64_t imag_num, int64_t imag_den)
	Create a rational complex number from integer components.
dc_complex_frac	dc_frac_from_df (df_frac real, df_frac imag)
	Create a rational complex number from fraction components.
dc_complex_frac	dc_frac_zero (void)
	Get the rational complex zero (0/1 + 0/1 i)
dc_complex_frac	dc_frac_one (void)
	Get the rational complex one (1/1 + 0/1 i)
dc_complex_frac	dc_frac_i (void)
	Get the rational complex i (0/1 + 1/1 i)
dc_complex_frac	dc_frac_neg_one (void)
	Get the rational complex -1 (-1/1 + 0/1 i)
dc_complex_frac	dc_frac_neg_i (void)
	Get the rational complex -i (0/1 + -1/1 i)
dc_complex_frac	dc_frac_retain (dc_complex_frac c)
	Increment reference count and return the same object.
void	dc_frac_release (dc_complex_frac *c)
	Decrement reference count and possibly free memory.
dc_complex_frac	dc_frac_copy (dc_complex_frac c)
	Create a new copy with reference count 1.
dc_complex_frac	dc_frac_add (dc_complex_frac a, dc_complex_frac b)
	Add two rational complex numbers.
dc_complex_frac	dc_frac_sub (dc_complex_frac a, dc_complex_frac b)
	Subtract two rational complex numbers.
dc_complex_frac	dc_frac_mul (dc_complex_frac a, dc_complex_frac b)
	Multiply two rational complex numbers.
dc_complex_frac	dc_frac_div (dc_complex_frac a, dc_complex_frac b)
	Divide two rational complex numbers.
dc_complex_frac	dc_frac_negate (dc_complex_frac c)
	Negate a rational complex number.
dc_complex_frac	dc_frac_conj (dc_complex_frac c)
	Complex conjugate of a rational complex number.
dc_complex_frac	dc_frac_reciprocal (dc_complex_frac c)
	Reciprocal of a rational complex number.
df_frac	dc_frac_real (dc_complex_frac c)
	Get the real part of a rational complex number.
df_frac	dc_frac_imag (dc_complex_frac c)
	Get the imaginary part of a rational complex number.
bool	dc_frac_eq (dc_complex_frac a, dc_complex_frac b)
	Test if two rational complex numbers are equal.
bool	dc_frac_is_zero (dc_complex_frac c)
	Test if a rational complex number is zero.
bool	dc_frac_is_real (dc_complex_frac c)
	Test if a rational complex number is real (imaginary part is zero)
bool	dc_frac_is_imag (dc_complex_frac c)
	Test if a rational complex number is purely imaginary (real part is zero)
bool	dc_frac_is_gaussian_int (dc_complex_frac c)
	Test if a rational complex number is actually a Gaussian integer.
char *	dc_frac_to_string (dc_complex_frac c)
	Convert rational complex number to mathematical string representation.

Detailed Description

Functions for rational complex numbers.

Function Documentation

dc_frac_add()

dc_complex_frac dc_frac_add ( dc_complex_frac  a, dc_complex_frac  b  )

extern

Add two rational complex numbers.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

New complex number a + b

Note

Result has reference count of 1

Result automatically reduced to lowest terms

dc_frac_conj()

dc_complex_frac dc_frac_conj ( dc_complex_frac  c )

extern

Complex conjugate of a rational complex number.

Parameters

c	The operand (must not be NULL)

Returns

New complex number with imaginary part negated

Note

Result has reference count of 1

For a+bi, returns a-bi

dc_frac_copy()

dc_complex_frac dc_frac_copy ( dc_complex_frac  c )

extern

Create a new copy with reference count 1.

Parameters

c	The complex number to copy (must not be NULL)

Returns

New complex number with same value

Note

Result has reference count of 1

dc_frac_div()

dc_complex_frac dc_frac_div ( dc_complex_frac  a, dc_complex_frac  b  )

extern

Divide two rational complex numbers.

Parameters

a	Dividend (must not be NULL)
b	Divisor (must not be NULL and not zero)

Returns

New complex number a / b

Note

Result has reference count of 1

Result automatically reduced to lowest terms

Uses formula: (a+bi)/(c+di) = ((ac+bd)+(bc-ad)i)/(c²+d²)

dc_frac_eq()

bool dc_frac_eq ( dc_complex_frac  a, dc_complex_frac  b  )

extern

Test if two rational complex numbers are equal.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

true if a == b, false otherwise

Note

Compares reduced forms for exact equality

dc_frac_from_df()

dc_complex_frac dc_frac_from_df ( df_frac  real, df_frac  imag  )

extern

Create a rational complex number from fraction components.

Parameters

real	The real part (must not be NULL)
imag	The imaginary part (must not be NULL)

Returns

New rational complex number (must be released)

Note

Result has reference count of 1

Input fractions are retained

dc_frac_from_ints()

dc_complex_frac dc_frac_from_ints ( int64_t  real_num, int64_t  real_den, int64_t  imag_num, int64_t  imag_den  )

extern

Create a rational complex number from integer components.

Parameters

real_num	Numerator of real part
real_den	Denominator of real part (must not be zero)
imag_num	Numerator of imaginary part
imag_den	Denominator of imaginary part (must not be zero)

Returns

New rational complex number (must be released)

Note

Result has reference count of 1

Automatically reduced to lowest terms

Denominators normalized to be positive

dc_frac_i()

dc_complex_frac dc_frac_i ( void  )

extern

Get the rational complex i (0/1 + 1/1 i)

Returns

Singleton imaginary unit

Note

This is a singleton with high reference count

dc_frac_imag()

df_frac dc_frac_imag ( dc_complex_frac  c )

extern

Get the imaginary part of a rational complex number.

Parameters

c	The complex number (must not be NULL)

Returns

New dynamic fraction (must be released)

Note

Result has reference count of 1

dc_frac_is_gaussian_int()

bool dc_frac_is_gaussian_int ( dc_complex_frac  c )

extern

Test if a rational complex number is actually a Gaussian integer.

Parameters

c	The complex number (must not be NULL)

Returns

true if both real and imaginary parts are integers, false otherwise

Note

Useful after dc_int_div() to check if result simplified to integer

dc_frac_is_imag()

bool dc_frac_is_imag ( dc_complex_frac  c )

extern

Test if a rational complex number is purely imaginary (real part is zero)

Parameters

c	The complex number (must not be NULL)

Returns

true if real part is zero, false otherwise

dc_frac_is_real()

bool dc_frac_is_real ( dc_complex_frac  c )

extern

Test if a rational complex number is real (imaginary part is zero)

Parameters

c	The complex number (must not be NULL)

Returns

true if imaginary part is zero, false otherwise

dc_frac_is_zero()

bool dc_frac_is_zero ( dc_complex_frac  c )

extern

Test if a rational complex number is zero.

Parameters

c	The complex number (must not be NULL)

Returns

true if c == 0+0i, false otherwise

dc_frac_mul()

dc_complex_frac dc_frac_mul ( dc_complex_frac  a, dc_complex_frac  b  )

extern

Multiply two rational complex numbers.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

New complex number a * b

Note

Result has reference count of 1

Result automatically reduced to lowest terms

Uses formula: (a+bi)(c+di) = (ac-bd) + (ad+bc)i

dc_frac_neg_i()

dc_complex_frac dc_frac_neg_i ( void  )

extern

Get the rational complex -i (0/1 + -1/1 i)

Returns

Singleton negative imaginary unit

Note

This is a singleton with high reference count

dc_frac_neg_one()

dc_complex_frac dc_frac_neg_one ( void  )

extern

Get the rational complex -1 (-1/1 + 0/1 i)

Returns

Singleton negative one complex number

Note

This is a singleton with high reference count

dc_frac_negate()

dc_complex_frac dc_frac_negate ( dc_complex_frac  c )

extern

Negate a rational complex number.

Parameters

c	The operand (must not be NULL)

Returns

New complex number -c

Note

Result has reference count of 1

dc_frac_one()

dc_complex_frac dc_frac_one ( void  )

extern

Get the rational complex one (1/1 + 0/1 i)

Returns

Singleton one complex number

Note

This is a singleton with high reference count

dc_frac_real()

df_frac dc_frac_real ( dc_complex_frac  c )

extern

Get the real part of a rational complex number.

Parameters

c	The complex number (must not be NULL)

Returns

New dynamic fraction (must be released)

Note

Result has reference count of 1

dc_frac_reciprocal()

dc_complex_frac dc_frac_reciprocal ( dc_complex_frac  c )

extern

Reciprocal of a rational complex number.

Parameters

c	The operand (must not be NULL and not zero)

Returns

New complex number 1/c

Note

Result has reference count of 1

Equivalent to dc_frac_div(dc_frac_one(), c)

dc_frac_release()

void dc_frac_release ( dc_complex_frac *  c )

extern

Decrement reference count and possibly free memory.

Parameters

c	Pointer to complex number pointer (gracefully handles NULL)

Note

Sets *c to NULL after release

Only frees memory when reference count reaches 0

Singletons are never freed

dc_frac_retain()

dc_complex_frac dc_frac_retain ( dc_complex_frac  c )

extern

Increment reference count and return the same object.

Parameters

c	The complex number to retain (must not be NULL)

Returns

The same object passed in

Note

Increases reference count by 1

dc_frac_sub()

dc_complex_frac dc_frac_sub ( dc_complex_frac  a, dc_complex_frac  b  )

extern

Subtract two rational complex numbers.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

New complex number a - b

Note

Result has reference count of 1

Result automatically reduced to lowest terms

dc_frac_to_string()

char * dc_frac_to_string ( dc_complex_frac  c )

extern

Convert rational complex number to mathematical string representation.

Parameters

c	The complex number (must not be NULL)

Returns

Newly allocated string (must be freed with free())

Note

Format examples: "3/4+2/3i", "1/2-1/3i", "2/3i", "-i", "5/7", "0"

Uses mathematical notation with 'i' for imaginary unit

Shows fractions in reduced form

dc_frac_zero()

dc_complex_frac dc_frac_zero ( void  )

extern

Get the rational complex zero (0/1 + 0/1 i)

Returns

Singleton zero complex number

Note

This is a singleton with high reference count