const type: complex

Complex numbers represented with float real part and imaginary part. Complex literals do not exist.

const func complex: (attr complex) conv (in integer: re)

Convert an integer to a complex.

Returns:

the result of the conversion.

const func complex: (attr complex) conv (in float: re)

Conversion a float to a complex.

Returns:

the result of the conversion.

const func boolean: (ref complex: number1) = (ref complex: number2)

Check if two complex numbers are equal.

Returns:

TRUE if both numbers are equal, FALSE otherwise.

const func boolean: (ref complex: number1) <> (ref complex: number2)

Check if two complex numbers are not equal.

Returns:

FALSE if both numbers are equal, TRUE otherwise.

const func complex: + (in complex: number)

Plus sign for complex numbers.

Returns:

its operand unchanged.

const func complex: - (in complex: number)

Minus sign, negate a complex number.

Returns:

the negated value of the number.

const func complex: conj (in complex: number)

Compute the conjugated value of a complex number.

Returns:

the complex conjugate of the number.

const func complex: (in complex: summand1) + (in complex: summand2)

Add two complex numbers.

Returns:

the sum of the two numbers.

const func complex: (in complex: minuend) - (in complex: subtrahend)

Compute the subtraction of two complex numbers.

Returns:

the difference of the two numbers.

const func complex: (in complex: factor1) * (in complex: factor2)

Multiply two complex numbers.

Returns:

the product of the two numbers.

const func complex: (in complex: dividend) / (in complex: divisor)

Copmpute the division of two complex numbers.

Returns:

the quotient of the division.

const proc: (inout complex: number) +:= (in complex: delta)

Increment a complex number by a delta.

const proc: (inout complex: number) -:= (in complex: delta)

Decrement a complex number by a delta.

const proc: (inout complex: number) *:= (in complex: factor)

Multiply a complex number by a factor and assign the result back to number.

const proc: (inout complex: number) /:= (in complex: divisor)

Divide a complex number by a divisor and assign the result back to number.

const func complex: (in complex: base) ** (in integer: exponent)

Compute the exponentiation of a complex base with an integer exponent.

Returns:

the result of the exponentiation.

const func complex: (attr complex) parse (in string: stri)

Convert a string to a complex number. The string must contain real and imaginary part (e.g.: "1.5-2.8i"). Real and imaginary part must be separated with a + or - sign.

Returns:

the complex result of the conversion.

Raises:

RANGE_ERROR - If stri contains not a valid complex value.

const func string: (in complex: number) digits (in integer: precision)

Convert a complex to a string in decimal fixed point notation. The number is converted to a string with real and imaginary part (e.g.: "1.5-2.8i"). Real and imaginary part are separated with a + or - sign. The precision parameter specifies the number of digits after the decimal point of the real and imaginary part. If the precision is zero the decimal point is omitted.

complex(3.1415) digits 2   returns "3.14+0.00i"

Returns:

the string result of the conversion.

Raises:

RANGE_ERROR - If the precision is negative.

MEMORY_ERROR - Not enough memory to represent the result.

const func string: (in complex: number) sci (in integer: precision)

Convert a complex to a string in scientific notation. The number is converted to a string with real and imaginary part (e.g.: "1.5e+2-2.8e+0i"). Real and imaginary part are separated with a + or - sign. The precision parameter specifies the number of digits after the decimal point of the real and imaginary part. If the precision is zero the decimal point is omitted.

complex(31415.9, 27182.8) sci 4   returns "3.1416e+4+2.7183e+4i"

Returns:

the string result of the conversion.

Raises:

RANGE_ERROR - If the precision is negative.

MEMORY_ERROR - Not enough memory to represent the result.

const func complex: complex (in float: re, in float: im)

Create a complex number from its real and imaginary part.

Returns:

the created complex number.

const func complex: complex (in float: re)

Create a complex number from its real part.

Returns:

the created complex number.

const func complex: polar (in float: magnitude, in float: angle)

Create a complex number from polar coordinates.

Returns:

the created complex number.

const func complex: complex (in integer: re)

Convert an integer to a complex.

Returns:

the result of the conversion.

const func float: abs (in complex: number)

Compute the absolute value of a complex number.

Returns:

the absolute value.

const func float: sqrAbs (in complex: number)

Compute the square of the absolute value of a complex number.

Returns:

the square of the absolute value.

const func float: arg (in complex: number)

Compute the argument of a complex number. This is the angle of the polar form of the complex number.

Returns:

the argument of the complex number.

const func integer: compare (in complex: number1, in complex: number2)

Compare two complex numbers in lexicographic order.

Returns:

-1, 0 or 1 if the first argument is considered to be respectively less than, equal to, or greater than the second.

const func integer: hashCode (in complex: num)

Compute the hash value of a complex number.

Returns:

the hash value.

const func string: str (in complex: number)

Convert a complex number to a string. The number is converted to a string with real and imaginary part (e.g.: "1.5-2.8i"). Real and imaginary part are separated with a + or - sign.

Returns:

the string result of the conversion.

Raises:

MEMORY_ERROR - Not enough memory to represent the result.

const func complex: complex (in string: stri)

Convert a string to a complex number. The string must contain real and imaginary part (e.g.: "1.5-2.8i"). Real and imaginary part must be separated with a + or - sign.

Returns:

the complex result of the conversion.

Raises:

RANGE_ERROR - If stri contains not a valid complex value.