--- name: "Complex" section: "3" platform: "linux" package: "objc-poc" version: "3.1.3-2" release: "Debian 2.2 (Potato)" platforms: ["linux"] url: "https://new.carta.tech/Complex" --- # Complex(3) ## Complex **Inherits from:** CAObject **Maturity Index:** Relatively immature ## Class Description A complex object consists of two real objects, a *real* and *imaginary* part. Real objects could be arbitrary Computer Algebra Kit objects, but the class has been used so far only for the *Gaussian integers* i.e., complex numbers over the integers. The imaginary unit is represented by the symbol *I* . ## Method types **Creation** \* real:\ \* real:imaginary:\ \* copy\ \* deepCopy **Identity** \* real\ \* imaginary\ \* isReal\ \* notReal\ \* hash\ \* isEqual: **Conjugation** \* conjugate\ \* norm\ \* asReal **Addition** \* zero\ \* isZero\ \* isOpposite:\ \* negate\ \* double\ \* add:\ \* subtract: **Multiplication** \* I\ \* one\ \* isOne\ \* isMinusOne\ \* isUnit\ \* square\ \* multiply:\ \* power: **Complex Division** \* divide:\ \* inverse\ \* quotient:\ \* remainder:quotient: **Greatest Common Divisor** \* gcd: **Printing** \* printOn: ## Methods real: \+ **real** : *aReal* Returns a new complex object with real part set to *aReal* and the imaginary part set to the real zero. real:imaginary: \+ **real** : *aReal* **imaginary** : *anotherReal* Returns a new complex object with real part set to *aReal* and the imaginary part set to *anotherReal* . copy \- **copy** Returns a new copy of the complex object. deepCopy \- **deepCopy** Returns a new copy of the complex object; sends **deepCopy** messages to real and imaginary part. real \- **real** Returns the real part of a complex number. imaginary \- **imaginary** Returns the imaginary part of a complex number. isReal \- ( BOOL ) **isReal** Whether the imaginary part is equal to zero. notReal \- ( BOOL ) **notReal** Whether the **isReal** returns NO. hash \- ( unsigned ) **hash** Returns a small integer that is the same for objects that are equal in the sense of **isEqual:** . isEqual: \- ( BOOL ) **isEqual** : *b* Whether real and imaginary parts are equal to each other. conjugate \- **conjugate** Returns a new reference to the object if it is real. Otherwise, returns a new object that is equal to the complex conjugate of the object. The conjugate of *a* + I *b* is *a* - I *b* . norm \- **norm** Returns a new *real* object, the norm of the complex object i.e., the object multiplied by its conjugate. asReal \- **asReal** If the imaginary part of the object is zero, this method returns a new reference to the real part of the object. zero \- **zero** Returns a new complex object with real and imaginary part equal to zero. isZero \- ( BOOL ) **isZero** Whether real and imaginary part are equal to zero. isOpposite: \- ( BOOL ) **isOpposite** : *b* Whether real and imaginary parts are opposite to each other. negate \- **negate** Returns a new complex number, by negating real and imaginary parts. double \- **double** Returns a new complex number, by doubling real and imaginary parts. add: \- **add** : *b* Returns the sum of the complex numbers; adds real and imaginary parts together. subtract: \- **subtract** : *b* Returns the difference of the complex numbers; subtracts real and imaginary parts from each other. I \- **I** Returns a new reference to the imaginary unit. one \- **one** Returns a new object with real part equal to one and imaginary part equal to zero. isOne \- ( BOOL ) **isOne** Whether the complex object is a multiplicative unit. The complex units consist of the real units and the real units multiplied by the imaginary unit *i* . isMinusOne \- ( BOOL ) **isMinusOne** Whether the complex object is a multiplicative unit. The complex units consist of the real units and the real units multiplied by the imaginary unit *i* . isUnit \- ( BOOL ) **isUnit** Whether the complex object is a multiplicative unit. The complex units consist of the real units and the real units multiplied by the imaginary unit *i* . square \- **square** Returns the complex number multiplied by itself, computed by the rule : (a+I b)^2 == (a^2 - b^2) + I (2 a b)\ multiply: \- **multiply** : *b* Returns the product of the two complex numbers, computed by the rule : (a+I b)(c+I d) == (ac-bd) + I (ad+bc)\ power: \- **power** :(int) *n* Returns the complex number raised to the *n* -th power. If the object is real, simply computes the *n* -th power as a real. Otherwise, computes the power by the binary exponentation algorithm. divide: \- **divide** : *b* Returns the exact quotient of the complex number by the complex number *b* . Multiplies by the conjugate of *b* and then divides by the norm of *b* , or returns **nil** if the latter division is not exact. inverse \- **inverse** Returns the conjugate of the complex number divided by its norm, or **nil** if the latter division is not exact. quotient: \- **quotient** : *b* Returns the quotient on division by *b* . **Note:** I'm not sure about the algorithm I'm using here ! remainder:quotient: \- **remainder** : *b* **quotient** :(id \*) *q* Computes the remainder, and if *q* is non-NULL pointer, the quotient on division by *b* . gcd: \- **gcd** : *b* If both objects are real, returns a complex object with real part set to the (real) gcd of the objects. Otherwise, computes the greatest common divisor by the Euclidean algorithm. printOn: \- **printOn** :(IOD) *aFile* Prints the number to *aStream* .