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Filename : cdesc-Complex.ri
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U:RDoc::NormalClass[iI"Complex:ET@I"Numeric;To:RDoc::Markup::Document:@parts[o;;[?o:RDoc::Markup::Paragraph;[I"0A \Complex object houses a pair of values, ;TI"Ogiven when the object is created as either <i>rectangular coordinates</i> ;TI"!or <i>polar coordinates</i>.;To:RDoc::Markup::BlankLine�S:RDoc::Markup::Heading:
leveli:	textI"Rectangular Coordinates;T@o;	;[I"5The rectangular coordinates of a complex number ;TI"2are called the _real_ and _imaginary_ parts; ;TI"ssee {Complex number definition}[https://en.wikipedia.org/wiki/Complex_number#Definition_and_basic_operations].;T@o;	;[I"HYou can create a \Complex object from rectangular coordinates with:;T@o:RDoc::Markup::List:
@type:BULLET:@items[	o:RDoc::Markup::ListItem:@label0;[o;	;[I"IA {complex literal}[rdoc-ref:syntax/literals.rdoc@Complex+Literals].;To;;0;[o;	;[I"\Method Complex.rect.;To;;0;[o;	;[I"\\Method Kernel#Complex, either with numeric arguments or with certain string arguments.;To;;0;[o;	;[I".\Method String#to_c, for certain strings.;T@o;	;[I"PNote that each of the stored parts may be a an instance one of the classes ;TI"+Complex, Float, Integer, or Rational; ;TI"they may be retrieved:;T@o;;;;[o;;0;[o;	;[I"ASeparately, with methods Complex#real and Complex#imaginary.;To;;0;[o;	;[I"(Together, with method Complex#rect.;T@o;	;[I"@The corresponding (computed) polar values may be retrieved:;T@o;;;;[o;;0;[o;	;[I":Separately, with methods Complex#abs and Complex#arg.;To;;0;[o;	;[I")Together, with method Complex#polar.;T@S;;i;
I"Polar Coordinates;T@o;	;[I"/The polar coordinates of a complex number ;TI"5are called the _absolute_ and _argument_ parts; ;TI"Xsee {Complex polar plane}[https://en.wikipedia.org/wiki/Complex_number#Polar_form].;T@o;	;[I"&In this class, the argument part ;TI"Bin expressed {radians}[https://en.wikipedia.org/wiki/Radian] ;TI"C(not {degrees}[https://en.wikipedia.org/wiki/Degree_(angle)]).;T@o;	;[I"BYou can create a \Complex object from polar coordinates with:;T@o;;;;[o;;0;[o;	;[I"\Method Complex.polar.;To;;0;[o;	;[I";\Method Kernel#Complex, with certain string arguments.;To;;0;[o;	;[I".\Method String#to_c, for certain strings.;T@o;	;[I"PNote that each of the stored parts may be a an instance one of the classes ;TI"+Complex, Float, Integer, or Rational; ;TI"they may be retrieved:;T@o;;;;[o;;0;[o;	;[I":Separately, with methods Complex#abs and Complex#arg.;To;;0;[o;	;[I")Together, with method Complex#polar.;T@o;	;[I"FThe corresponding (computed) rectangular values may be retrieved:;T@o;;;;[o;;0;[o;	;[I"<Separately, with methods Complex#real and Complex#imag.;To;;0;[o;	;[I"(Together, with method Complex#rect.;T@S;;i;
I"What's Here;T@o;	;[I"First, what's elsewhere:;T@o;;;;[o;;0;[o;	;[I"7\Class \Complex inherits (directly or indirectly) ;TI"<from classes {Numeric}[rdoc-ref:Numeric@What-27s+Here] ;TI"1and {Object}[rdoc-ref:Object@What-27s+Here].;To;;0;[o;	;[I"RIncludes (indirectly) module {Comparable}[rdoc-ref:Comparable@What-27s+Here].;T@o;	;[I"*Here, class \Complex has methods for:;T@S;;i;
I"Creating \Complex Objects;T@o;;;;[o;;0;[o;	;[I"M::polar: Returns a new \Complex object based on given polar coordinates.;To;;0;[o;	;[I"+::rect (and its alias ::rectangular): ;TI"JReturns a new \Complex object based on given rectangular coordinates.;T@S;;i;
I"
Querying;T@o;;;;[o;;0;[o;	;[I"L#abs (and its alias #magnitude): Returns the absolute value for +self+.;To;;0;[o;	;[I"/#arg (and its aliases #angle and #phase): ;TI"8Returns the argument (angle) for +self+ in radians.;To;;0;[o;	;[I"5#denominator: Returns the denominator of +self+.;To;;0;[o;	;[I"L#finite?: Returns whether both +self.real+ and +self.image+ are finite.;To;;0;[o;	;[I"6#hash: Returns the integer hash value for +self+.;To;;0;[o;	;[I"N#imag (and its alias #imaginary): Returns the imaginary value for +self+.;To;;0;[o;	;[I"I#infinite?: Returns whether +self.real+ or +self.image+ is infinite.;To;;0;[o;	;[I"1#numerator: Returns the numerator of +self+.;To;;0;[o;	;[I"=#polar: Returns the array <tt>[self.abs, self.arg]</tt>.;To;;0;[o;	;[I"9#inspect: Returns a string representation of +self+.;To;;0;[o;	;[I".#real: Returns the real value for +self+.;To;;0;[o;	;[I"C#real?: Returns +false+; for compatibility with Numeric#real?.;To;;0;[o;	;[I")#rect (and its alias #rectangular): ;TI"7Returns the array <tt>[self.real, self.imag]</tt>.;T@S;;i;
I"Comparing;T@o;;;;[o;;0;[o;	;[I"]#<=>: Returns whether +self+ is less than, equal to, or greater than the given argument.;To;;0;[o;	;[I"@#==: Returns whether +self+ is equal to the given argument.;T@S;;i;
I"Converting;T@o;;;;[o;;0;[o;	;[I"D#rationalize: Returns a Rational object whose value is exactly ;TI"?or approximately equivalent to that of <tt>self.real</tt>.;To;;0;[o;	;[I"#to_c: Returns +self+.;To;;0;[o;	;[I"5#to_d: Returns the value as a BigDecimal object.;To;;0;[o;	;[I"L#to_f: Returns the value of <tt>self.real</tt> as a Float, if possible.;To;;0;[o;	;[I"O#to_i: Returns the value of <tt>self.real</tt> as an Integer, if possible.;To;;0;[o;	;[I"O#to_r: Returns the value of <tt>self.real</tt> as a Rational, if possible.;To;;0;[o;	;[I"6#to_s: Returns a string representation of +self+.;T@S;;i;
I""Performing Complex Arithmetic;T@o;;;;[o;;0;[o;	;[I"=#*: Returns the product of +self+ and the given numeric.;To;;0;[o;	;[I">#**: Returns +self+ raised to power of the given numeric.;To;;0;[o;	;[I"9#+: Returns the sum of +self+ and the given numeric.;To;;0;[o;	;[I"@#-: Returns the difference of +self+ and the given numeric.;To;;0;[o;	;[I")#-@: Returns the negation of +self+.;To;;0;[o;	;[I">#/: Returns the quotient of +self+ and the given numeric.;To;;0;[o;	;[I"H#abs2: Returns square of the absolute value (magnitude) for +self+.;To;;0;[o;	;[I"G#conj (and its alias #conjugate): Returns the conjugate of +self+.;To;;0;[o;	;[I"P#fdiv: Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>.;T@S;;i;
I"Working with JSON;T@o;;;;[o;;0;[o;	;[I"3::json_create: Returns a new \Complex object, ;TI"1deserialized from the given serialized hash.;To;;0;[o;	;[I"A#as_json: Returns a serialized hash constructed from +self+.;To;;0;[o;	;[I"9#to_json: Returns a JSON string representing +self+.;T@o;	;[I"qThese methods are provided by the {JSON gem}[https://github.com/ruby/json]. To make these methods available:;T@o:RDoc::Markup::Verbatim;[I"require 'json/add/complex';T:@format0:
@fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0o;;[�;I"%ext/json/lib/json/add/complex.rb;T;0;0;0[�[U:RDoc::Constant[i�I"I;TI"Complex::I;T:public0o;;[o;	;[I"Equivalent ;TI"$to <tt>Complex.rect(0, 1)</tt>:;T@o;;[I"Complex::I # => (0+1i);T;0;@{;0@{@cRDoc::NormalClass0[�[[I"
class;T[[;[	[I"json_create;TI"%ext/json/lib/json/add/complex.rb;T[I"
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real?;T@�[@�@�[I"rectangular;T@�[I"	to_c;T@�[I"	to_f;T@�[I"	to_i;T@�[I"to_json;T@�[I"	to_r;T@�[I"	to_s;T@�[;[�[;[�[�[U:RDoc::Context::Section[i�0o;;[�;0;0[@{@~@~cRDoc::TopLevel