JezK
Edit File: complex.rbs
# <!-- rdoc-file=complex.c --> # A complex number can be represented as a paired real number with imaginary # unit; a+bi. Where a is real part, b is imaginary part and i is imaginary # unit. Real a equals complex a+0i mathematically. # # You can create a Complex object explicitly with: # # * A [complex literal](doc/syntax/literals_rdoc.html#label-Complex+Literals). # # # You can convert certain objects to Complex objects with: # # * Method [Complex](Kernel.html#method-i-Complex). # # # Complex object can be created as literal, and also by using Kernel#Complex, # Complex::rect, Complex::polar or to_c method. # # 2+1i #=> (2+1i) # Complex(1) #=> (1+0i) # Complex(2, 3) #=> (2+3i) # Complex.polar(2, 3) #=> (-1.9799849932008908+0.2822400161197344i) # 3.to_c #=> (3+0i) # # You can also create complex object from floating-point numbers or strings. # # Complex(0.3) #=> (0.3+0i) # Complex('0.3-0.5i') #=> (0.3-0.5i) # Complex('2/3+3/4i') #=> ((2/3)+(3/4)*i) # Complex('1@2') #=> (-0.4161468365471424+0.9092974268256817i) # # 0.3.to_c #=> (0.3+0i) # '0.3-0.5i'.to_c #=> (0.3-0.5i) # '2/3+3/4i'.to_c #=> ((2/3)+(3/4)*i) # '1@2'.to_c #=> (-0.4161468365471424+0.9092974268256817i) # # A complex object is either an exact or an inexact number. # # Complex(1, 1) / 2 #=> ((1/2)+(1/2)*i) # Complex(1, 1) / 2.0 #=> (0.5+0.5i) # class Complex < Numeric # <!-- # rdoc-file=complex.c # - Complex.polar(abs[, arg]) -> complex # --> # Returns a complex object which denotes the given polar form. # # Complex.polar(3, 0) #=> (3.0+0.0i) # Complex.polar(3, Math::PI/2) #=> (1.836909530733566e-16+3.0i) # Complex.polar(3, Math::PI) #=> (-3.0+3.673819061467132e-16i) # Complex.polar(3, -Math::PI/2) #=> (1.836909530733566e-16-3.0i) # def self.polar: (Numeric, ?Numeric) -> Complex # <!-- # rdoc-file=complex.c # - Complex.rect(real[, imag]) -> complex # - Complex.rectangular(real[, imag]) -> complex # --> # Returns a complex object which denotes the given rectangular form. # # Complex.rectangular(1, 2) #=> (1+2i) # def self.rect: (Numeric, ?Numeric) -> Complex # <!-- # rdoc-file=complex.c # - Complex.rect(real[, imag]) -> complex # - Complex.rectangular(real[, imag]) -> complex # --> # Returns a complex object which denotes the given rectangular form. # # Complex.rectangular(1, 2) #=> (1+2i) # alias self.rectangular self.rect public # <!-- # rdoc-file=complex.c # - cmp * numeric -> complex # --> # Performs multiplication. # # Complex(2, 3) * Complex(2, 3) #=> (-5+12i) # Complex(900) * Complex(1) #=> (900+0i) # Complex(-2, 9) * Complex(-9, 2) #=> (0-85i) # Complex(9, 8) * 4 #=> (36+32i) # Complex(20, 9) * 9.8 #=> (196.0+88.2i) # def *: (Numeric) -> Complex # <!-- # rdoc-file=complex.c # - cmp ** numeric -> complex # --> # Performs exponentiation. # # Complex('i') ** 2 #=> (-1+0i) # Complex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i) # def **: (Numeric) -> Complex # <!-- # rdoc-file=complex.c # - cmp + numeric -> complex # --> # Performs addition. # # Complex(2, 3) + Complex(2, 3) #=> (4+6i) # Complex(900) + Complex(1) #=> (901+0i) # Complex(-2, 9) + Complex(-9, 2) #=> (-11+11i) # Complex(9, 8) + 4 #=> (13+8i) # Complex(20, 9) + 9.8 #=> (29.8+9i) # def +: (Numeric) -> Complex def +@: () -> Complex # <!-- # rdoc-file=complex.c # - cmp - numeric -> complex # --> # Performs subtraction. # # Complex(2, 3) - Complex(2, 3) #=> (0+0i) # Complex(900) - Complex(1) #=> (899+0i) # Complex(-2, 9) - Complex(-9, 2) #=> (7+7i) # Complex(9, 8) - 4 #=> (5+8i) # Complex(20, 9) - 9.8 #=> (10.2+9i) # def -: (Numeric) -> Complex # <!-- # rdoc-file=complex.c # - -cmp -> complex # --> # Returns negation of the value. # # -Complex(1, 2) #=> (-1-2i) # def -@: () -> Complex # <!-- # rdoc-file=complex.c # - cmp / numeric -> complex # - cmp.quo(numeric) -> complex # --> # Performs division. # # Complex(2, 3) / Complex(2, 3) #=> ((1/1)+(0/1)*i) # Complex(900) / Complex(1) #=> ((900/1)+(0/1)*i) # Complex(-2, 9) / Complex(-9, 2) #=> ((36/85)-(77/85)*i) # Complex(9, 8) / 4 #=> ((9/4)+(2/1)*i) # Complex(20, 9) / 9.8 #=> (2.0408163265306123+0.9183673469387754i) # def /: (Numeric) -> Complex def <: (Numeric) -> bot def <=: (Numeric) -> bot # <!-- # rdoc-file=complex.c # - cmp <=> object -> 0, 1, -1, or nil # --> # If `cmp`'s imaginary part is zero, and `object` is also a real number (or a # Complex number where the imaginary part is zero), compare the real part of # `cmp` to object. Otherwise, return nil. # # Complex(2, 3) <=> Complex(2, 3) #=> nil # Complex(2, 3) <=> 1 #=> nil # Complex(2) <=> 1 #=> 1 # Complex(2) <=> 2 #=> 0 # Complex(2) <=> 3 #=> -1 # def <=>: (untyped) -> Integer? # <!-- # rdoc-file=complex.c # - cmp == object -> true or false # --> # Returns true if cmp equals object numerically. # # Complex(2, 3) == Complex(2, 3) #=> true # Complex(5) == 5 #=> true # Complex(0) == 0.0 #=> true # Complex('1/3') == 0.33 #=> false # Complex('1/2') == '1/2' #=> false # def ==: (untyped) -> bool def >: (Numeric) -> bot def >=: (Numeric) -> bot # <!-- # rdoc-file=complex.c # - cmp.abs -> real # - cmp.magnitude -> real # --> # Returns the absolute part of its polar form. # # Complex(-1).abs #=> 1 # Complex(3.0, -4.0).abs #=> 5.0 # def abs: () -> Numeric # <!-- # rdoc-file=complex.c # - cmp.abs2 -> real # --> # Returns square of the absolute value. # # Complex(-1).abs2 #=> 1 # Complex(3.0, -4.0).abs2 #=> 25.0 # def abs2: () -> Numeric # <!-- rdoc-file=complex.c --> # Returns the angle part of its polar form. # # Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966 # def angle: () -> Float # <!-- # rdoc-file=complex.c # - cmp.arg -> float # - cmp.angle -> float # - cmp.phase -> float # --> # Returns the angle part of its polar form. # # Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966 # alias arg angle def ceil: (*untyped) -> bot def coerce: (Numeric) -> [ Complex, Complex ] # <!-- rdoc-file=complex.c --> # Returns the complex conjugate. # # Complex(1, 2).conjugate #=> (1-2i) # def conj: () -> Complex # <!-- # rdoc-file=complex.c # - cmp.conj -> complex # - cmp.conjugate -> complex # --> # Returns the complex conjugate. # # Complex(1, 2).conjugate #=> (1-2i) # def conjugate: () -> Complex # <!-- # rdoc-file=complex.c # - cmp.denominator -> integer # --> # Returns the denominator (lcm of both denominator - real and imag). # # See numerator. # def denominator: () -> Integer def div: (Numeric) -> bot def divmod: (Numeric) -> bot def dup: () -> self def eql?: (untyped) -> bool # <!-- # rdoc-file=complex.c # - cmp.fdiv(numeric) -> complex # --> # Performs division as each part is a float, never returns a float. # # Complex(11, 22).fdiv(3) #=> (3.6666666666666665+7.333333333333333i) # def fdiv: (Numeric) -> Complex # <!-- # rdoc-file=complex.c # - cmp.finite? -> true or false # --> # Returns `true` if `cmp`'s real and imaginary parts are both finite numbers, # otherwise returns `false`. # def finite?: () -> bool def floor: (?Integer) -> bot # <!-- # rdoc-file=complex.c # - hash() # --> # def hash: () -> Integer def i: () -> bot # <!-- rdoc-file=complex.c --> # Returns the imaginary part. # # Complex(7).imaginary #=> 0 # Complex(9, -4).imaginary #=> -4 # def imag: () -> Numeric # <!-- # rdoc-file=complex.c # - cmp.imag -> real # - cmp.imaginary -> real # --> # Returns the imaginary part. # # Complex(7).imaginary #=> 0 # Complex(9, -4).imaginary #=> -4 # def imaginary: () -> Numeric # <!-- # rdoc-file=complex.c # - cmp.infinite? -> nil or 1 # --> # Returns `1` if `cmp`'s real or imaginary part is an infinite number, otherwise # returns `nil`. # # For example: # # (1+1i).infinite? #=> nil # (Float::INFINITY + 1i).infinite? #=> 1 # def infinite?: () -> Integer? # <!-- # rdoc-file=complex.c # - cmp.inspect -> string # --> # Returns the value as a string for inspection. # # Complex(2).inspect #=> "(2+0i)" # Complex('-8/6').inspect #=> "((-4/3)+0i)" # Complex('1/2i').inspect #=> "(0+(1/2)*i)" # Complex(0, Float::INFINITY).inspect #=> "(0+Infinity*i)" # Complex(Float::NAN, Float::NAN).inspect #=> "(NaN+NaN*i)" # def inspect: () -> String def integer?: () -> bool # <!-- rdoc-file=complex.c --> # Returns the absolute part of its polar form. # # Complex(-1).abs #=> 1 # Complex(3.0, -4.0).abs #=> 5.0 # alias magnitude abs def modulo: (Numeric) -> bot def negative?: () -> bot def nonzero?: () -> self? # <!-- # rdoc-file=complex.c # - cmp.numerator -> numeric # --> # Returns the numerator. # # 1 2 3+4i <- numerator # - + -i -> ---- # 2 3 6 <- denominator # # c = Complex('1/2+2/3i') #=> ((1/2)+(2/3)*i) # n = c.numerator #=> (3+4i) # d = c.denominator #=> 6 # n / d #=> ((1/2)+(2/3)*i) # Complex(Rational(n.real, d), Rational(n.imag, d)) # #=> ((1/2)+(2/3)*i) # # See denominator. # def numerator: () -> Complex # <!-- rdoc-file=complex.c --> # Returns the angle part of its polar form. # # Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966 # alias phase angle # <!-- # rdoc-file=complex.c # - cmp.polar -> array # --> # Returns an array; [cmp.abs, cmp.arg]. # # Complex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904] # def polar: () -> [ Numeric, Float ] def positive?: () -> bot # <!-- # rdoc-file=complex.c # - cmp / numeric -> complex # - cmp.quo(numeric) -> complex # --> # Performs division. # # Complex(2, 3) / Complex(2, 3) #=> ((1/1)+(0/1)*i) # Complex(900) / Complex(1) #=> ((900/1)+(0/1)*i) # Complex(-2, 9) / Complex(-9, 2) #=> ((36/85)-(77/85)*i) # Complex(9, 8) / 4 #=> ((9/4)+(2/1)*i) # Complex(20, 9) / 9.8 #=> (2.0408163265306123+0.9183673469387754i) # def quo: (Numeric) -> Complex # <!-- # rdoc-file=complex.c # - cmp.rationalize([eps]) -> rational # --> # Returns the value as a rational if possible (the imaginary part should be # exactly zero). # # Complex(1.0/3, 0).rationalize #=> (1/3) # Complex(1, 0.0).rationalize # RangeError # Complex(1, 2).rationalize # RangeError # # See to_r. # def rationalize: (?Numeric eps) -> Rational # <!-- # rdoc-file=complex.c # - cmp.real -> real # --> # Returns the real part. # # Complex(7).real #=> 7 # Complex(9, -4).real #=> 9 # def real: () -> Numeric # <!-- # rdoc-file=complex.c # - Complex(1).real? -> false # - Complex(1, 2).real? -> false # --> # Returns false, even if the complex number has no imaginary part. # def real?: () -> false # <!-- rdoc-file=complex.c --> # Returns a complex object which denotes the given rectangular form. # # Complex.rectangular(1, 2) #=> (1+2i) # def rect: () -> [ Numeric, Numeric ] # <!-- # rdoc-file=complex.c # - cmp.rect -> array # - cmp.rectangular -> array # --> # Returns an array; [cmp.real, cmp.imag]. # # Complex(1, 2).rectangular #=> [1, 2] # alias rectangular rect def reminder: (Numeric) -> bot def round: (*untyped) -> bot def step: (*untyped) ?{ (*untyped) -> untyped } -> bot # <!-- # rdoc-file=complex.c # - complex.to_c -> self # --> # Returns self. # # Complex(2).to_c #=> (2+0i) # Complex(-8, 6).to_c #=> (-8+6i) # def to_c: () -> Complex # <!-- # rdoc-file=complex.c # - cmp.to_f -> float # --> # Returns the value as a float if possible (the imaginary part should be exactly # zero). # # Complex(1, 0).to_f #=> 1.0 # Complex(1, 0.0).to_f # RangeError # Complex(1, 2).to_f # RangeError # def to_f: () -> Float # <!-- # rdoc-file=complex.c # - cmp.to_i -> integer # --> # Returns the value as an integer if possible (the imaginary part should be # exactly zero). # # Complex(1, 0).to_i #=> 1 # Complex(1, 0.0).to_i # RangeError # Complex(1, 2).to_i # RangeError # def to_i: () -> Integer alias to_int to_i # <!-- # rdoc-file=complex.c # - cmp.to_r -> rational # --> # Returns the value as a rational if possible (the imaginary part should be # exactly zero). # # Complex(1, 0).to_r #=> (1/1) # Complex(1, 0.0).to_r # RangeError # Complex(1, 2).to_r # RangeError # # See rationalize. # def to_r: () -> Rational # <!-- # rdoc-file=complex.c # - cmp.to_s -> string # --> # Returns the value as a string. # # Complex(2).to_s #=> "2+0i" # Complex('-8/6').to_s #=> "-4/3+0i" # Complex('1/2i').to_s #=> "0+1/2i" # Complex(0, Float::INFINITY).to_s #=> "0+Infinity*i" # Complex(Float::NAN, Float::NAN).to_s #=> "NaN+NaN*i" # def to_s: () -> String def truncate: (?Integer) -> bot def zero?: () -> bool end # <!-- rdoc-file=complex.c --> # The imaginary unit. # Complex::I: Complex