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/opt/alt/ruby21/share/ri/2.1.0/system/Rational/

//opt/alt/ruby21/share/ri/2.1.0/system/Rational/cdesc-Rational.ri

U:RDoc::NormalClass[iI" Rational:ET@I"Numeric;To:RDoc::Markup::Document:@parts[ o;;[o:RDoc::Markup::Paragraph;[I"NBigDecimal extends the native Rational class to provide the #to_d method.;To:RDoc::Markup::BlankLine�o; ;[I"JWhen you require BigDecimal in your application, this method will be ;TI"#available on Rational objects.;T: @fileI"*ext/bigdecimal/lib/bigdecimal/util.rb;T:0@omit_headings_from_table_of_contents_below0o;;[�;I"&ext/json/lib/json/add/rational.rb;T;0o;;[ o; ;[I"PWhen mathn is required Rational is changed to simplify the use of Rational ;TI"operations.;T@o; ;[I"Normal behaviour:;T@o:RDoc::Markup::Verbatim;[I"1Rational.new!(1,3) ** 2 # => Rational(1, 9) ;TI"$(1 / 3) ** 2 # => 0 ;T:@format0o; ;[I"require 'mathn' behaviour:;T@o; ;[I"%(1 / 3) ** 2 # => 1/9;T;0;I"lib/mathn.rb;T;0o;;[o; ;[I"FA rational number can be represented as a paired integer number; ;TI"Ga/b (b>0). Where a is numerator and b is denominator. Integer a ;TI"(equals rational a/1 mathematically.;T@o; ;[I"BIn ruby, you can create rational object with Rational, to_r, ;TI"\rationalize method or suffixing r to a literal. The return values will be irreducible.;T@o; ;[ I" Rational(1) #=> (1/1) ;TI" Rational(2, 3) #=> (2/3) ;TI"!Rational(4, -6) #=> (-2/3) ;TI" 3.to_r #=> (3/1) ;TI" 2/3r #=> (2/3) ;T;0o; ;[I"HYou can also create rational object from floating-point numbers or ;TI" strings.;T@o; ;[ I"?Rational(0.3) #=> (5404319552844595/18014398509481984) ;TI"!Rational('0.3') #=> (3/10) ;TI" Rational('2/3') #=> (2/3) ;TI" ;TI"?0.3.to_r #=> (5404319552844595/18014398509481984) ;TI"!'0.3'.to_r #=> (3/10) ;TI" '2/3'.to_r #=> (2/3) ;TI"!0.3.rationalize #=> (3/10) ;T;0o; ;[I"DA rational object is an exact number, which helps you to write ;TI")program without any rounding errors.;T@o; ;[I"J10.times.inject(0){|t,| t + 0.1} #=> 0.9999999999999999 ;TI"=10.times.inject(0){|t,| t + Rational('0.1')} #=> (1/1) ;T;0o; ;[I"HHowever, when an expression has inexact factor (numerical value or ;TI"0operation), will produce an inexact result.;T@o; ;[ I"#Rational(10) / 3 #=> (10/3) ;TI"/Rational(10) / 3.0 #=> 3.3333333333333335 ;TI" ;TI"$Rational(-8) ** Rational(1, 3) ;TI"D #=> (1.0000000000000002+1.7320508075688772i);T;0;I"rational.c;T;0;0;0[�[�[�[[I" class;T[[:public[[I"json_create;FI"&ext/json/lib/json/add/rational.rb;T[:protected[�[:private[�[I" instance;T[[;[[I"*;TI"rational.c;T[I"**;TI"lib/mathn.rb;T[I"+;T@x[I"-;T@x[I"/;T@x[I"<=>;T@x[I"==;T@x[I"as_json;F@l[I" ceil;T@x[I"denominator;T@x[I" fdiv;T@x[I" floor;T@x[I"inspect;T@x[I"numerator;T@x[I"quo;T@x[I"rationalize;T@x[I" round;T@x[I" to_d;FI"*ext/bigdecimal/lib/bigdecimal/util.rb;T[I" to_f;T@x[I" to_i;T@x[I"to_json;F@l[I" to_r;T@x[I" to_s;T@x[I" truncate;T@x[;[�[;[�[�[U:RDoc::Context::Section[i�0o;;[�;0;0[ @@@,@`@`cRDoc::TopLevel