
[index-ja]

Algebra::LocalizedRing

(ɽ경ĥ饹)

Ϳ줿ĤʬҡʬˤʬĤޤºݤΥ饹ˤϡ
饹᥽å ::create 뤤ϴؿ Algebra.LocalizedRing() Ѥޤ

ե̾:

  localized-ring.rb

ѡ饹:

  Object

󥯥롼ɤƤ⥸塼:

ʤ

Ϣؿ:

Algebra.LocalizedRing(ring)
    ::create(ring) ƱǤ
   
Algebra.RationalFunctionField(ring, obj)
     ringѿɽ֥Ȥ obj ȤͭؿΤޤ饹
    å ::var ѿ뤳ȤǤޤ
   
    : ¿༰Ĥξ
    require "localized-ring"
    F = RationalFunctionField(Integer, "x")
    x = F.var
    p ( 1 / (x**2 - 1) - 1 / (x**3 - 1) )
      #=> (x^3 - x^2)/(x^5 - x^3 - x^2 + 1)
   

饹᥽å:

::create(ring)
    饹ringɽĤθʬҡʬȤʬĤޤ
   
    ͤ Algebra::LocalizedRing 饹Υ֥饹ǤΥ֥饹
    ˤϥ饹᥽åɤȤ ::ground  ring ֤ޤ
   
    饹ˤϥ饹᥽å::[]졢ôĤθ x Фʬ
    θ x/1 ֤ޤ
   
    : ͭ
    require "localized-ring"
    F = Algebra.LocalizedRing(Integer)
    p F.new(1, 2) + F.new(2, 3) #=> 7/6
   
    : ¿༰Ĥξ
    require "polynomial"
    require "localized-ring"
    P = Algebra.Polynomial(Integer, "x")
    F = Algebra.LocalizedRing(P)
    x = F[P.var]
    p ( 1 / (x**2 - 1) - 1 / (x**3 - 1) )
      #=> (x^3 - x^2)/(x^5 - x^3 - x^2 + 1)
   
::zero
    ֤ޤ
   
::unity
    ñ̸֤ޤ
   

᥽å:

zero?
    ǤȤ֤ޤ
   
zero
    ֤ޤ
   
unity
    ñ̸֤ޤ
   
==(other)
    Ȥ֤ޤ
   
<=>(other)
    羮طޤ
   
+(other)
    ¤׻ޤ
   
-(other)
    ׻ޤ
   
*(other)
    Ѥ׻ޤ
   
**(n)
    n ׻ޤ
   
/(other)
    ׻ޤ
   

