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In message "[ruby-dev:5840] Re: Precision in Mathematica (Re: Bigfloat)"
    on 99/03/01, 石塚圭樹 <keiju@Rational.Com> writes:

>>ですね．石塚さんの4つの案を検討中です．
># 4つもあったかな??

# 4つ目ありがとうです (^^;; 

>SetAccuracyはいらないかなって気がしますね.
>SetPrecisionはprecの枠組にはいると嬉しいですよね.
>float.prec(Bigfloat, 1000)
>とか. 

まぁそうなんですが，prec のシグニチャを安易に2以上にして
いいのかどうかで悩んでます．また accuracy はいうなれば
絶対的な正しさをあたえるので，下の話とは関係あります．

>>また Rational.induced_from(complex) はどうするのかという
>>問題もあります．ちなみに Mathematica の Rationalize[complex] は
>>我々(?)の考える complex.prec(Rational) 相当で，実部と虚部を
>>Rational にします．それと，PI なんてものが現れた場合に備え
>>Rational.induced_from もしくは Rational[] で許容誤差を
>>与える方法も考えなければなりません．今までの案では関数の
>>オプションがもっとも適切に見えます．
>
>これって,
>
>  Rationalize[0.1] ==> 1/10
>  Rationalize[Pi] ==> Pi (円周率πに充分近い有理数は無い)
>  Rationalize[Pi, 1/9] ==> 22/7
>  Rationalize[Pi, 10^-10] ==> 21053343141/6701487259
>
>これの話しですよね? Piはともかく

です．

>  Rationalize[0.1, 10^-32]
>
>とかすると, すごい分母の分数になる??

Mathematica だと 0.1 はあくまで 1/10 です．
# 2進数を意識させない作りなので．
結局，0.1 をどうとらえるかの問題で，10進16桁と思えば 1/10 
だけど，2進52+1桁と思えば凄い分母ですね．

一つの考え方としては，prec の引数は好きに使うという
もので，例えば，prec(Rational, 10e-30) とか 
prec(Bigfloat, 100) とかですね．これの欠点は第2引数を
渡すインターフェイスを考えないといけないことと，
第1引数で第2引数の意味が変わって分かりにくいことです．

もっといい案がありそうな気もしますが，まだ分からない．
今のところ必要なのは，最大誤差と有効桁を指定すること
だからこれらを指定する方法があればいいのかも知れません．
ただ，返す値として Bigfloat 以上に適切なものが思い付き
ません(Mathematica の影響か)．

もう一つの思考を停止させる方法としては，Mathematica
というモジュールを作ってそいつで Bigfloat までの面倒を
みるというものがあります．

Mathematica.set_precision(float, 50)
Mathematica.rationalize(x, max_error)

とか(^^;;

-- gotoken

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