ruby-dev

けいじゅ＠日本ラショナルソフトウェアです.

In [ruby-dev :5816 ] the message: "[ruby-dev:5816] Re: Precision in
Mathematica (Re: Bigfloat) ", on Mar/01 14:30(JST) GOTO Kentaro
writes:

>ごとけんです

>>演算後に得られた値に対しての精度の計算方法が
>>問題になりそうだと言う事ですね。
>
>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??

># ちなみにワタクシの精度に関する気持の変化を表明して
># おきますと，Integer と Rational は誤差が0という意味で
># 無限精度だというのを認めますです(^^;;

おお. やった!!

># ただし，豊福さんが例としてあげた RationalOddDenomi 
># とかも同様なんですが，なにか Integer や Rational に
># 対しては歯抜けのような印象をいまだにもってます．
># どう頑張っても計算可能な範囲では歯抜けは必至なんだけど．

>Mathematica の SetPrecision や SetAccuracy は
>必要なのかというのと，Rational.induced_from(float) の
>動作がどうあるべきかなどを決め兼ねています．

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. 

>Bigfloat を頑張って組み込みにするなら(Math も頑張る必要が
>あります)，Bigfloat か Doublefloat を返す Numeric に
>set_prec や set_accuracy があっても良いような気もしますし，
>Rational.induced_from(float) はリテラルとの相性を踏まえ
>float の仮数10進16桁に対して行ったほうがよいような気も
>してます．

通常の動作としてはそうなんでしょうけども...

>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

  Rationalize[0.1, 10^-32]

とかすると, すごい分母の分数になる??

__
................................石塚 圭樹＠日本ラショナルソフトェア...
----------------------------------->> e-mail: keiju@rational.com <<---

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[#5868] Re: Precision in Mathematica (Re: Bigfloat) — "豊福" <toyofuku@...>

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