| version 1.6, 2000/01/24 07:49:58 |
version 1.11, 2001/08/27 05:39:15 |
|
|
| %% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.5 2000/01/24 07:36:35 noro Exp $ |
%% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.10 2001/04/10 11:56:29 takayama Exp $ |
| //&jp \section{ 数, 多項式 の CMO 表現 } |
//&jp \section{ 数, 多項式 の CMO 表現 } |
| //&eg \section{ CMOexpressions for numbers and polynomials } |
//&eg \section{ CMOexpressions for numbers and polynomials } |
| \label{sec:basic1} |
\label{sec:basic1} |
| Line 64 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
|
| Line 64 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
|
| \mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
\mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
| & & \mbox{ --- ユニバーサルな ゼロを表す. } \\ |
& & \mbox{ --- ユニバーサルな ゼロを表す. } \\ |
| \mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
\mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
| {\sl byte}\, \mbox{a[m]} ) \\ |
{\sl byte}\, \mbox{a[$|$f$|$]} ) \\ |
| &:& \mbox{ --- bignum をあらわす. a[i] についてはあとで説明}\\ |
&:& \mbox{ --- bignum をあらわす. a[i] についてはあとで説明}\\ |
| \mbox{QQ} &:& ({\tt CMO\_QQ}, {\sl ZZ}\, {\rm a}, {\sl ZZ}\, {\rm b}) \\ |
\mbox{QQ} &:& ({\tt CMO\_QQ}, |
| |
{\sl int32}\, {\rm m}, {\sl byte}\, \mbox{a[1]}, \ldots, {\sl byte}\, \mbox{a[$|$m$|$]}, |
| |
{\sl int32}\, {\rm n}, {\sl byte}\, \mbox{b[1]}, \ldots, {\sl byte}\, \mbox{b[$|$n$|$]})\\ |
| & & \mbox{ --- 有理数 $a/b$ を表す. } \\ |
& & \mbox{ --- 有理数 $a/b$ を表す. } \\ |
| \mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
\mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
| & & \mbox{ --- $a/b$ を表す. } \\ |
& & \mbox{ --- $a/b$ を表す. } \\ |
| Line 84 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
|
| Line 86 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
|
| \mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
\mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
| & & \mbox{ --- Universal zero } \\ |
& & \mbox{ --- Universal zero } \\ |
| \mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
\mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
| {\sl byte}\, \mbox{a[m]} ) \\ |
{\sl byte}\, \mbox{a[$|$m$|$]} ) \\ |
| &:& \mbox{ --- bignum. The meaning of a[i] will be explained later.}\\ |
&:& \mbox{ --- bignum. The meaning of a[i] will be explained later.}\\ |
| \mbox{QQ} &:& ({\tt CMO\_QQ}, {\sl ZZ}\, {\rm a}, {\sl ZZ}\, {\rm b}) \\ |
\mbox{QQ} &:& ({\tt CMO\_QQ}, |
| |
{\sl int32}\, {\rm m}, {\sl byte}\, \mbox{a[1]}, \ldots, {\sl byte}\, \mbox{a[$|$m$|$]}, |
| |
{\sl int32}\, {\rm n}, {\sl byte}\, \mbox{b[1]}, \ldots, {\sl byte}\, \mbox{b[$|$n$|$]})\\ |
| & & \mbox{ --- Rational number $a/b$. } \\ |
& & \mbox{ --- Rational number $a/b$. } \\ |
| \mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
\mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
| & & \mbox{ --- Rational expression $a/b$. } \\ |
& & \mbox{ --- Rational expression $a/b$. } \\ |
| Line 99 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
|
| Line 103 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
|
| */ |
*/ |
| |
|
| /*&jp |
/*&jp |
| |
\subsection{Indeterminate および Tree} |
| Indeterminate は変数名をあらわす. |
Indeterminate は変数名をあらわす. |
| v はバイト列であればなにを用いてもよいが, |
v はバイト列であればなにを用いてもよいが, |
| システム毎に変数名として用いられるバイト列は制限がある. |
システム毎に変数名として用いられるバイト列は制限がある. |
| Line 110 escape sequence を用いて実現するのは, 無理があるようで |
|
| Line 115 escape sequence を用いて実現するのは, 無理があるようで |
|
| テーブルを作成する必要があるであろう.) |
テーブルを作成する必要があるであろう.) |
| */ |
*/ |
| /*&eg |
/*&eg |
| |
\subsection{Indetermnate and Tree} |
| Indeterminate is a name of a variable. |
Indeterminate is a name of a variable. |
| v may be any sequence of bytes, but each system has its own |
v may be any sequence of bytes, but each system has its own |
| restrictions on the names of variables. |
restrictions on the names of variables. |
| Line 124 Group CMObject/Tree requires CMObject/Basic. \\ |
|
| Line 130 Group CMObject/Tree requires CMObject/Basic. \\ |
|
| Tree, Lambda $\in$ CMObject/Basic. \\ |
Tree, Lambda $\in$ CMObject/Basic. \\ |
| \begin{eqnarray*} |
\begin{eqnarray*} |
| \mbox{Tree} &:& ({\tt CMO\_TREE}, {\sl Cstring}\, {\rm name}, |
\mbox{Tree} &:& ({\tt CMO\_TREE}, {\sl Cstring}\, {\rm name}, |
| {\sl Cstring}\, {\rm cdname}, {\sl List}\, {\rm leaves}) \\ |
{\sl List}\, {\rm attributes}, {\sl List}\, {\rm leaves}) \\ |
| & & \mbox{ --- 名前 name の定数または関数. 関数の評価はおこなわない. } \\ |
& & \mbox{ --- 名前 name の定数または関数. 関数の評価はおこなわない. } \\ |
| & & \mbox{ --- cdname は空文字列でなければ name の意味が説明されている }\\ |
& & \mbox{ --- attributes は空リストでなければ name の属性を保持している. }\\ |
| & & \mbox{ --- OpenMath CD (content dictionary) の名前. } \\ |
& & \mbox{ --- 属性リストは, key と 値のペアである. }\\ |
| \mbox{Lambda} &:& ({\tt CMO\_LAMBDA}, {\sl List}\, {\rm args}, |
\mbox{Lambda} &:& ({\tt CMO\_LAMBDA}, {\sl List}\, {\rm args}, |
| {\sl Tree} {\rm body}) \\ |
{\sl Tree} {\rm body}) \\ |
| & & \mbox{ --- body を args を引数とする関数とする. } \\ |
& & \mbox{ --- body を args を引数とする関数とする. } \\ |
| Line 141 Group CMObject/Tree requires CMObject/Basic. \\ |
|
| Line 147 Group CMObject/Tree requires CMObject/Basic. \\ |
|
| Tree, Lambda $\in$ CMObject/Basic. \\ |
Tree, Lambda $\in$ CMObject/Basic. \\ |
| \begin{eqnarray*} |
\begin{eqnarray*} |
| \mbox{Tree} &:& ({\tt CMO\_TREE}, {\sl Cstring}\, {\rm name}, |
\mbox{Tree} &:& ({\tt CMO\_TREE}, {\sl Cstring}\, {\rm name}, |
| {\sl Cstring}\, {\rm cdname}, {\sl List}\, {\rm leaves}) \\ |
{\sl List}\, {\rm attributes}, {\sl List}\, {\rm leaves}) \\ |
| & & \mbox{ --- A function or a constant of name. Functions are not evaluated. } \\ |
& & \mbox{ --- A function or a constant of name. Functions are not evaluated. } \\ |
| & & \mbox{ --- cdname may be a null. If it is not null, it is the name of}\\ |
& & \mbox{ --- attributes may be a null list. If it is not null, it is a list of}\\ |
| & & \mbox{ --- the OpenMath CD (content dictionary). } \\ |
& & \mbox{ --- key and value pairs. } \\ |
| \mbox{Lambda} &:& ({\tt CMO\_LAMBDA}, {\sl List}\, {\rm args}, |
\mbox{Lambda} &:& ({\tt CMO\_LAMBDA}, {\sl List}\, {\rm args}, |
| {\sl Tree} {\rm body}) \\ |
{\sl Tree} {\rm body}) \\ |
| & & \mbox{ --- a function with the arguments body. } \\ |
& & \mbox{ --- a function with the arguments body. } \\ |
| Line 185 stack machine commands for delayed evaluation. |
|
| Line 191 stack machine commands for delayed evaluation. |
|
| However it makes the implementation of stack machines complicated. |
However it makes the implementation of stack machines complicated. |
| It is desirable that CMObject is independent of OX stack machine. |
It is desirable that CMObject is independent of OX stack machine. |
| Therefore we introduce an OpenMath like tree representation for CMO |
Therefore we introduce an OpenMath like tree representation for CMO |
| tree object. |
Tree object. |
| This method allows us to implement tree structure easily |
This method allows us to implement tree structure easily |
| on individual OpenXM systems. |
on individual OpenXM systems. |
| Note that CMO Tree corresponds to Symbol and Application in OpenMath. |
Note that CMO Tree corresponds to Symbol and Application in OpenMath. |
| Line 208 It is the same as the Lambda expression in Lisp. |
|
| Line 214 It is the same as the Lambda expression in Lisp. |
|
| //&jp 例: $sin(x+e)$ の表現. |
//&jp 例: $sin(x+e)$ の表現. |
| //&eg Example: the expression of $sin(x+e)$. |
//&eg Example: the expression of $sin(x+e)$. |
| \begin{verbatim} |
\begin{verbatim} |
| (CMO_TREE, (CMO_STRING, "sin"), (CMO_STRING, "basic"), |
(CMO_TREE, (CMO_STRING, "sin"), |
| |
(CMO_LIST,[size=]1,(CMO_LIST,[size=]2,(CMO_STRING, "cdname"), |
| |
(CMO_STRING,"basic"))) |
| (CMO_LIST,[size=]1, |
(CMO_LIST,[size=]1, |
| (CMO_TREE, (CMO_STRING, "plus"), (CMO_STRING, "basic"), |
(CMO_TREE, (CMO_STRING, "plus"), (CMO_STRING, "basic"), |
| (CMO_LIST,[size=]2, (CMO_INDETERMINATE,"x"), |
(CMO_LIST,[size=]2, (CMO_INDETERMINATE,"x"), |
| Line 219 It is the same as the Lambda expression in Lisp. |
|
| Line 227 It is the same as the Lambda expression in Lisp. |
|
| ) |
) |
| ) |
) |
| \end{verbatim} |
\end{verbatim} |
| |
//&jp Leave の成分には, 多項式を含む任意のオブジェクトがきてよい. |
| |
//&eg Elements of the leave may be any objects including polynomials. |
| |
|
| \noindent |
\noindent |
| Example: |
Example: |
| \begin{verbatim} |
\begin{verbatim} |
| sm1> [(plus) (Basic) [(123).. (345)..]] [(class) (tree)] dc :: |
sm1> [(plus) (Basic) [(123).. (345)..]] [(class) (tree)] dc :: |
| Class.tree [ $plus$ , $Basic$ , [ 123 , 345 ] ] |
Class.tree [ $plus$ , $basic$ , [ 123 , 345 ] ] |
| \end{verbatim} |
\end{verbatim} |
| |
|
| |
|
| Line 551 $\in$ CMObject/RecursivePolynomial \\ |
|
| Line 561 $\in$ CMObject/RecursivePolynomial \\ |
|
| \mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
\mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
| \mbox{RringDefinition} |
\mbox{RringDefinition} |
| & : & \mbox{ {\sl List} v } \\ |
& : & \mbox{ {\sl List} v } \\ |
| & & \quad \mbox{ --- v は, 変数名(indeterminate) のリスト. } \\ |
& & \quad \mbox{ --- v は, 変数名(indeterminate) または Tree のリスト. } \\ |
| & & \quad \mbox{ --- 順序の高い順. } \\ |
& & \quad \mbox{ --- 順序の高い順. } \\ |
| \end{eqnarray*} |
\end{eqnarray*} |
| */ |
*/ |
| Line 581 $\in$ CMObject/RecursivePolynomial \\ |
|
| Line 591 $\in$ CMObject/RecursivePolynomial \\ |
|
| \mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
\mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
| \mbox{RringDefinition} |
\mbox{RringDefinition} |
| & : & \mbox{ {\sl List} v } \\ |
& : & \mbox{ {\sl List} v } \\ |
| & & \quad \mbox{ --- v is a list of names of indeterminates. } \\ |
& & \quad \mbox{ --- v is a list of names of indeterminates or trees. } \\ |
| & & \quad \mbox{ --- It is sorted in the decreasing order. } \\ |
& & \quad \mbox{ --- It is sorted in the decreasing order. } \\ |
| \end{eqnarray*} |
\end{eqnarray*} |
| */ |
*/ |
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to cmo-basic1.tex CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / doc / OpenXM-specs