=================================================================== RCS file: /home/cvs/OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v retrieving revision 1.7 retrieving revision 1.11 diff -u -p -r1.7 -r1.11 --- OpenXM/doc/OpenXM-specs/cmo-basic1.tex 2000/01/24 12:32:49 1.7 +++ OpenXM/doc/OpenXM-specs/cmo-basic1.tex 2001/08/27 05:39:15 1.11 @@ -1,4 +1,4 @@ -%% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.6 2000/01/24 07:49:58 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 } //&eg \section{ CMOexpressions for numbers and polynomials } \label{sec:basic1} @@ -64,9 +64,11 @@ ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B \mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ & & \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 -{\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{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{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ & & \mbox{ --- $a/b$ を表す. } \\ @@ -84,9 +86,11 @@ ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B \mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ & & \mbox{ --- Universal zero } \\ \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{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} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ & & \mbox{ --- Rational expression $a/b$. } \\ @@ -99,6 +103,7 @@ ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B */ /*&jp +\subsection{Indeterminate および Tree} 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, 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. @@ -110,6 +115,7 @@ 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.) */ /*&eg +\subsection{Indetermnate and Tree} Indeterminate is a name of a variable. v may be any sequence of bytes, but each system has its own restrictions on the names of variables. @@ -124,10 +130,10 @@ Group CMObject/Tree requires CMObject/Basic. \\ Tree, Lambda $\in$ CMObject/Basic. \\ \begin{eqnarray*} \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{ --- cdname は空文字列でなければ name の意味が説明されている }\\ -& & \mbox{ --- OpenMath CD (content dictionary) の名前. } \\ +& & \mbox{ --- attributes は空リストでなければ name の属性を保持している. }\\ +& & \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}, {\sl Tree} {\rm body}) \\ & & \mbox{ --- body を args を引数とする関数とする. } \\ @@ -141,10 +147,10 @@ Group CMObject/Tree requires CMObject/Basic. \\ Tree, Lambda $\in$ CMObject/Basic. \\ \begin{eqnarray*} \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{ --- cdname may be a null. If it is not null, it is the name of}\\ -& & \mbox{ --- the OpenMath CD (content dictionary). } \\ +& & \mbox{ --- attributes may be a null list. If it is not null, it is a list of}\\ +& & \mbox{ --- key and value pairs. } \\ \mbox{Lambda} &:& ({\tt CMO\_LAMBDA}, {\sl List}\, {\rm args}, {\sl Tree} {\rm body}) \\ & & \mbox{ --- a function with the arguments body. } \\ @@ -208,7 +214,9 @@ It is the same as the Lambda expression in Lisp. //&jp 例: $sin(x+e)$ の表現. //&eg Example: the expression of $sin(x+e)$. \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_TREE, (CMO_STRING, "plus"), (CMO_STRING, "basic"), (CMO_LIST,[size=]2, (CMO_INDETERMINATE,"x"), @@ -219,12 +227,14 @@ It is the same as the Lambda expression in Lisp. ) ) \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 Example: \begin{verbatim} sm1> [(plus) (Basic) [(123).. (345)..]] [(class) (tree)] dc :: -Class.tree [ $plus$ , $Basic$ , [ 123 , 345 ] ] +Class.tree [ $plus$ , $basic$ , [ 123 , 345 ] ] \end{verbatim} @@ -551,7 +561,7 @@ $\in$ CMObject/RecursivePolynomial \\ \mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ \mbox{RringDefinition} & : & \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. } \\ \end{eqnarray*} */ @@ -581,7 +591,7 @@ $\in$ CMObject/RecursivePolynomial \\ \mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ \mbox{RringDefinition} & : & \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. } \\ \end{eqnarray*} */