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version 1.6, 2000/01/24 07:49:58 version 1.10, 2001/04/10 11:56:29
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 %% $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 1.9 2000/09/12 23:09:18 noro 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 185  stack machine commands for delayed evaluation.
Line 189  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 219  It is the same as the Lambda expression in Lisp.
Line 223  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 557  $\in$ 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 587  $\in$ 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*}
 */  */
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