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version 1.8, 2000/02/28 14:10:27 version 1.10, 2001/04/10 11:56:29
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 %% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.7 2000/01/24 12:32:49 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 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:
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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