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Diff for /OpenXM/src/asir-doc/parts/builtin/array.texi between version 1.11 and 1.14

version 1.11, 2009/03/24 08:00:50 version 1.14, 2011/12/09 05:13:52
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.10 2005/02/10 04:59:21 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.13 2009/03/24 17:02:06 ohara Exp $
 \BJP  \BJP
 @node $BG[Ns(B,,, $BAH$_9~$_H!?t(B  @node $BG[Ns(B,,, $BAH$_9~$_H!?t(B
 @section $BG[Ns(B  @section $BG[Ns(B
Line 14 
Line 14 
 * vtol::  * vtol::
 * newbytearray::  * newbytearray::
 * newmat matrix::  * newmat matrix::
   * mat matr matc::
 * size::  * size::
 * det nd_det invmat::  * det nd_det invmat::
   * rowx rowm rowa colx colm cola::
   
 * qsort::  * qsort::
 @end menu  @end menu
Line 167  separated simply by a `blank space', while those of a 
Line 169  separated simply by a `blank space', while those of a 
 @table @t  @table @t
 \JP @item $B;2>H(B  \JP @item $B;2>H(B
 \EG @item References  \EG @item References
 @fref{newmat}, @fref{size}, @fref{ltov}, @fref{vtol}.  @fref{newmat matrix}, @fref{size}, @fref{ltov}, @fref{vtol}.
 @end table  @end table
   
 \JP @node ltov,,, $BG[Ns(B  \JP @node ltov,,, $BG[Ns(B
Line 213  See also @code{newvect()}.
Line 215  See also @code{newvect()}.
 @table @t  @table @t
 \JP @item $B;2>H(B  \JP @item $B;2>H(B
 \EG @item References  \EG @item References
 @fref{newvect}, @fref{vtol}.  @fref{newvect vector vect}, @fref{vtol}.
 @end table  @end table
   
 \JP @node vtol,,, $BG[Ns(B  \JP @node vtol,,, $BG[Ns(B
Line 263  A conversion from a list to a vector is done by @code{
Line 265  A conversion from a list to a vector is done by @code{
 @table @t  @table @t
 \JP @item $B;2>H(B  \JP @item $B;2>H(B
 \EG @item References  \EG @item References
 @fref{newvect}, @fref{ltov}.  @fref{newvect vector vect}, @fref{ltov}.
 @end table  @end table
   
 \JP @node newbytearray,,, $BG[Ns(B  \JP @node newbytearray,,, $BG[Ns(B
Line 319  similar to that of @code{newvect}.
Line 321  similar to that of @code{newvect}.
 @table @t  @table @t
 \JP @item $B;2>H(B  \JP @item $B;2>H(B
 \EG @item References  \EG @item References
 @fref{newvect}.  @fref{newvect vector vect}.
 @end table  @end table
   
 \JP @node newmat matrix,,, $BG[Ns(B  \JP @node newmat matrix,,, $BG[Ns(B
Line 412  return to toplevel
Line 414  return to toplevel
 @table @t  @table @t
 \JP @item $B;2>H(B  \JP @item $B;2>H(B
 \EG @item References  \EG @item References
 @fref{newvect}, @fref{size}, @fref{det nd_det invmat}.  @fref{newvect vector vect}, @fref{size}, @fref{det nd_det invmat}.
 @end table  @end table
   
   \JP @node mat matr matc,,, $BG[Ns(B
   \EG @node mat matr matc,,, Arrays
   @subsection @code{mat}, @code{matr}, @code{matc}
   @findex mat
   @findex matr
   @findex matc
   
   @table @t
   @item mat(@var{vector}[,...])
   @item matr(@var{vector}[,...])
   \JP :: $B9T%Y%/%H%k$NJB$S$+$i9TNs$r@8@.$9$k(B.
   \EG :: Creates a new matrix by list of row vectors.
   @item matc(@var{vector}[,...])
   \JP :: $BNs%Y%/%H%k$NJB$S$+$i9TNs$r@8@.$9$k(B.
   \EG :: Creates a new matrix by list of column vectors.
   @end table
   
   @table @var
   @item return
   \JP $B9TNs(B
   \EG matrix
   @item @var{vector}
   \JP $BG[Ns$^$?$O%j%9%H(B
   \EG array or list
   @end table
   
   @itemize @bullet
   \BJP
   @item
   @code{mat} $B$O(B @code{matr} $B$NJLL>$G$"$k(B.
   @item
   $B0z?t$N3F%Y%/%H%k$OF1$8D9$5$r$b$D(B.
   $B3FMWAG$O(B, $B@hF,$+$i=g$K;H$o$l(B, $BB-$j$J$$J,$O(B 0 $B$,Kd$a$i$l$k(B.
   \E
   \BEG
   @item
   @code{mat} is an alias of @code{matr}.
   @item
   Each vector has same length.
   Elements are used from the first through the last.
   If the list is short, 0's are filled in the remaining matrix elements.
   \E
   @end itemize
   
   @example
   [0] matr([1,2,3],[4,5,6],[7,8]);
   [ 1 2 3 ]
   [ 4 5 6 ]
   [ 7 8 0 ]
   [1] matc([1,2,3],[4,5,6],[7,8]);
   [ 1 4 7 ]
   [ 2 5 8 ]
   [ 3 6 0 ]
   @end example
   
   @table @t
   \JP @item $B;2>H(B
   \EG @item References
   @fref{newmat matrix}
   @end table
   
 \JP @node size,,, $BG[Ns(B  \JP @node size,,, $BG[Ns(B
 \EG @node size,,, Arrays  \EG @node size,,, Arrays
 @subsection @code{size}  @subsection @code{size}
Line 518  in a rational expression.
Line 581  in a rational expression.
 @item  @item
 @code{det} $B$*$h$S(B @code{nd_det} $B$O9TNs(B @var{mat} $B$N9TNs<0$r5a$a$k(B.  @code{det} $B$*$h$S(B @code{nd_det} $B$O9TNs(B @var{mat} $B$N9TNs<0$r5a$a$k(B.
 @code{invmat} $B$O9TNs(B @var{mat} $B$N5U9TNs$r5a$a$k(B. $B5U9TNs$O(B @code{[$BJ,Jl(B, $BJ,;R(B]}  @code{invmat} $B$O9TNs(B @var{mat} $B$N5U9TNs$r5a$a$k(B. $B5U9TNs$O(B @code{[$BJ,Jl(B, $BJ,;R(B]}
 $B$N7A$GJV$5$l(B, @code{$BJ,Jl(B}$B$,9TNs(B, @code{$BJ,Jl(B/$BJ,;R(B} $B$,5U9TNs$H$J$k(B.  $B$N7A$GJV$5$l(B, @code{$BJ,Jl(B}$B$,9TNs(B, @code{$BJ,;R(B/$BJ,Jl(B} $B$,5U9TNs$H$J$k(B.
 @item  @item
 $B0z?t(B @var{mod} $B$,$"$k;~(B, GF(@var{mod}) $B>e$G$N9TNs<0$r5a$a$k(B.  $B0z?t(B @var{mod} $B$,$"$k;~(B, GF(@var{mod}) $B>e$G$N9TNs<0$r5a$a$k(B.
 @item  @item
Line 587  and it computes the determinant faster than @code{det}
Line 650  and it computes the determinant faster than @code{det}
 @table @t  @table @t
 \JP @item $B;2>H(B  \JP @item $B;2>H(B
 \EG @item References  \EG @item References
 @fref{newmat}.  @fref{newmat matrix}.
 @end table  @end table
   
 \JP @node qsort,,, $BG[Ns(B  \JP @node qsort,,, $BG[Ns(B
Line 656  are exchanged.
Line 719  are exchanged.
 \JP @item $B;2>H(B  \JP @item $B;2>H(B
 \EG @item References  \EG @item References
 @fref{ord}, @fref{vars}.  @fref{ord}, @fref{vars}.
   @end table
   
   \JP @node rowx rowm rowa colx colm cola,,, $BG[Ns(B
   \EG @node rowx rowm rowa colx colm cola,,, Arrays
   @subsection @code{rowx}, @code{rowm}, @code{rowa}, @code{colx}, @code{colm}, @code{cola}
   @findex rowx
   @findex rowm
   @findex rowa
   @findex colx
   @findex colm
   @findex cola
   
   @table @t
   @item rowx(@var{matrix},@var{i},@var{j})
   \JP :: $BBh(B @var{i} $B9T$HBh(B @var{j} $B9T$r8r49$9$k(B.
   \EG :: Exchanges the @var{i}-th and @var{j}-th rows.
   @item rowm(@var{matrix},@var{i},@var{c})
   \JP :: $BBh(B @var{i} $B9T$r(B @var{c} $BG\$9$k(B.
   \EG :: Multiplies the @var{i}-th row by @var{c}.
   @item rowa(@var{matrix},@var{i},@var{c})
   \JP :: $BBh(B @var{i} $B9T$KBh(B @var{i} $B9T$N(B @var{c} $BG\$r2C$($k(B.
   \EG :: Appends @var{c} times the @var{j}-th row to the @var{j}-th row.
   @item colx(@var{matrix},@var{i},@var{j})
   \JP :: $BBh(B @var{i} $B9T$HBh(B @var{j} $B9T$r8r49$9$k(B.
   \EG :: Exchanges the @var{i}-th and @var{j}-th columns.
   @item colm(@var{matrix},@var{i},@var{c})
   \JP :: $BBh(B @var{i} $B9T$r(B @var{c} $BG\$9$k(B.
   \EG :: Multiplies the @var{i}-th column by @var{c}.
   @item cola(@var{matrix},@var{i},@var{c})
   \JP :: $BBh(B @var{i} $B9T$KBh(B @var{i} $B9T$N(B @var{c} $BG\$r2C$($k(B.
   \EG :: Appends @var{c} times the @var{j}-th column to the @var{j}-th column.
   @end table
   
   @table @var
   @item return
   \JP $B9TNs(B
   \EG matrix
   @item @var{i}, @var{j}
   \JP $B@0?t(B
   \EG integers
   @item @var{c}
   \JP $B78?t(B
   \EG coefficient
   @end table
   
   @itemize @bullet
   \BJP
   @item
   $B9TNs$N4pK\JQ7A$r9T$&$?$a$N4X?t$G$"$k(B.
   @item
   $B9TNs$,GK2u$5$l$k$3$H$KCm0U$9$k(B.
   \E
   \BEG
   @item
   These operations are destructive for the matrix.
   \E
   @end itemize
   
   @example
   [0] A=newmat(3,3,[[1,2,3],[4,5,6],[7,8,9]]);
   [ 1 2 3 ]
   [ 4 5 6 ]
   [ 7 8 9 ]
   [1] rowx(A,1,2)$
   [2] A;
   [ 1 2 3 ]
   [ 7 8 9 ]
   [ 4 5 6 ]
   [3] rowm(A,2,x);
   [ 1 2 3 ]
   [ 7 8 9 ]
   [ 4*x 5*x 6*x ]
   [4] rowa(A,0,1,z);
   [ 7*z+1 8*z+2 9*z+3 ]
   [ 7 8 9 ]
   [ 4*x 5*x 6*x ]
   @end example
   
   @table @t
   \JP @item $B;2>H(B
   \EG @item References
   @fref{newmat matrix}
 @end table  @end table
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