===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/parts/builtin/array.texi,v
retrieving revision 1.2
retrieving revision 1.10
diff -u -p -r1.2 -r1.10
--- OpenXM/src/asir-doc/parts/builtin/array.texi	1999/12/21 02:47:33	1.2
+++ OpenXM/src/asir-doc/parts/builtin/array.texi	2005/02/10 04:59:21	1.10
@@ -1,4 +1,4 @@
-@comment $OpenXM$
+@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.9 2003/12/18 10:26:20 ohara Exp $
 \BJP
 @node 配列,,, 組み込み函数
 @section 配列
@@ -10,10 +10,13 @@
 
 @menu
 * newvect::
+* ltov::
 * vtol::
+* newbytearray::
 * newmat::
 * size::
-* det::
+* det nd_det invmat::
+
 * qsort::
 @end menu
 
@@ -143,9 +146,55 @@ separated simply by a `blank space', while those of a 
 @table @t
 \JP @item 参照
 \EG @item References
-@fref{newmat}, @fref{size}.
+@fref{newmat}, @fref{size}, @fref{ltov}, @fref{vtol}.
 @end table
 
+\JP @node ltov,,, 配列
+\EG @node ltov,,, Arrays
+@subsection @code{ltov}
+@findex ltov
+
+@table @t
+@item ltov(@var{list})
+\JP :: リストをベクトルに変換する. 
+\EG :: Converts a list into a vector.
+@end table
+
+@table @var
+@item return
+\JP ベクトル
+\EG vector
+@item list
+\JP リスト
+\EG list
+@end table
+
+@itemize @bullet
+\BJP
+@item
+リスト @var{list} を同じ長さのベクトルに変換する. 
+@item
+この関数は @code{newvect(length(@var{list}), @var{list})} に等しい.
+\E
+\BEG
+@item 
+Converts a list @var{list} into a vector of same length.
+See also @code{newvect()}.
+\E
+@end itemize
+
+@example
+[3] A=[1,2,3];
+[4] ltov(A);
+[ 1 2 3 ]
+@end example
+
+@table @t
+\JP @item 参照
+\EG @item References
+@fref{newvect}, @fref{vtol}.
+@end table
+
 \JP @node vtol,,, 配列
 \EG @node vtol,,, Arrays
 @subsection @code{vtol}
@@ -193,6 +242,62 @@ A conversion from a list to a vector is done by @code{
 @table @t
 \JP @item 参照
 \EG @item References
+@fref{newvect}, @fref{ltov}.
+@end table
+
+\JP @node newbytearray,,, 配列
+\EG @node newbytearray,,, Arrays
+@subsection @code{newbytearray}
+@findex newbytearray
+
+@table @t
+@item newbytearray(@var{len},[@var{listorstring}])
+\JP :: 長さ @var{len} の byte array を生成する.
+\EG :: Creates a new byte array.
+@end table
+
+@table @var
+@item return
+byte array
+@item len
+\JP 自然数
+\EG non-negative integer
+@item listorstring
+\JP リストまたは文字列
+\EG list or string
+@end table
+
+@itemize @bullet
+@item
+\JP @code{newvect} と同様にして byte array を生成する.
+\EG This function generates a byte array. The specification is
+similar to that of @code{newvect}.
+@item
+\JP 文字列で初期値を指定することも可能である.
+\EG The initial value can be specified by a character string.
+@item
+\JP byte array の要素のアクセスは配列と同様である.
+\EG One can access elements of a byte array just as an array.
+@end itemize
+
+@example
+[182] A=newbytearray(3);
+|00 00 00|
+[183] A=newbytearray(3,[1,2,3]);
+|01 02 03|
+[184] A=newbytearray(3,"abc");  
+|61 62 63|
+[185] A[0];
+97
+[186] A[1]=123;
+123
+[187] A;
+|61 7b 63|
+@end example
+
+@table @t
+\JP @item 参照
+\EG @item References
 @fref{newvect}.
 @end table
 
@@ -202,7 +307,7 @@ A conversion from a list to a vector is done by @code{
 @findex newmat
 
 @table @t
-@item newmat(@var{row},@var{col} [,@var{[[a,b,}...@var{],[c,d,}...@var{],}...@var{]}])
+@item newmat(@var{row},@var{col} [,[[@var{a},@var{b},...],[@var{c},@var{d},...],...]])
 \JP :: @var{row} 行 @var{col} 列の行列を生成する. 
 \EG :: Creates a new matrix with @var{row} rows and @var{col} columns.
 @end table
@@ -211,10 +316,10 @@ A conversion from a list to a vector is done by @code{
 @item return
 \JP 行列
 \EG matrix
-@item row,col
+@item row col
 \JP 自然数
 \EG non-negative integer
-@item a,b,c,d
+@item a b c d
 \JP 任意
 \EG arbitrary
 @end table
@@ -280,7 +385,7 @@ return to toplevel
 @table @t
 \JP @item 参照
 \EG @item References
-@fref{newvect}, @fref{size}, @fref{det}.
+@fref{newvect}, @fref{size}, @fref{det nd_det invmat}.
 @end table
 
 \JP @node size,,, 配列
@@ -314,9 +419,11 @@ or a list containing row size and column size of the g
 @itemize @bullet
 \BJP
 @item
-@var{vect} 又は, @var{mat} のサイズをリストで出力する. 
+@var{vect} の長さ, または @var{mat} の大きさをリストで出力する. 
 @item
-@var{list} のサイズは @code{length()}を, 有理式に現れる単項式の数は @code{nmono()} を用いる. 
+@var{vect} の長さは @code{length()} で求めることもできる.
+@item
+@var{list} の長さは @code{length()}を, 有理式に現れる単項式の数は @code{nmono()} を用いる. 
 \E
 \BEG
 @item 
@@ -335,10 +442,12 @@ in a rational expression.
 [ 0 0 0 0 ]
 [1] size(A);
 [4]
-[2] B = newmat(2,3,[[1,2,3],[4,5,6]]);
+[2] length(A);
+4
+[3] B = newmat(2,3,[[1,2,3],[4,5,6]]);
 [ 1 2 3 ]
 [ 4 5 6 ]
-[3] size(B);
+[4] size(B);
 [2,3]
 @end example
 
@@ -348,21 +457,26 @@ in a rational expression.
 @fref{car cdr cons append reverse length}, @fref{nmono}.
 @end table
 
-\JP @node det,,, 配列
-\EG @node det,,, Arrays
-@subsection @code{det}
+\JP @node det nd_det invmat,,, 配列
+\EG @node det nd_det invmat,,, Arrays
+@subsection @code{det},@code{invmat}
 @findex det
+@findex invmat
 
 @table @t
 @item det(@var{mat}[,@var{mod}])
+@itemx nd_det(@var{mat}[,@var{mod}])
 \JP :: @var{mat} の行列式を求める. 
 \EG :: Determinant of @var{mat}.
+@item invmat(@var{mat})
+\JP :: @var{mat} の逆行列を求める. 
+\EG :: Inverse matrix of @var{mat}.
 @end table
 
 @table @var
 @item return
-\JP 式
-\EG expression
+\JP @code{det}: 式, @code{invmat}: リスト
+\EG @code{det}: expression, @code{invmat}: list
 @item mat
 \JP 行列
 \EG matrix
@@ -374,22 +488,37 @@ in a rational expression.
 @itemize @bullet
 \BJP
 @item
-行列 @var{mat} の行列式を求める. 
+@code{det} および @code{nd_det} は行列 @var{mat} の行列式を求める. 
+@code{invmat} は行列 @var{mat} の逆行列を求める. 逆行列は @code{[分母, 分子]}
+の形で返され, @code{分母}が行列, @code{分母/分子} が逆行列となる. 
 @item
 引数 @var{mod} がある時, GF(@var{mod}) 上での行列式を求める. 
 @item
 分数なしのガウス消去法によっているため, 多変数多項式を成分とする
 行列に対しては小行列式展開による方法のほうが効率がよい場合もある. 
+@item
+@code{nd_det} は有理数または有限体上の多項式行列の行列式
+計算専用である. アルゴリズムはやはり分数なしのガウス消去法だが,
+データ構造および乗除算の工夫により, 一般に @code{det} より高速に
+計算できる.
 \E
 \BEG
 @item 
-Determinant of matrix @var{mat}.
+@code{det} and @code{nd_det} compute the determinant of matrix @var{mat}.
+@code{invmat} computes the inverse matrix of matrix @var{mat}.
+@code{invmat} returns a list @code{[num,den]}, where @code{num}
+is a matrix and @code{num/den} represents the inverse matrix.
 @item 
 The computation is done over GF(@var{mod}) if @var{mod} is specitied.
 @item 
 The fraction free Gaussian algorithm is employed.  For matrices with
 multi-variate polynomial entries, minor expansion algorithm sometimes
 is more efficient than the fraction free Gaussian algorithm.
+@item
+@code{nd_det} can be used for computing the determinant of a matrix with
+polynomial entries over the rationals or finite fields. The algorithm
+is an improved vesion of the fraction free Gaussian algorithm
+and it computes the determinant faster than @code{det}.
 \E
 @end itemize
 
@@ -405,8 +534,26 @@ is more efficient than the fraction free Gaussian algo
 [ 1 u u^2 u^3 u^4 ]
 [ 1 v v^2 v^3 v^4 ]
 [95] fctr(det(A));
-[[1,1],[u-v,1],[-z+v,1],[-z+u,1],[-y+u,1],[y-v,1],[-y+z,1],[-x+u,1],[-x+z,1],
-[-x+v,1],[-x+y,1]]
+[[1,1],[u-v,1],[-z+v,1],[-z+u,1],[-y+u,1],[y-v,1],[-y+z,1],[-x+u,1],
+[-x+z,1],[-x+v,1],[-x+y,1]]
+[96] A = newmat(3,3)$
+[97] for(I=0;I<3;I++)for(J=0,B=A[I],W=V[I];J<3;J++)B[J]=W^J;
+[98] A;
+[ 1 x x^2 ]
+[ 1 y y^2 ]
+[ 1 z z^2 ]
+[99] invmat(A);
+[[ -z*y^2+z^2*y z*x^2-z^2*x -y*x^2+y^2*x ]
+[ y^2-z^2 -x^2+z^2 x^2-y^2 ]
+[ -y+z x-z -x+y ],(-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y]
+[100] A*B[0];
+[ (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 0 ]
+[ 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 ]
+[ 0 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y ]
+[101] map(red,A*B[0]/B[1]);
+[ 1 0 0 ]
+[ 0 1 0 ]
+[ 0 0 1 ]
 @end example
 
 @table @t