| version 1.7, 2003/04/20 08:01:28 |
version 1.15, 2011/12/09 05:18:41 |
|
|
| @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.6 2003/04/19 15:44:58 noro Exp $ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.14 2011/12/09 05:13:52 nisiyama 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 |
|
|
| \E |
\E |
| |
|
| @menu |
@menu |
| * newvect:: |
* newvect vector vect:: |
| * newbytearray:: |
* ltov:: |
| * vtol:: |
* vtol:: |
| * newmat:: |
* newbytearray:: |
| |
* newmat matrix:: |
| |
* mat matr matc:: |
| * size:: |
* size:: |
| * det invmat:: |
* det nd_det invmat:: |
| |
* rowx rowm rowa colx colm cola:: |
| |
|
| * qsort:: |
* qsort:: |
| @end menu |
@end menu |
| |
|
| \JP @node newvect,,, $BG[Ns(B |
\JP @node newvect vector vect,,, $BG[Ns(B |
| \EG @node newvect,,, Arrays |
\EG @node newvect vector vect,,, Arrays |
| @subsection @code{newvect} |
@subsection @code{newvect}, @code{vector}, @code{vect} |
| @findex newvect |
@findex newvect |
| |
@findex vector |
| |
@findex vect |
| |
|
| @table @t |
@table @t |
| @item newvect(@var{len}[,@var{list}]) |
@item newvect(@var{len}[,@var{list}]) |
| |
@item vector(@var{len}[,@var{list}]) |
| \JP :: $BD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B. |
\JP :: $BD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B. |
| \EG :: Creates a new vector object with its length @var{len}. |
\EG :: Creates a new vector object with its length @var{len}. |
| |
@item vect([@var{elements}]) |
| |
\JP :: @var{elements} $B$rMWAG$H$9$k%Y%/%H%k$r@8@.$9$k(B. |
| |
\EG :: Creates a new vector object by @var{elements}. |
| @end table |
@end table |
| |
|
| @table @var |
@table @var |
|
|
| @item list |
@item list |
| \JP $B%j%9%H(B |
\JP $B%j%9%H(B |
| \EG list |
\EG list |
| |
@item elements |
| |
\JP $BMWAG$NJB$S(B |
| |
\EG elements of the vector |
| @end table |
@end table |
| |
|
| @itemize @bullet |
@itemize @bullet |
| \BJP |
\BJP |
| @item |
@item |
| $BD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B. $BBh(B 2 $B0z?t$,$J$$>l9g(B, |
@code{vect} $B$OMWAG$NJB$S$+$i%Y%/%H%k$r@8@.$9$k(B. |
| |
@item |
| |
@code{vector} $B$O(B @code{newvect} $B$NJLL>$G$"$k(B. |
| |
@item |
| |
@code{newvect} $B$OD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B. $BBh(B 2 $B0z?t$,$J$$>l9g(B, |
| $B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 2 $B0z?t$,$"$k>l9g(B, |
$B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 2 $B0z?t$,$"$k>l9g(B, |
| $B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B%j%9%H$N(B |
$B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B%j%9%H$N(B |
| $B3FMWAG$K$h$j=i4|2=$5$l$k(B. $B3FMWAG$O(B, $B@hF,$+$i=g$K(B |
$B3FMWAG$K$h$j=i4|2=$5$l$k(B. $B3FMWAG$O(B, $B@hF,$+$i=g$K(B |
|
|
| $B$r=q$-49$($k$3$H$,$G$-$k(B. |
$B$r=q$-49$($k$3$H$,$G$-$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| |
@item |
| |
@code{vect} creates a new vector object by its elements. |
| |
@item |
| |
@code{vector} is an alias of @code{newvect}. |
| @item |
@item |
| Creates a new vector object with its length @var{len} and its elements |
@code{newvect} creates a new vector object with its length @var{len} and its elements |
| all cleared to value 0. |
all cleared to value 0. |
| If the second argument, a list, is given, the vector is initialized by |
If the second argument, a list, is given, the vector is initialized by |
| the list elements. |
the list elements. |
| Line 135 separated simply by a `blank space', while those of a |
|
| Line 156 separated simply by a `blank space', while those of a |
|
| [5,6] |
[5,6] |
| [4] size(A); |
[4] size(A); |
| [5] |
[5] |
| [5] def afo(V) @{ V[0] = x; @} |
[5] length(A); |
| [6] afo(A)$ |
5 |
| [7] A; |
[6] vect(1,2,3,4,[5,6]); |
| |
[ 1 2 3 4 [5,6] ] |
| |
[7] def afo(V) @{ V[0] = x; @} |
| |
[8] afo(A)$ |
| |
[9] A; |
| [ x 2 3 4 [5,6] ] |
[ x 2 3 4 [5,6] ] |
| @end example |
@end example |
| |
|
| @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{vtol}. |
@fref{newmat matrix}, @fref{size}, @fref{ltov}, @fref{vtol}. |
| @end table |
@end table |
| |
|
| |
\JP @node ltov,,, $BG[Ns(B |
| |
\EG @node ltov,,, Arrays |
| |
@subsection @code{ltov} |
| |
@findex ltov |
| |
|
| |
@table @t |
| |
@item ltov(@var{list}) |
| |
\JP :: $B%j%9%H$r%Y%/%H%k$KJQ49$9$k(B. |
| |
\EG :: Converts a list into a vector. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
\JP $B%Y%/%H%k(B |
| |
\EG vector |
| |
@item list |
| |
\JP $B%j%9%H(B |
| |
\EG list |
| |
@end table |
| |
|
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@itemize @bullet |
| |
\BJP |
| |
@item |
| |
$B%j%9%H(B @var{list} $B$rF1$8D9$5$N%Y%/%H%k$KJQ49$9$k(B. |
| |
@item |
| |
$B$3$N4X?t$O(B @code{newvect(length(@var{list}), @var{list})} $B$KEy$7$$(B. |
| |
\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 $B;2>H(B |
| |
\EG @item References |
| |
@fref{newvect vector vect}, @fref{vtol}. |
| |
@end table |
| |
|
| \JP @node vtol,,, $BG[Ns(B |
\JP @node vtol,,, $BG[Ns(B |
| \EG @node vtol,,, Arrays |
\EG @node vtol,,, Arrays |
| @subsection @code{vtol} |
@subsection @code{vtol} |
| Line 194 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{newvect vector vect}, @fref{ltov}. |
| @end table |
@end table |
| |
|
| \JP @node newbytearray,,, $BG[Ns(B |
\JP @node newbytearray,,, $BG[Ns(B |
| Line 250 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,,, $BG[Ns(B |
\JP @node newmat matrix,,, $BG[Ns(B |
| \EG @node newmat,,, Arrays |
\EG @node newmat matrix,,, Arrays |
| @subsection @code{newmat} |
@subsection @code{newmat}, @code{matrix} |
| @findex newmat |
@findex newmat |
| |
@findex matrix |
| |
|
| @table @t |
@table @t |
| @item newmat(@var{row},@var{col} [,[[@var{a},@var{b},...],[@var{c},@var{d},...],...]]) |
@item newmat(@var{row},@var{col} [,[[@var{a},@var{b},...],[@var{c},@var{d},...],...]]) |
| |
@item matrix(@var{row},@var{col} [,[[@var{a},@var{b},...],[@var{c},@var{d},...],...]]) |
| \JP :: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. |
\JP :: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. |
| \EG :: Creates a new matrix with @var{row} rows and @var{col} columns. |
\EG :: Creates a new matrix with @var{row} rows and @var{col} columns. |
| @end table |
@end table |
| Line 279 similar to that of @code{newvect}. |
|
| Line 352 similar to that of @code{newvect}. |
|
| @itemize @bullet |
@itemize @bullet |
| \BJP |
\BJP |
| @item |
@item |
| |
@code{matrix} $B$O(B @code{newmat} $B$NJLL>$G$"$k(B. |
| |
@item |
| @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. $BBh(B 3 $B0z?t$,$J$$>l9g(B, |
@var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. $BBh(B 3 $B0z?t$,$J$$>l9g(B, |
| $B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 3 $B0z?t$,$"$k>l9g(B, |
$B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 3 $B0z?t$,$"$k>l9g(B, |
| $B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B3F9T$,(B, $B%j%9%H$N(B |
$B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B3F9T$,(B, $B%j%9%H$N(B |
| Line 295 similar to that of @code{newvect}. |
|
| Line 370 similar to that of @code{newvect}. |
|
| $B$r=q$-49$($k$3$H$,$G$-$k(B. |
$B$r=q$-49$($k$3$H$,$G$-$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| |
@item |
| |
@code{matrix} is an alias of @code{newmat}. |
| @item |
@item |
| If the third argument, a list, is given, the newly created matrix |
If the third argument, a list, is given, the newly created matrix |
| is initialized so that each element of the list (again a list) |
is initialized so that each element of the list (again a list) |
| Line 337 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 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 |
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@findex matc |
| |
|
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@table @t |
| |
@item mat(@var{vector}[,...]) |
| |
@item matr(@var{vector}[,...]) |
| |
\JP :: $B9T%Y%/%H%k$NJB$S$+$i9TNs$r@8@.$9$k(B. |
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\EG :: Creates a new matrix by list of row vectors. |
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@item matc(@var{vector}[,...]) |
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\JP :: $BNs%Y%/%H%k$NJB$S$+$i9TNs$r@8@.$9$k(B. |
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\EG :: Creates a new matrix by list of column vectors. |
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@end table |
| |
|
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@table @var |
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@item return |
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\JP $B9TNs(B |
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\EG matrix |
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@item @var{vector} |
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\JP $BG[Ns$^$?$O%j%9%H(B |
| |
\EG array or list |
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@end table |
| |
|
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@itemize @bullet |
| |
\BJP |
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@item |
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@code{mat} $B$O(B @code{matr} $B$NJLL>$G$"$k(B. |
| |
@item |
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$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 |
| |
|
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@example |
| |
[0] matr([1,2,3],[4,5,6],[7,8]); |
| |
[ 1 2 3 ] |
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[ 4 5 6 ] |
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[ 7 8 0 ] |
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[1] matc([1,2,3],[4,5,6],[7,8]); |
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[ 1 4 7 ] |
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[ 2 5 8 ] |
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[ 3 6 0 ] |
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@end example |
| |
|
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@table @t |
| |
\JP @item $B;2>H(B |
| |
\EG @item References |
| |
@fref{newmat matrix} |
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@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 371 or a list containing row size and column size of the g |
|
| Line 509 or a list containing row size and column size of the g |
|
| @itemize @bullet |
@itemize @bullet |
| \BJP |
\BJP |
| @item |
@item |
| @var{vect} $BKt$O(B, @var{mat} $B$N%5%$%:$r%j%9%H$G=PNO$9$k(B. |
@var{vect} $B$ND9$5(B, $B$^$?$O(B @var{mat} $B$NBg$-$5$r%j%9%H$G=PNO$9$k(B. |
| @item |
@item |
| @var{list} $B$N%5%$%:$O(B @code{length()}$B$r(B, $BM-M}<0$K8=$l$kC19`<0$N?t$O(B @code{nmono()} $B$rMQ$$$k(B. |
@var{vect} $B$ND9$5$O(B @code{length()} $B$G5a$a$k$3$H$b$G$-$k(B. |
| |
@item |
| |
@var{list} $B$ND9$5$O(B @code{length()}$B$r(B, $BM-M}<0$K8=$l$kC19`<0$N?t$O(B @code{nmono()} $B$rMQ$$$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| @item |
@item |
| Line 392 in a rational expression. |
|
| Line 532 in a rational expression. |
|
| [ 0 0 0 0 ] |
[ 0 0 0 0 ] |
| [1] size(A); |
[1] size(A); |
| [4] |
[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 ] |
[ 1 2 3 ] |
| [ 4 5 6 ] |
[ 4 5 6 ] |
| [3] size(B); |
[4] size(B); |
| [2,3] |
[2,3] |
| @end example |
@end example |
| |
|
| Line 405 in a rational expression. |
|
| Line 547 in a rational expression. |
|
| @fref{car cdr cons append reverse length}, @fref{nmono}. |
@fref{car cdr cons append reverse length}, @fref{nmono}. |
| @end table |
@end table |
| |
|
| \JP @node det invmat,,, $BG[Ns(B |
\JP @node det nd_det invmat,,, $BG[Ns(B |
| \EG @node det invmat,,, Arrays |
\EG @node det nd_det invmat,,, Arrays |
| @subsection @code{det},@code{invmat} |
@subsection @code{det}, @code{nd_det}, @code{invmat} |
| @findex det |
@findex det |
| |
@findex nd_det |
| @findex invmat |
@findex invmat |
| |
|
| @table @t |
@table @t |
| @item det(@var{mat}[,@var{mod}]) |
@item det(@var{mat}[,@var{mod}]) |
| |
@itemx nd_det(@var{mat}[,@var{mod}]) |
| \JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B. |
\JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B. |
| \EG :: Determinant of @var{mat}. |
\EG :: Determinant of @var{mat}. |
| @item invmat(@var{mat}) |
@item invmat(@var{mat}) |
| \JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B. |
\JP :: @var{mat} $B$N5U9TNs$r5a$a$k(B. |
| \EG :: Inverse matrix of @var{mat}. |
\EG :: Inverse matrix of @var{mat}. |
| @end table |
@end table |
| |
|
| Line 435 in a rational expression. |
|
| Line 579 in a rational expression. |
|
| @itemize @bullet |
@itemize @bullet |
| \BJP |
\BJP |
| @item |
@item |
| @code{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,;R(B, $BJ,Jl(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{$BJ,;R(B}$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 |
| $BJ,?t$J$7$N%,%&%9>C5nK!$K$h$C$F$$$k$?$a(B, $BB?JQ?tB?9`<0$r@.J,$H$9$k(B |
$BJ,?t$J$7$N%,%&%9>C5nK!$K$h$C$F$$$k$?$a(B, $BB?JQ?tB?9`<0$r@.J,$H$9$k(B |
| $B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B. |
$B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B. |
| |
@item |
| |
@code{nd_det} $B$OM-M}?t$^$?$OM-8BBN>e$NB?9`<09TNs$N9TNs<0(B |
| |
$B7W;;@lMQ$G$"$k(B. $B%"%k%4%j%:%`$O$d$O$jJ,?t$J$7$N%,%&%9>C5nK!$@$,(B, |
| |
$B%G!<%?9=B$$*$h$S>h=|;;$N9)IW$K$h$j(B, $B0lHL$K(B @code{det} $B$h$j9bB.$K(B |
| |
$B7W;;$G$-$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| @item |
@item |
| @code{det} computes the 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} computes the inverse matrix of matrix @var{mat}. |
| @code{invmat} returns a list @code{[num,den]}, where @code{num} |
@code{invmat} returns a list @code{[num,den]}, where @code{num} |
| is a matrix and @code{num/den} represents the inverse matrix. |
is a matrix and @code{num/den} represents the inverse matrix. |
| Line 456 The computation is done over GF(@var{mod}) if @var{mod |
|
| Line 605 The computation is done over GF(@var{mod}) if @var{mod |
|
| The fraction free Gaussian algorithm is employed. For matrices with |
The fraction free Gaussian algorithm is employed. For matrices with |
| multi-variate polynomial entries, minor expansion algorithm sometimes |
multi-variate polynomial entries, minor expansion algorithm sometimes |
| is more efficient than the fraction free Gaussian algorithm. |
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 |
\E |
| @end itemize |
@end itemize |
| |
|
| Line 496 is more efficient than the fraction free Gaussian algo |
|
| Line 650 is more efficient than the fraction free Gaussian algo |
|
| @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 |
|
|
| \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 |
| |
|
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\JP @node rowx rowm rowa colx colm cola,,, $BG[Ns(B |
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\EG @node rowx rowm rowa colx colm cola,,, Arrays |
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@subsection @code{rowx}, @code{rowm}, @code{rowa}, @code{colx}, @code{colm}, @code{cola} |
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@findex rowx |
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@findex rowm |
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@findex rowa |
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@findex colx |
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@findex colm |
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@findex cola |
| |
|
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@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. |
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\EG :: Exchanges the @var{i}-th and @var{j}-th rows. |
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@item rowm(@var{matrix},@var{i},@var{c}) |
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\JP :: $BBh(B @var{i} $B9T$r(B @var{c} $BG\$9$k(B. |
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\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}) |
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\JP :: $BBh(B @var{i} $B9T$HBh(B @var{j} $B9T$r8r49$9$k(B. |
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\EG :: Exchanges the @var{i}-th and @var{j}-th columns. |
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@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. |
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@end table |
| |
|
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@table @var |
| |
@item return |
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\JP $B9TNs(B |
| |
\EG matrix |
| |
@item @var{i}, @var{j} |
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\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 |
| |
|
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@example |
| |
[0] A=newmat(3,3,[[1,2,3],[4,5,6],[7,8,9]]); |
| |
[ 1 2 3 ] |
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[ 4 5 6 ] |
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[ 7 8 9 ] |
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[1] rowx(A,1,2)$ |
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[2] A; |
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[ 1 2 3 ] |
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[ 7 8 9 ] |
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[ 4 5 6 ] |
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[3] rowm(A,2,x); |
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[ 1 2 3 ] |
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[ 7 8 9 ] |
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[ 4*x 5*x 6*x ] |
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[4] rowa(A,0,1,z); |
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[ 7*z+1 8*z+2 9*z+3 ] |
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[ 7 8 9 ] |
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[ 4*x 5*x 6*x ] |
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@end example |
| |
|
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@table @t |
| |
\JP @item $B;2>H(B |
| |
\EG @item References |
| |
@fref{newmat matrix} |
| @end table |
@end table |
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