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version 1.1, 1999/12/08 05:47:44

version 1.2, 1999/12/21 02:47:33

Line 1

@comment $OpenXM$

\BJP

@node $BG[Ns(B,,, $BAH$_9~$_H!?t(B

@section $BG[Ns(B

\BEG

@node Arrays,,, Built-in Function

@section Arrays

@menu

* newvect::

Line 10

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* qsort::

@end menu

@node newvect,,, $BG[Ns(B

\JP @node newvect,,, $BG[Ns(B

\EG @node newvect,,, Arrays

@subsection @code{newvect}

@findex newvect

@table @t

@item newvect(@var{len}[,@var{list}])

:: $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}.

@end table

@table @var

@item return

$B%Y%/%H%k(B

\JP $B%Y%/%H%k(B

\EG vector

@item len

$B<+A3?t(B

\JP $B<+A3?t(B

\EG non-negative integer

@item list

$B%j%9%H(B

\JP $B%j%9%H(B

\EG list

@end table

@itemize @bullet

\BJP

@item

$BD9$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,

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@item

$BH!?t$N0z?t$H$7$F%Y%/%H%k$rEO$7$?>l9g(B, $BEO$5$l$?H!?t$O(B, $B$=$N%Y%/%H%k$N@.J,(B

$B$r=q$-49$($k$3$H$,$G$-$k(B.

\BEG

@item

Creates a new vector object with its length @var{len} and its elements

all cleared to value 0.

If the second argument, a list, is given, the vector is initialized by

the list elements.

Elements are used from the first through the last.

If the list is short for initializing the full vector,

0's are filled in the remaining vector elements.

@item

Elements are indexed from 0 through @var{len}-1. Note that the first

element has not index 1.

@item

List and vector are different types in @b{Asir}.

Lists are conveniently used for representing many data objects whose

size varies dynamically as computation proceeds.

By its flexible expressive power, it is also conveniently used to

describe initial values for other structured objects as you see

for vectors.

Access for an element of a list is performed by following pointers to

next elements. By this, access costs for list elements differ for

each element.

In contrast to lists, vector elements can be accessed in a same time,

because they are accessed by computing displacements from the top memory

location of the vector object.

Note also, in @b{Asir}, modification of an element of a vector causes

modification of the whole vector itself,

while modification of a list element does not cause the modification

of the whole list object.

By this, in @b{Asir} language,

a vector element designator can be a left value of

assignment statement, but a list element designator can NOT be a left

value of assignment statement.

@item

No distinction of column vectors and row vectors in @b{Asir}.

If a matrix is applied to a vector from left, the vector shall be taken

as a column vector, and if from right it shall be taken as a row vector.

@item

The length (or size or dimension) of a vector is given by function

@code{size()}.

@item

When a vector is passed to a function as its argument

(actual parameter), the vector element can be modified in that

function.

@item

A vector is displayed in a similar format as for a list.

Note, however, there is a distinction: Elements of a vector are

separated simply by a `blank space', while those of a list by a `comma.'

@end itemize

@example

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@end example

@table @t

@item $B;2>H(B

\JP @item $B;2>H(B

\EG @item References

@fref{newmat}, @fref{size}.

@end table

@node vtol,,, $BG[Ns(B

\JP @node vtol,,, $BG[Ns(B

\EG @node vtol,,, Arrays

@subsection @code{vtol}

@findex vtol

@table @t

@item vtol(@var{vect})

:: $B%Y%/%H%k$r%j%9%H$KJQ49$9$k(B.

\JP :: $B%Y%/%H%k$r%j%9%H$KJQ49$9$k(B.

\EG :: Converts a vector into a list.

@end table

@table @var

@item return

$B%j%9%H(B

\JP $B%j%9%H(B

\EG list

@item vect

$B%Y%/%H%k(B

\JP $B%Y%/%H%k(B

\EG vector

@end table

@itemize @bullet

\BJP

@item

$BD9$5(B @var{n} $B$N%Y%/%H%k(B @var{vect} $B$r(B

@code{[@var{vect}[0],...,@var{vect}[@var{n}-1]]} $B$J$k%j%9%H$KJQ49$9$k(B.

@item

$B%j%9%H$+$i%Y%/%H%k$X$NJQ49$O(B @code{newvect()} $B$G9T$&(B.

\BEG

@item

Converts a vector @var{vect} of length @var{n} into

a list @code{[@var{vect}[0],...,@var{vect}[@var{n}-1]]}.

@item

A conversion from a list to a vector is done by @code{newvect()}.

@end itemize

@example

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@end example

@table @t

@item $B;2>H(B

\JP @item $B;2>H(B

\EG @item References

@fref{newvect}.

@end table

@node newmat,,, $BG[Ns(B

\JP @node newmat,,, $BG[Ns(B

\EG @node newmat,,, Arrays

@subsection @code{newmat}

@findex newmat

@table @t

@item newmat(@var{row},@var{col} [,@var{[[a,b,}...@var{],[c,d,}...@var{],}...@var{]}])

:: @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.

@end table

@table @var

@item return

$B9TNs(B

\JP $B9TNs(B

\EG matrix

@item row,col

$B<+A3?t(B

\JP $B<+A3?t(B

\EG non-negative integer

@item a,b,c,d

$BG$0U(B

\JP $BG$0U(B

\EG arbitrary

@end table

@itemize @bullet

\BJP

@item

@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,

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@item

$BH!?t$N0z?t$H$7$F9TNs$rEO$7$?>l9g(B, $BEO$5$l$?H!?t$O(B, $B$=$N9TNs$N@.J,(B

$B$r=q$-49$($k$3$H$,$G$-$k(B.

\BEG

@item

If the third argument, a list, is given, the newly created matrix

is initialized so that each element of the list (again a list)

initializes each of the rows of the matrix.

Elements are used from the first through the last.

If the list is short, 0's are filled in the remaining matrix elements.

If no third argument is given all the elements are cleared to 0.

@item

The size of a matrix is given by function @code{size()}.

@item

Let @code{M} be a program variable assigned to a matrix.

Then, @code{M[I]} denotes a (row) vector which corresponds with

the @code{I}-th row of the matrix.

Note that the vector shares its element with the original matrix.

Subsequently, if an element of the vector is modified, then the

corresponding matrix element is also modified.

@item

When a matrix is passed to a function as its argument

(actual parameter), the matrix element can be modified within that

function.

@end itemize

@example

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@end example

@table @t

@item $B;2>H(B

\JP @item $B;2>H(B

\EG @item References

@fref{newvect}, @fref{size}, @fref{det}.

@end table

@node size,,, $BG[Ns(B

\JP @node size,,, $BG[Ns(B

\EG @node size,,, Arrays

@subsection @code{size}

@findex size

@table @t

@item size(@var{vect|mat})

:: @code{[@var{vect} $B$ND9$5(B]} $B$^$?$O(B @code{[@var{mat} $B$N9T?t(B,@var{mat} $B$NNs?t(B]}.

\JP :: @code{[@var{vect} $B$ND9$5(B]} $B$^$?$O(B @code{[@var{mat} $B$N9T?t(B,@var{mat} $B$NNs?t(B]}.

\BEG

:: A list containing the number of elements of the given vector,

@code{[size of @var{vect}]},

or a list containing row size and column size of the given matrix,

@code{[row size of @var{mat}, column size of @var{mat}]}.

@end table

@table @var

@item return

$B%j%9%H(B

\JP $B%j%9%H(B

\EG list

@item vect

$B%Y%/%H%k(B

\JP $B%Y%/%H%k(B

\EG vector

@item mat

$B9TNs(B

\JP $B9TNs(B

\EG matrix

@end table

@itemize @bullet

\BJP

@item

@var{vect} $BKt$O(B, @var{mat} $B$N%5%$%:$r%j%9%H$G=PNO$9$k(B.

@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.

\BEG

@item

Return a list consisting of the dimension of the vector @var{vect},

or a list consisting of the row size and column size of the matrix

@var{matrix}.

@item

Use @code{length()} for the size of @var{list}, and

@code{nmono()} for the number of monomials with non-zero coefficients

in a rational expression.

@end itemize

@example

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@end example

@table @t

@item $B;2>H(B

\JP @item $B;2>H(B

\EG @item References

@fref{car cdr cons append reverse length}, @fref{nmono}.

@end table

@node det,,, $BG[Ns(B

\JP @node det,,, $BG[Ns(B

\EG @node det,,, Arrays

@subsection @code{det}

@findex det

@table @t

@item det(@var{mat}[,@var{mod}])

:: @var{mat} $B$N9TNs<0$r5a$a$k(B.

\JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B.

\EG :: Determinant of @var{mat}.

@end table

@table @var

@item return

$B<0(B

\JP $B<0(B

\EG expression

@item mat

$B9TNs(B

\JP $B9TNs(B

\EG matrix

@item mod

$BAG?t(B

\JP $BAG?t(B

\EG prime

@end table

@itemize @bullet

\BJP

@item

$B9TNs(B @var{mat} $B$N9TNs<0$r5a$a$k(B.

@item

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@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

$B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B.

\BEG

@item

Determinant of matrix @var{mat}.

@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.

@end itemize

@example

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@end example

@table @t

@item $B;2>H(B

\JP @item $B;2>H(B

\EG @item References

@fref{newmat}.

@end table

@node qsort,,, $BG[Ns(B

\JP @node qsort,,, $BG[Ns(B

\EG @node qsort,,, Arrays

@subsection @code{qsort}

@findex qsort

@table @t

@item qsort(@var{array}[,@var{func}])

:: $B0l<!85G[Ns(B @var{array} $B$r%=!<%H$9$k(B.

\JP :: $B0l<!85G[Ns(B @var{array} $B$r%=!<%H$9$k(B.

\EG :: Sorts an array @var{array}.

@end table

@table @var

@item return

@var{array} ($BF~NO$HF1$8(B; $BMWAG$N$_F~$lBX$o$k(B)

\JP @var{array} ($BF~NO$HF1$8(B; $BMWAG$N$_F~$lBX$o$k(B)

\EG @var{array} (The same as the input; Only the elements are exchanged.)

@item array

$B0l<!85G[Ns(B

\JP $B0l<!85G[Ns(B

\EG array

@item func

$BHf3SMQ4X?t(B

\JP $BHf3SMQ4X?t(B

\EG function for comparison

@end table

@itemize @bullet

\BJP

@item

$B0l<!85G[Ns$r(B quick sort $B$G%=!<%H$9$k(B.

@item

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$B$b$N$+$i=g$KJB$Y49$($i$l$k(B.

@item

$BG[Ns$O?7$?$K@8@.$5$l$:(B, $B0z?t$NG[Ns$NMWAG$N$_F~$lBX$o$k(B.

\BEG

@item

This function sorts an array by @var{quick sort}.

@item

If @var{func} is not specified, the built-in comparison function

is used and the array is sorted in increasing order.

@item

If a function of two arguments @var{func} which returns 0, 1, or -1

is provided, then an ordering is detemined so that

@code{A<B} if @code{@var{func}(A,B)=1} holds, and

the array is sorted in increasing order with respect to the ordering.

@item

The returned array is the same as the input. Only the elements

are exchanged.

@end itemize

@example

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@end example

@table @t

@item $B;2>H(B

\JP @item $B;2>H(B

\EG @item References

@fref{ord}, @fref{vars}.

@end table

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