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Diff for /OpenXM/src/asir-doc/parts/builtin/num.texi between version 1.2 and 1.8

version 1.2, 1999/12/21 02:47:34

version 1.8, 2003/04/19 15:44:59

Line 1

@comment $OpenXM$

@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/num.texi,v 1.7 2002/09/03 01:50:59 noro Exp $

\BJP

@node $B?t$N1i;;(B,,, $BAH$_9~$_H!?t(B

@section $B?t$N1i;;(B

Line 19

* mt_save mt_load::

* nm dn::

* conj real imag::

* eval::

* eval deval::

* pari::

* setprec::

* setmod::

* lrandom::

* ntoint32 int32ton::

@end menu

\JP @node idiv irem,,, $B?t$N1i;;(B

Line 45

Line 46

@item return

\JP $B@0?t(B

\EG integer

@item i1,i2

@item i1 i2

\JP $B@0?t(B

\EG integer

@end table

Line 158 Returns 0 if the argument @var{i} is negative.

Line 159 Returns 0 if the argument @var{i} is negative.

@item return

\JP $B@0?t(B

\EG integer

@item i1,i2,i

@item i1 i2 i

\JP $B@0?t(B

\EG integer

@end table

Line 259 In most cases @code{3} is the fastest, but there are e

Line 260 In most cases @code{3} is the fastest, but there are e

@item return

\JP $B@0?t(B

\EG integer

@item i1,i2

@item i1 i2

\JP $B@0?t(B

\EG integer

@end table

Line 301 If one of argument is equal to 0, the return 0.

Line 302 If one of argument is equal to 0, the return 0.

@item return

\JP $B@0?t(B

\EG integer

@item i,m

@item i m

\JP $B@0?t(B

\EG integer

@end table

Line 418 function

Line 419 function

@findex random

@table @t

@item radom([@var{seed}])

@item random([@var{seed}])

\JP :: $BMp?t$r@8@.$9$k(B.

@end table

Line 481 one can trace a single random number sequence arcoss m

Line 482 one can trace a single random number sequence arcoss m

@findex lrandom

@table @t

@item lradom(@var{bit})

@item lrandom(@var{bit})

\JP :: $BB?G\D9Mp?t$r@8@.$9$k(B.

\EG :: Generates a long random number.

@end table

Line 692 These functions works also for polynomials with comple

Line 693 These functions works also for polynomials with comple

[2,11,(2-11*@@i)]

@end example

\JP @node eval,,, $B?t$N1i;;(B

\JP @node eval deval ,,, $B?t$N1i;;(B

\EG @node eval,,, Numbers

\EG @node eval deval,,, Numbers

@subsection @code{eval}

@subsection @code{eval}, @code{deval}

@findex eval

@findex deval

@cindex PARI

@table @t

@item eval(@var{obj}[,@var{prec}])

@item deval(@var{obj})

\JP :: @var{obj} $B$NCM$NI>2A(B.

\EG :: Evaluate @var{obj} numerically.

@end table

Line 721 These functions works also for polynomials with comple

Line 724 These functions works also for polynomials with comple

@item

@var{obj} $B$K4^$^$l$kH!?t$NCM$r2DG=$J8B$jI>2A$9$k(B.

@item

$B7W;;$O(B @b{PARI} (@xref{pari}) $B$,9T$&(B.

@code{deval} $B$OG\@:EYIbF0>.?t$r7k2L$H$7$F(B

@code{eval} $B$N>l9g(B, $BM-M}?t$O$=$N$^$^;D$k(B.

@item

@code{eval} $B$K$*$$$F$O(B, $B7W;;$O(B @b{PARI} (@ref{pari}) $B$,9T$&(B.

@code{deval} $B$K$*$$$F$O(B, $B7W;;$O(B C $B?t3X%i%$%V%i%j$N4X?t$rMQ$$$F9T$&(B.

@item

@code{deval} $B$OJ#AG?t$O07$($J$$(B.

@item

@code{eval} $B$K$*$$$F$O(B,

@var{prec} $B$r;XDj$7$?>l9g(B, $B7W;;$O(B, 10 $B?J(B @var{prec} $B7eDxEY$G9T$o$l$k(B.

@var{prec} $B$N;XDj$,$J$$>l9g(B, $B8=:_@_Dj$5$l$F$$$k@:EY$G9T$o$l$k(B.

(@xref{setprec})

(@xref{setprec}.)

@item

@table @t

@item $B07$($kH!?t$O(B, $B<!$NDL$j(B.

Line 740 These functions works also for polynomials with comple

Line 750 These functions works also for polynomials with comple

@code{exp}, @code{log}, @code{pow(a,b) (a^b)}

@end table

@item

$B0J2<$N5-9f$r?t$H$7$FI>2A$G$-$k(B.

$B0J2<$N5-9f$r?t$H$7$FI>2A$G$-$k(B. $B$?$@$7(B @code{@@i} $B$r07$($k$N$O(B

@code{eval}, @code{deval} $B$N$_$G$"$k(B.

@table @t

@item @@i

$B5u?tC10L(B

Line 755 These functions works also for polynomials with comple

Line 766 These functions works also for polynomials with comple

Evaluates the value of the functions contained in @var{obj} as far as

possible.

@item

The computation is done by @b{PARI} (@xref{pari}).

@code{deval} returns

double float. Rational numbers remain unchanged in results from @code{eval}.

@item

In @code{eval} the computation is done

by @b{PARI}. (@xref{pari}.) In @code{deval} the computation is

done by the C math library.

@item

@code{deval} cannot handle complex numbers.

@item

When @var{prec} is specified, computation will be performed with a

precision of about @var{prec}-digits.

If @var{prec} is not specified, computation is performed with the

precision set currently. (@xref{setprec})

precision set currently. (@xref{setprec}.)

@item

Currently available numerical functions are listed below.

Note they are only a small part of whole @b{PARI} functions.

Line 776 Note they are only a small part of whole @b{PARI} func

Line 794 Note they are only a small part of whole @b{PARI} func

@code{exp}, @code{log}, @code{pow(a,b) (a^b)}

@end table

@item

Symbols for special values are as the followings.

Symbols for special values are as the followings. Note that

@code{@@i} cannot be handled by @code{deval}.

@table @t

@item @@i

unit of imaginary number

Line 798 Napier's number (@t{exp}(1))

Line 817 Napier's number (@t{exp}(1))

0.86602540378443864674620506632

[121] eval(sin(@@pi/3)-3^(1/2)/2,50);

-2.78791084448179148471 E-58

[122] eval(1/2);

1/2

[123] deval(sin(1)^2+cos(1)^2);

@end example

@table @t

Line 960 For details of individual functions, refer to the @b{P

Line 983 For details of individual functions, refer to the @b{P

@code{lngamma},

@code{logagm},

@code{mat},

@code{matinvr},

@code{matrixqz2},

@code{matrixqz3},

@code{matsize},

Line 1075 We will improve @b{Asir} so that it can provide more f

Line 1097 We will improve @b{Asir} so that it can provide more f

$B0z?t$,$"$k>l9g(B, @b{bigfloat} $B$N7e?t$r(B @var{n} $B7e$K@_Dj$9$k(B.

$B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B.

@item

@b{bigfloat} $B$N7W;;$O(B @b{PARI} (@xref{pari}) $B$K$h$C$F9T$o$l$k(B.

@b{bigfloat} $B$N7W;;$O(B @b{PARI} (@ref{pari}) $B$K$h$C$F9T$o$l$k(B.

@item

@b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B.

@b{bigfloat} $B$N(B flag $B$r(B on $B$K$9$kJ}K!$O(B, @code{ctrl} $B$r;2>H(B.

Line 1091 The return value is always the previous precision in d

Line 1113 The return value is always the previous precision in d

the existence of an argument.

@item

@b{Bigfloat} operations are done by @b{PARI}. (@xref{pari})

@b{Bigfloat} operations are done by @b{PARI}. (@xref{pari}.)

@item

This is effective for computations in @b{bigfloat}.

Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.'

Line 1113 Therefore, it is safe to specify a larger value.

Line 1135 Therefore, it is safe to specify a larger value.

@table @t

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

@fref{ctrl}, @fref{eval}, @fref{pari}.

@fref{ctrl}, @fref{eval deval}, @fref{pari}.

@end table

\JP @node setmod,,, $B?t$N1i;;(B

Line 1177 return to toplevel

Line 1199 return to toplevel

\EG @fref{dp_mod dp_rat}, @fref{Types of numbers}.

@end table

\JP @node ntoint32 int32ton,,, $B?t$N1i;;(B

\EG @node ntoint32 int32ton,,, Numbers

@subsection @code{ntoint32}, @code{int32ton}

@findex ntoint32

@findex int32ton

@table @t

@item ntoint32(@var{n})

@itemx int32ton(@var{int32})

\JP :: $BHsIi@0?t$HId9f$J$7(B 32bit $B@0?t$N4V$N7?JQ49(B.

\EG :: Type-conversion between a non-negative integer and an unsigned 32bit integer.

@end table

@table @var

@item return

\JP $BId9f$J$7(B 32bit $B@0?t$^$?$OHsIi@0?t(B

\EG unsigned 32bit integer or non-negative integer

@item n

\JP 2^32 $BL$K~$NHsIi@0?t(B

\EG non-negative interger less than 2^32

@item int32

\JP $BId9f$J$7(B 32bit $B@0?t(B

\EG unsigned 32bit integer

@end table

@itemize @bullet

\BJP

@item $BHsIi@0?t(B ($B<1JL;R(B 1) $B$NId9f$J$7(B 32bit $B@0?t(B ($B<1JL;R(B 10) $B$X$NJQ49(B,

$B$^$?$O$=$N5UJQ49$r9T$&(B.

@item 32bit $B@0?t$O(B @b{OpenXM} $B$N4pK\9=@.MWAG$G$"$j(B, $B@0?t$r$=$N7?$GAw?.(B

$B$9$kI,MW$,$"$k>l9g$KMQ$$$k(B.

\BEG

@item These functions do conversions between non-negative

integers (the type id 1) and unsigned 32bit integers (the type id 10).

@item An unsigned 32bit integer is a fundamental construct of @b{OpenXM}

and one often has to send an integer to a server as an unsigned 32bit

integer. These functions are used in such a case.

@end itemize

@table @t

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

\EG @item References

\JP @fref{$BJ,;67W;;(B}, @fref{$B?t$N7?(B}.

\EG @fref{Distributed computation}, @fref{Types of numbers}.

@end table

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