| version 1.5, 2002/07/19 02:23:32 |
version 1.9, 2003/12/18 10:26:20 |
|
|
| @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/num.texi,v 1.4 2001/03/12 05:01:19 noro Exp $ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/num.texi,v 1.8 2003/04/19 15:44:59 noro Exp $ |
| \BJP |
\BJP |
| @node $B?t$N1i;;(B,,, $BAH$_9~$_H!?t(B |
@node $B?t$N1i;;(B,,, $BAH$_9~$_H!?t(B |
| @section $B?t$N1i;;(B |
@section $B?t$N1i;;(B |
|
|
| @item return |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i1,i2 |
@item i1 i2 |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
| Line 159 Returns 0 if the argument @var{i} is negative. |
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| Line 159 Returns 0 if the argument @var{i} is negative. |
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| @item return |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i1,i2,i |
@item i1 i2 i |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
| Line 260 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 |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i1,i2 |
@item i1 i2 |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
| Line 287 If one of argument is equal to 0, the return 0. |
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| Line 287 If one of argument is equal to 0, the return 0. |
|
| @fref{igcd igcdcntl}, @fref{mt_save mt_load}. |
@fref{igcd igcdcntl}, @fref{mt_save mt_load}. |
| @end table |
@end table |
| |
|
| |
\JP @node isqrt,,, $B?t$N1i;;(B |
| |
\EG @node isqrt,,, Numbers |
| |
@subsection @code{isqrt} |
| |
@findex isqrt |
| |
|
| |
@table @t |
| |
@item isqrt(@var{n}) |
| |
\JP :: $BJ?J}:,$r1[$($J$$:GBg$N@0?t$r5a$a$k(B. |
| |
\EG :: The integer square root of @var{n}. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
\JP $BHsIi@0?t(B |
| |
\EG non-negative integer |
| |
@item n |
| |
\JP $BHsIi@0?t(B |
| |
\EG non-negative integer |
| |
@end table |
| |
|
| \JP @node inv,,, $B?t$N1i;;(B |
\JP @node inv,,, $B?t$N1i;;(B |
| \EG @node inv,,, Numbers |
\EG @node inv,,, Numbers |
| @subsection @code{inv} |
@subsection @code{inv} |
| Line 302 If one of argument is equal to 0, the return 0. |
|
| Line 322 If one of argument is equal to 0, the return 0. |
|
| @item return |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i,m |
@item i m |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
| Line 727 These functions works also for polynomials with comple |
|
| Line 747 These functions works also for polynomials with comple |
|
| @code{deval} $B$OG\@:EYIbF0>.?t$r7k2L$H$7$F(B |
@code{deval} $B$OG\@:EYIbF0>.?t$r7k2L$H$7$F(B |
| @code{eval} $B$N>l9g(B, $BM-M}?t$O$=$N$^$^;D$k(B. |
@code{eval} $B$N>l9g(B, $BM-M}?t$O$=$N$^$^;D$k(B. |
| @item |
@item |
| @code{eval} $B$K$*$$$F$O(B, $B7W;;$O(B @b{PARI} (@xref{pari}) $B$,9T$&(B. |
@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$$$F9T$&(B. |
@code{deval} $B$K$*$$$F$O(B, $B7W;;$O(B C $B?t3X%i%$%V%i%j$N4X?t$rMQ$$$F9T$&(B. |
| @item |
@item |
| @code{deval} $B$OJ#AG?t$O07$($J$$(B. |
@code{deval} $B$OJ#AG?t$O07$($J$$(B. |
| Line 735 These functions works also for polynomials with comple |
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| Line 755 These functions works also for polynomials with comple |
|
| @code{eval} $B$K$*$$$F$O(B, |
@code{eval} $B$K$*$$$F$O(B, |
| @var{prec} $B$r;XDj$7$?>l9g(B, $B7W;;$O(B, 10 $B?J(B @var{prec} $B7eDxEY$G9T$o$l$k(B. |
@var{prec} $B$r;XDj$7$?>l9g(B, $B7W;;$O(B, 10 $B?J(B @var{prec} $B7eDxEY$G9T$o$l$k(B. |
| @var{prec} $B$N;XDj$,$J$$>l9g(B, $B8=:_@_Dj$5$l$F$$$k@:EY$G9T$o$l$k(B. |
@var{prec} $B$N;XDj$,$J$$>l9g(B, $B8=:_@_Dj$5$l$F$$$k@:EY$G9T$o$l$k(B. |
| (@xref{setprec}) |
(@xref{setprec}.) |
| @item |
@item |
| @table @t |
@table @t |
| @item $B07$($kH!?t$O(B, $B<!$NDL$j(B. |
@item $B07$($kH!?t$O(B, $B<!$NDL$j(B. |
|
|
| double float. Rational numbers remain unchanged in results from @code{eval}. |
double float. Rational numbers remain unchanged in results from @code{eval}. |
| @item |
@item |
| In @code{eval} the computation is done |
In @code{eval} the computation is done |
| by @b{PARI} (@xref{pari}). In @code{deval} the computation is |
by @b{PARI}. (@xref{pari}.) In @code{deval} the computation is |
| done by the C math library. |
done by the C math library. |
| @item |
@item |
| @code{deval} cannot handle complex numbers. |
@code{deval} cannot handle complex numbers. |
| Line 778 done by the C math library. |
|
| Line 798 done by the C math library. |
|
| When @var{prec} is specified, computation will be performed with a |
When @var{prec} is specified, computation will be performed with a |
| precision of about @var{prec}-digits. |
precision of about @var{prec}-digits. |
| If @var{prec} is not specified, computation is performed with the |
If @var{prec} is not specified, computation is performed with the |
| precision set currently. (@xref{setprec}) |
precision set currently. (@xref{setprec}.) |
| @item |
@item |
| Currently available numerical functions are listed below. |
Currently available numerical functions are listed below. |
| Note they are only a small part of whole @b{PARI} functions. |
Note they are only a small part of whole @b{PARI} functions. |
| Line 983 For details of individual functions, refer to the @b{P |
|
| Line 1003 For details of individual functions, refer to the @b{P |
|
| @code{lngamma}, |
@code{lngamma}, |
| @code{logagm}, |
@code{logagm}, |
| @code{mat}, |
@code{mat}, |
| @code{matinvr}, |
|
| @code{matrixqz2}, |
@code{matrixqz2}, |
| @code{matrixqz3}, |
@code{matrixqz3}, |
| @code{matsize}, |
@code{matsize}, |
| Line 1098 We will improve @b{Asir} so that it can provide more f |
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| Line 1117 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$,$"$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. |
$B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B. |
| @item |
@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 |
@item |
| @b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B. |
@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. |
@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 1114 The return value is always the previous precision in d |
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| Line 1133 The return value is always the previous precision in d |
|
| the existence of an argument. |
the existence of an argument. |
| |
|
| @item |
@item |
| @b{Bigfloat} operations are done by @b{PARI}. (@xref{pari}) |
@b{Bigfloat} operations are done by @b{PARI}. (@xref{pari}.) |
| @item |
@item |
| This is effective for computations in @b{bigfloat}. |
This is effective for computations in @b{bigfloat}. |
| Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.' |
Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.' |
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