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Fixed typos.

%% $OpenXM: OpenXM/src/asir-contrib/packages/doc/ox_pari/ox_pari-en.texi,v 1.3 2020/08/28 00:58:10 takayama Exp $
%% debug に ln -s ../texinfo-ja.tex . をしておく.
%% xetex ox_pari-ja.texi   (.texi までつける. ) 
%% 以下コメントは @comment で始める.  \input texinfo 以降は普通の tex 命令は使えない.
\input texinfo-ja
@iftex
@catcode`@#=6
@def@fref#1{@xrefX[#1,,@code{#1},,,]}
@def@b#1{{@bf #1}}
@catcode`@#=@other
@end iftex
@c tex
@c \overfullrule=0pt
@c end tex
@documentlanguage ja
@c -*-texinfo-*-
@comment %**start of header
@comment --- おまじない終り ---

@comment --- GNU info ファイルの名前 ---
@setfilename ox_pari-en

@comment --- タイトル ---
@settitle ox_pari

@comment %**end of header
@comment %@setchapternewpage odd

@comment --- おまじない ---
@ifinfo
@macro fref{name}
@ref{\name\,,@code{\name\}}
@end macro
@end ifinfo

@iftex
@comment @finalout
@end iftex

@titlepage
@comment --- おまじない終り ---

@comment --- タイトル, バージョン, 著者名, 著作権表示 ---
@title ox_pari
@subtitle Risa/Asir ox_pari server
@subtitle 1.0 版
@subtitle August 27, 2020.

@author  by Risa/Asir committers
@page
@vskip 0pt plus 1filll
Copyright @copyright{} Risa/Asir committers
2020--2020. All rights reserved.
@end titlepage

@comment --- おまじない ---
@synindex vr fn
@comment --- おまじない終り ---

@comment --- @node は GNU info, HTML 用 ---
@comment --- @node  の引数は node-name,  next,  previous,  up ---
@node Top,, (dir), (dir)

@comment --- @menu は GNU info, HTML 用 ---
@comment --- chapter 名を正確に並べる ---
@comment --- この文書では chapter XYZ, Chapter Index がある.
@comment ---  Chapter XYZ には section XYZについて, section XYZに関する関数がある.
@menu
* About ox_pari
* ox_pari functions::
* Index::
@end menu

@comment --- chapter の開始 ---
@comment --- 親 chapter 名を正確に. 親がない場合は Top ---
@node About ox_pari,,, Top
@chapter About ox_pari

The ox_pari is an OpenXM server for the number theory system pari.
Pari functions can be called as
@example
pari(function name, argument 1, ...);
@end example
@noindent
The function names which can be called by the OpenXM are listed 
in the next chapter.

@sp 3
@noindent
Pari/gp is a system for the number theory developed 
at Bordeaux university.
See the following web page.
@itemize @bullet
@item [pari-gp] 
@uref{http://pari.math.u-bordeaux.fr/index.html}
@end itemize

@node ox_pari functions,,, Top
@chapter ox_pari functions

@menu
* pari::
@end menu

@comment **********************************************************
@comment --- ◯◯◯◯  の説明 
@comment --- 個々の関数の説明の開始 ---
@comment --- section 名を正確に ---
@node pari,,, ox_pari functions
@section @code{ox_pari}
@comment --- 索引用キーワード
@findex pari

@table @t
@item pari(@var{func},@var{arg1},@var{arg2}, ...)
:: Call the pari function @var{func}.
@end table

@comment --- 引数の簡単な説明 ---  以下まだ書いてない.
@table @var
@item return
Result by the pari function.
@item argn
Argument for the pari function.
@end table

@comment --- ここで関数の詳しい説明 ---
@comment --- @itemize〜@end itemize は箇条書き ---
@comment --- @bullet は黒点付き ---
@itemize @bullet
@item
ox_pari server starts automatically when the user calls the pari function
first time.
The number number can be obtained by ctrl("oxpari_id") or ox_get_serverinfo().
In order to interrupt ox_pari or shutdown ox_pari, use
ox_reset(server number) and ox_shutdown(server number) respectively.
As to these functions, refer to the Risa/Asir manual
(see, e.g., documents of @uref{http://www.openxm.org}).
@item 
pari library functions are 
described in @uref{https://pari.math.u-bordeaux.fr/dochtml/html/}
@item 
The pari library listed below can be called from Risa/Asir. 
Note that names of library functions are sometimes different with gp function names.
@end itemize

@comment OpenXM/src/ox_pari/pari_ftab.c を取り込む.
@smallformat
@verbatim
/* type=1 : one num/poly/mat arg */
/* type=2 : 1starg=num/poly/mat arg, 2ndarg=0(flag) */

struct parif parif_tab[] = {
/* (ulong)allocatemoremem(ulong) */
  {"allocatemem",(GEN (*)())allocatemoremem,0},
/* num/num */
  {"abs",gabs,1},
  {"erfc",gerfc,1},
  {"arg",garg,1},
  {"isqrt",racine,1},
  {"gamma",ggamma,1},
  {"zeta",gzeta,1},
  {"floor",gfloor,1},
  {"frac",gfrac,1},
  {"imag",gimag,1},
  {"conj",gconj,1},
  {"ceil",gceil,1},
  {"isprime",gisprime,2},
  {"bigomega",gbigomega,1},
  {"denom",denom,1},
  {"numer",numer,1},
  {"lngamma",glngamma,1},
  {"logagm",glogagm,1},
  {"classno",classno,1},
  {"dilog",dilog,1},
  {"disc",discsr,1},
  {"discf",discf,1},
  {"nextprime",nextprime,1},
  {"eintg1",eint1,1},
  {"eta",eta,1},
  {"issqfree",gissquarefree,1},
  {"issquare",gcarreparfait,1},
  {"gamh",ggamd,1},
  {"hclassno",classno3,1},

  /* num/array */
  {"binary",binaire,1},
  {"factorint",factorint,2},
  {"factor",Z_factor,1},
  {"cf",gcf,1},
  {"divisors",divisors,1},
  {"smallfact",smallfact,1},

  /* poly/poly */
  {"centerlift",centerlift,1},
  {"content",content,1},

  /* poly/array */
  {"galois",galois,1},
  {"roots",roots,1},
  {"factpol",factpol,1},

  /* mat/mat */
  {"adj",adj,1},
  {"lll",lll,1},
  {"lllgen",lllgen,1},
  {"lllgram",lllgram,1},
  {"lllgramgen",lllgramgen,1},
  {"lllgramint",lllgramint,1},
  {"lllgramkerim",lllgramkerim,1},
  {"lllgramkerimgen",lllgramkerimgen,1},
  {"lllint",lllint,1},
  {"lllkerim",lllkerim,1},
  {"lllkerimgen",lllkerimgen,1},
  {"trans",gtrans,1},
  {"eigen",eigen,1},
  {"hermite",hnf,1},
  {"mat",gtomat,1},
  {"matrixqz2",matrixqz2,1},
  {"matrixqz3",matrixqz3,1},
  {"hess",hess,1},
  {"ker",ker,1},
  {"keri",keri,1},
  {"kerint",kerint,1},
  {"kerintg1",kerint1,1},

  /* mat/poly */
  {"det",det,1},
  {"det2",det2,1},

  /* not examined yet */
  {"image",image,1},
  {"image2",image2,1},
  {"indexrank",indexrank,1},
  {"indsort",indexsort,1},
  {"initalg",initalg,1},
  {"isfund",gisfundamental,1},
  {"ispsp",gispsp,1},
  {"jacobi",jacobi,1},
  {"jell",jell,1},
  {"length",(GEN(*)())glength,1},
  {"lexsort",lexsort,1},
  {"lift",lift,1},
  {"lindep",lindep,1},
  {"modreverse",polymodrecip,1},
  {"mu",gmu,1},
  {"norm",gnorm,1},
  {"norml2",gnorml2,1},
  {"numdiv",numbdiv,1},
  {"omega",gomega,1},
  {"order",order,1},
  {"ordred",ordred,1},
  {"phi",phi,1},
  {"pnqn",pnqn,1},
  {"primroot",gener,1},
  {"psi",gpsi,1},
  {"quadgen",quadgen    ,1},
  {"quadpoly",quadpoly    ,1},
  {"recip",polrecip       ,1},
  {"redreal",redreal       ,1},
  {"regula",regula  ,1},
  {"reorder",reorder  ,1},
  {"rhoreal",rhoreal       ,1},
  {"sigma",sumdiv,1},
  {"signat",signat,1},
  {"simplify",simplify,1},
  {"smith",smith,1},
  {"smith2",smith2,1},
  {"sort",sort,1},
  {"sqr",gsqr,1},
  {"sqred",sqred,1},
  {"sqrt",gsqrt,1},
  {"supplement",suppl,1},
  {"trace",gtrace,1},
  {"trunc",gtrunc,1},
  {"unit",fundunit,1},
  {"wf",wf,1},
  {"wf2",wf2,1},
};
@end verbatim
@end smallformat

@sp 3
@noindent
Example,
finding 
Ker(P: Z^4 ---> Z^2).
@example
pari(kerint,P=newmat(2,4,[[1,1,1],[0,1,3,4]]));
@end example
@noindent
In order to find a description of kerint,
please visit
@uref{https://pari.math.u-bordeaux.fr/dochtml/html/}
(the function name in gp is matkerint.)


@comment --- 参照(リンク)を書く ---
@table @t
@item 参照
@comment @ref{pari}
@end table

@comment --- ChangeLog を書く. ソースコードの位置. 変更日時 など CVSサーバを見るため
@noindent
ChangeLog
@itemize @bullet
@item
The table is in OpenXM/src/ox_pari/pari_ftab.c
@end itemize



@comment --- おまじない ---
@node Index,,, Top
@unnumbered Index
@printindex fn
@printindex cp
@iftex
@vfill @eject
@end iftex
@summarycontents
@contents
@bye
@comment --- おまじない終り ---


@comment テンプレート.  start_of_template.
@comment **********************************************************
@comment --- ◯◯◯◯  の説明 
@comment --- 個々の関数の説明の開始 ---
@comment --- section 名を正確に ---
@node gtt_ekn3.hoge,,, 超幾何関数E(k,n)
@subsection @code{gtt_ekn3.hoge}
@comment --- 索引用キーワード
@findex gtt_ekn3.hoge

@table @t
@item gtt_ekn3.hoge(@var{i})
:: 
@end table

@comment --- 引数の簡単な説明 ---  以下まだ書いてない.
@table @var
@item i  hage
@item return  
@end table

@comment --- ここで関数の詳しい説明 ---
@comment --- @itemize〜@end itemize は箇条書き ---
@comment --- @bullet は黒点付き ---
@itemize @bullet
@item 説明.
@end itemize

@comment --- @example〜@end example は実行例の表示 ---
例: 
@example
[2221] gtt_ekn3.hoge([[1,4],[2,3]]);
@end example


@comment --- 参照(リンク)を書く ---
@table @t
@item 参照
@ref{gtt_ekn3.nc}
@ref{gtt_ekn3.gmvector}
@end table

@comment --- ChangeLog を書く. ソースコードの位置. 変更日時 など CVSサーバを見るため
@noindent
ChangeLog
@itemize @bullet
@item
@end itemize
@comment end_of_template