File: [local] / OpenXM / src / asir-doc / exp / exp-ja.texi (download)
Revision 1.38, Wed Feb 10 05:49:58 2010 UTC (14 years, 4 months ago) by takayama
Branch: MAIN
CVS Tags: R_1_3_1-2
Changes since 1.37: +64 -1
lines
fj_simplify.rr is a collection of functions to simplify expressions containing
x^a.
This initial version is written by M.Fujimoto.
Example:
load("fj_simplify.rr");
simplify(x^(1/2)*x^(-1/2));
|
%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.38 2010/02/10 05:49:58 takayama Exp $
\input texinfo
@iftex
@catcode`@#=6
@def@fref#1{@xrefX[#1,,@code{#1},,,]}
@def@b#1{{@bf@gt #1}}
@catcode`@#=@other
@end iftex
@overfullrule=0pt
@c -*-texinfo-*-
@comment %**start of header
@comment --- $B$*$^$8$J$$=*$j(B ---
@comment --- GNU info $B%U%!%$%k$NL>A0(B ---
@setfilename xyzman
@comment --- $B%?%$%H%k(B ---
@settitle $B<B83E*;EMM$N4X?t(B
@comment %**end of header
@comment %@setchapternewpage odd
@comment --- $B$*$^$8$J$$(B ---
@ifinfo
@macro fref{name}
@ref{\name\,,@code{\name\}}
@end macro
@end ifinfo
@iftex
@comment @finalout
@end iftex
@titlepage
@comment --- $B$*$^$8$J$$=*$j(B ---
@comment --- $B%?%$%H%k(B, $B%P!<%8%g%s(B, $BCx<TL>(B, $BCx:n8"I=<((B ---
@title $B<B83E*;EMM$N4X?t(B
@subtitle Risa/Asir $B<B83E*;EMM4X?t@bL@=q(B
@subtitle 1.0 $BHG(B
@subtitle 2010 $BG/(B 2 $B7n(B
@author by Risa/Asir committers
@page
@vskip 0pt plus 1filll
Copyright @copyright{} Risa/Asir committers
2004--2010. All rights reserved.
@end titlepage
@comment --- $B$*$^$8$J$$(B ---
@synindex vr fn
@comment --- $B$*$^$8$J$$=*$j(B ---
@comment --- @node $B$O(B GNU info, HTML $BMQ(B ---
@comment --- @node $B$N0z?t$O(B node-name, next, previous, up ---
@node Top,, (dir), (dir)
@comment --- @menu $B$O(B GNU info, HTML $BMQ(B ---
@comment --- chapter $BL>$r@53N$KJB$Y$k(B ---
@comment --- $B$3$NJ8=q$G$O(B chapter XYZ, Chapter Index $B$,$"$k(B.
@comment --- Chapter XYZ $B$K$O(B section XYZ$B$K$D$$$F(B, section XYZ$B$K4X$9$k4X?t$,$"$k(B.
@menu
* $B<B83E*;EMM$N4X?t@bL@=q$K$D$$$F(B::
* $B<B83E*;EMM$N4X?t(B::
* Index::
@end menu
@comment --- chapter $B$N3+;O(B ---
@comment --- $B?F(B chapter $BL>$r@53N$K(B. $B?F$,$J$$>l9g$O(B Top ---
@node $B<B83E*;EMM$N4X?t@bL@=q$K$D$$$F(B,,, Top
@chapter $B<B83E*;EMM$N4X?t@bL@=q$K$D$$$F(B
$B$3$N@bL@=q$G$O(B
@b{Asir} $B$KF3F~$5$l$?<B83E*;EMM$N4X?t$K$D$$$F@bL@$9$k(B.
$B@5<0$J4X?t$H$7$FF3F~$5$l$?$b$N$N5-=R$O(B Risa/Asir $B%^%K%e%"%k(B
$B$K0\F0$5$l$k(B.
ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvsweb $B$G(B
$B%=!<%9%3!<%I$rFI$`;~$N=u$1$K$J$k>pJs$,=q$+$l$F$$$k(B.
@node $B<B83E*;EMM$N4X?t(B,,, Top
@chapter $B<B83E*;EMM$N4X?t(B
@comment --- section ``$B<B83E*4X?t(B'' $B$N(B subsection xyz_abc
@comment --- subsection xyz_pqr xyz_stu $B$,$"$k(B.
@menu
* quotetotex::
* quotetotex_env::
* objtoquote::
* copyright::
* string_to_tb::
* tb_to_string::
* write_to_tb::
* dp_gr_main::
* asir-port.sh::
* asir-install.sh::
* get_struct_name::
* get_element_names::
* get_element_at::
* put_element_at::
* dp_initial_term::
* dp_order::
* dp_weyl_gr_main::
* list::
* mapat::
* set_print_function::
* small_jacobi::
* flatten_quote::
* printf::
* fprintf::
* sprintf::
* quote_to_funargs::
* funargs_to_quote::
* get_function_name::
* remove_paren::
* set_secure_mode::
* set_secure_flag::
* initialize_static_variable::
* eval_quote::
* nqt_match::
* nqt_match_rewrite::
* qt_normalize::
* qt_set_coef::
* qt_set_ord::
* qt_set_weight::
* nqt_comp::
* qt_is_var::
* qt_is_ceof::
* qt_rewrite::
* asirgui.hnd::
* noro_matrix.rr:
* f_res::
* chdir::
* pwd::
* dcurrenttime::
* nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module)::
* nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option)::
* tk_pf.rkn::
@end menu
@node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B
@section $B%/%*!<%H(B
@comment --- $B"~"~"~"~(B $B4X?t(B quotetotex, quotetotex_env $B$N@bL@(B $B"~"~"~"~(B
@comment --- $B8D!9$N4X?t$N@bL@$N3+;O(B ---
@comment --- section $BL>$r@53N$K(B ---
@node quotetotex quotetotex_env,,, $B%/%*!<%H(B
@subsection @code{quotetotex}, @code{quotetotex_env}
@comment --- $B:w0zMQ%-!<%o!<%I(B
@findex quotetotex
@findex quotetotex_env
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item quotetotex(@var{q})
:: @var{q} $B$r(B latex $B7A<0$GI=8=$7$?J8;zNs$KJQ49$9$k(B.
@item quotetotex_env(@var{key},@var{value})
:: quotetotex $B$NF0:n$r@)8f$9$k%Q%i%a!<%?$rJQ99$9$k(B.
@item quotetotex_env()
:: quotetotex $B$NF0:n$r@)8f$9$k%Q%i%a!<%?$N8=:_CM$rLa$9(B.
@item quotetotex_env(0)
:: quotetotex $B$NF0:n$r@)8f$9$k%Q%i%a!<%?$r%G%U%)!<%k%HCM$KLa$9(B.
@end table
@comment --- $B0z?t$N4JC1$J@bL@(B ---
@table @var
@item return
$BJ8;zNs(B(quotetotex) $B$^$?$O(B $B%j%9%H$^$?$O%*%V%8%'%/%H(B(quotetotex_env)
@item q
quote
@item key
$BJ8;zNs(B
@item value
$B%*%V%8%'%/%H(B
@end table
@comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
@comment --- @bullet $B$O9uE@IU$-(B ---
@itemize @bullet
@item
quotetotex $B$O(B @var{q} $B$r(B latex $B7A<0$GI=8=$7$?J8;zNs$KJQ49$9$k(B.
@item
$B0J2<(B quotetotex_env $B$N%Q%i%a!<%?$N0UL#$r@bL@$9$k(B.
@item
conv_rule: 3 $B%S%C%H$rMQ$$$FJQ49%k!<%k$r;XDj$9$k(B.
0$B%S%C%HL\$O(B symbol_table $B$K$h$kJQ49$r9T$&$+(B,
1$B%S%C%HL\$OE:;zJQ49$r9T$&$+(B,
2$B%S%C%HL\$O(B d $B$+$i;O$^$kJQ?tL>$rHyJ,:nMQAG$H$_$J$7$F=hM}$9$k$+(B,
$B$r0UL#$9$k(B.
$B$?$H$($P(B conv_rule $B$H$7$F(B 3 $B$r;XDj$9$k$H(B,
0$B%S%C%HL\(B, 1 $B%S%C%HL\$,(B 1 $B$H$J$k$N$G(B
symbol_table $B$K$h$kJQ49$r9T$$(B, $BE:;zJQ49$r$*$3$J$&(B.
$BE:;zJQ49$O?t;z$H1Q;z$N6-L\$*$h$S(B _ $B5-9f$r6h@Z$j$H$9$k(B.
symbol_table $B$K$h$kJQ49$,:G=i$KE,MQ$5$l$k(B.
alpha, beta, $BEy$O<+F0E*$r%.%j%7%cJ8;z$KJQ49$9$k%F!<%V%k$O(B
$BFbB"$:$_(B.
@item
dp_vars_prefix: $BJ,;6I=8=B?9`<0$O(B
@iftex
@tex
$x_0, x_1, \cdots$
@end tex
@end iftex
@ifinfo
x0, x1, ...
@end ifinfo
$B$NB?9`<0$H$7$F(B latex $B7A<0$KJQ49$5$l$k$,$3$N(B
x $B$NItJ,$rJQ99$9$k(B.
@item
dp_vars_origin: $B%$%s%G%C%/%9$N;O$^$j$NCM$r;XDj$9$k(B.
$B%G%U%)!<%k%H$O(B 0.
@item
dp_vars_hweyl: $BJ,;6I=8=B?9`<0$r%o%$%kBe?t$N85$H$_$J$7$F(B
latex $B7A<0$KJQ49$9$k(B.
$B6v?t8DJQ?t$,$"$k$H$-$O(B $B:G=i$NH>J,$r(B
@iftex
@tex
$x_0, x_1, \cdots$
@end tex
$B$K8eH>$NH>J,$r(B
@tex
$\partial_0, \partial_1, \cdots$
@end tex
@end iftex
@ifinfo
x0, x1, ... $B$K8eH>$NH>J,$r(B dx0, dx1, ...
@end ifinfo
$B$KJQ49$9$k(B.
$B4q?t8D$N>l9g$O:G8e$NJQ?t$,F1;~2=JQ?t$H$7$F(B h $B$GI=<($5$l$k(B.
@item
dp_dvars_prefix: dp_vars_hweyl $B$,(B 1 $B$N;~$K8eH>ItJ,$N(B prefix $B$r;XDj$9$k(B.
$B%G%U%)!<%k%H$O(B @tex $\partial$ @end tex
@item
dp_dvars_origin: dp_vars_hweyl $B$,(B 1 $B$N;~$N%$%s%G%C%/%9$N;O$^$j$NCM(B.
@item
conv_func: $B%f!<%6Dj5A$NJQ494X?t$r$h$V(B.
@end itemize
@comment --- @example$B!A(B@end example $B$O<B9TNc$NI=<((B ---
@example
[3] quotetotex(quote(1/(x+1)));
\frac@{ 1@} @{ ( @{x@}+ 1)@}
[4] quotetotex(objtoquote(diff(x^x,x)));
@{x@}^@{ @{x@}- 1@} @{x@}+ \log( @{x@}) @{x@}^@{ @{x@}@}
[5] quotetotex_env("conv_rule",3);
[6] quotetotex(objtoquote( (alpha2beta+x_i_j)^2));
@{\alpha@}_@{2,\beta@}^@{ 2@} + 2 @{x@}_@{i,j@} @{\alpha@}_@{2,\beta@}+ @{x@}_@{i,j@}^@{ 2@}
@end example
@comment --- $B;2>H(B($B%j%s%/(B)$B$r=q$/(B ---
@table @t
@item $B;2>H(B
@ref{objtoquote}
print_tex_form(contrib)
@end table
@comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$N4X?t$O(B 2004$BG/(B2$B7nKv$+$i(B3$B7n$K$+$1$F(B asir $B$r(B
knoppix $BHG(B texmacs $B$KBP1~$5$;$k$?$a$K=q$+$l$?(B.
Asir-contrib $B$N(B print_tex_form $B$,$=$N867?$G$"$j(B, $B$=$l$r8zN(2=$7$^$?(B
$B=PNO7A<0$r2~A1$7$?(B.
OpenXM/src/kxx/ox_texmacs.c, OpenXM/src/texmacs $B$b;2>H(B.
@item
OpenXM/src/asir-contrib/packages/src/noro_print.rr 1.1--1.8,
noro_print_default.rr 1.1--1.3 $B$b;2>H(B.
@item
$BJQ99$r<u$1$?%U%!%$%k$O(B OpenXM_contrib2/asir2000 $B$N2<$N<!$N%U%!%$%k(B.
builtin/strobj.c 1.14--1.43,
include/ca.h 1.46, io/cexpr.c 1.18, io/pexpr.c 1.32, io.sexpr.c 1.29,
parse/arith.c 1.12, parse/parse.h 1.28--1.29,
parse/quote.c 1.7--1.8, 1.12.
@item
knoppix/math $B$O(B $BJ!2,Bg3X$N_@ED$5$s$,Cf?4$H$J$j3+H/$5$l$F$$$k(B.
@item
dp_dvars_prefix, *_origin $B$O(B builtin/strobj.c 1.46 $B$GF3F~$5$l$?(B.
@item
Todo: quotetoterminalform ($BJ,;6I=8=B?9`<0$N8+0W$$=PNO(B).
@end itemize
@comment --- $B"~"~"~"~(B $B4X?t(B objtoquote $B$N@bL@(B $B"~"~"~"~(B
@node objtoquote,,, $B%/%*!<%H(B
@subsection @code{objtoquote}
@findex objtoquote
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item objtoquote(@var{ob})
:: $B%*%V%8%'%/%H$H(B quote $B7?$N%G!<%?$KJQ49$9$k(B.
@end table
@table @var
@item return
quote
@item ob
$B%*%V%8%'%/%H(B
@end table
@itemize @bullet
@item
@code{objtoquote(ob)} $B$O(B, @var{ob} $B$r(B quote $B7?$N%G!<%?$KJQ49$9$k(B.
@end itemize
@example
[1150] quotetolist(quote(1+2));
[b_op,+,[internal,1],[internal,2]]
[1151] quotetolist(objtoquote(1+x));
[b_op,+,[internal,x],[internal,1]]3
@end example
@table @t
@item $B;2>H(B
@ref{quotetotex} @ref{quotetolist}
@end table
@comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B quotetotex $B$NA0=hM}$r$9$k$?$a$K=q$+$l$?(B.
@item asir-contrib $B$N4X?t(B quote_to_quote $B$b;2>H(B.
@item OpenXM_contrib2/asir2000/builtin/print.c 1.16.
@end itemize
@node flatten_quote,,, $B%/%*!<%H(B
@subsection @code{flatten_quote}
@findex flatten_quote
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item flatten_quote(@var{q},@var{op})
:: quote $B$N3g8L$r$H$j$5$k(B.
@end table
@table @var
@item return
Quote
@item q
Quote
@item op
$B1i;;;R$rI=$9J8;zNs(B.
@end table
@itemize @bullet
@item
Quote $B7?$N%G!<%?$OLZ9=B$$r$7$F$$$k(B
( quotetolist $B;2>H(B ).
@code{quote_flatten()} $B$O(B, @var{q} $B$NCf$K$"$i$l$k1i;;;R(B @var{op}
$B$N;R6!%N!<%I$rJ?Ey$K$9$k(B.
$B$D$^$j1i;;;R(B @var{op} $B$K4X$9$k3g8L$E$1$,$"$C$?>l9g$=$l$r$9$Y$F$H$j$5$k(B.
$B$?$H$($P(B (1+2)+(3+4) $B$H$$$&I=8=$r(B 1+2+3+4 $B$KJQ49$9$k(B.
@item
$B8=:_$N<BAu$G$O(B n-ary $B$N1i;;;R$ODj5A$5$l$F$$$J$$$N$G(B,
1+2+3 $B$O<B$O(B 1+(2+3) $B$HI=8=$5$l$F$$$k(B.
$B$D$^$j(B + $B1i;;;R$O1&7k9gE*$G$"$k(B.
@item R=0; for (I=0; I<N; I++) R = R+ P[I]; $B$J$kB-$7;;$r7+$jJV$9$H(B,
+ $B$O:87k9gE*$K$J$k(B. $B1&7k9gE*$KJQ49$9$k$K$O(B flatten_quote $B$r8F$V(B.
@item $BL>A0$O(B quote_flatten $B$G$J$/(B flatten_quote $B$G$"$k(B.
@end itemize
@example
[1288] flatten_quote(quote((1+2)+(3+4*(x+3))),"+");
quote(1+2+3+4*(x+3))
[1289] flatten_quote(quote( (x*y)*(p*3)-(x*y)*z),"*");
quote(x*y*p*3-x*y*z)
[1290] quotetolist(quote(1+2+3));
[b_op,+,[b_op,+,[internal,1],[internal,2]],[internal,3]]
@end example
@table @t
@item $B;2>H(B
@ref{quotetolist}, @ref{print_tex_form}(contrib)
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$N4X?t$O(B 2004-7-7 $B$+$i(B 2004-7-8 $B$K$+$1$F(B
quote $B$K4X$9$kA`:n$r8&5f$9$k$?$a$K<B83E*$K=q$+$l$?(B.
OpenXM/fb $B$GC_@Q$5$l$?8x<0$NITMW$J3g8L$r$H$j$O$:$7(B, tex $B7A<0$KJQ49$9$k$N$K(B
$B1~MQ(B.
@item
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B
builtin/strobj.c 1.47,
parse/eval.c 1.35,
parse/parse.h 1.31,
parse/quote.c 1.14--1.16.
@end itemize
@node quote_to_funargs,,, $B%/%*!<%H(B
@subsection @code{quote_to_funargs}, @code{funargs_to_quote}, @code{remove_paren}
@findex quote_to_funargs
@findex funargs_to_quote
@findex remove_paren
@table @t
@item quote_to_funargs(@var{q})
:: quote $B$r(B funarg $B7A<0(B($B%j%9%H(B) $B$X(B.
@item funargs_to_quote(@var{f})
:: funarg $B7A<0$r(B quote $B$X(B.
@item get_function_name(@var{f})
:: funarg $B7A<0$N(B op $B$rJ8;zNs$X(B.
@item remove_paren(@var{q})
:: $B>e$N4X?t$rMQ$$$F=q$+$l$?M>J,$J3g8L$r<h$j5n$k(B simplifier (asir-contrib $B%^%K%e%"%k$X(B: todo)
@end table
@table @var
@item return
quote(funargs_to_quote, remove_paren) $B$+(B $B%j%9%H(B(quote_to_funargs)
@item q
quote
@item f
$B%j%9%H(B
@end table
@itemize @bullet
@item
@code{quote_to_funargs} $B$O(B quote $B7?$N%G!<%?(B ($BFbItE*$K$O(B FNODE) $B$r(B
quote $B$X$NI|852DG=$J7A$G%j%9%H$XJQ49$9$k(B.
@code{quotetolist} $B$O(B quote $B$r%j%9%H$XJQ49$9$k$,(B, $B0lIt$N>pJs$r<N$F$k$?$a(B
$B$b$H$N(B quote $B$NI|85$O$G$-$J$$(B.
@item
@code{quote_to_funargs} $B$NLa$jCM$O(B [fid, op, arg1, arg2, ...]
$B$J$k7A<0$r$7$F$$$k(B.
$B$3$3$G(B op $B$O(B node $B$NL>A0$G$"$j(B,
$B4X?t(B @code{get_function_name} $B$rMQ$$$F?M4V$,FI$a$k7A<0(B
$B$G<h$j$@$;$k(B.
$B$?$H$($P(B @code{get_function_name(quote_to_funargs(quote(1+2))[1])}
$B$O(B "+" $B$rLa$9(B.
@item
$BL>A0(B@code{get_function_name} $B$O$=$N$&$AJQ99$5$l$k$@$m$&(B.
@item
$B2<$NNc$G(B
quote_to_funargs(FA[2]);
[34,[b_op,+,[internal,x],[internal,1]]]
$B$H$J$k(B.
34 $B$O(B @code{I_PAREN} $B$r0UL#$9$k(B.
$B?t$H0UL#$NBP1~I=$O(B @code{OpenXM/src/asir-contrib/packages/src/noro_simplify.rr}
$B$^$?$O(B @code{OpenXM_contrib2/asir2000/parse/parse.h} $B$r8+$h(B.
$B0J2<$N(B fid $B$,(B 0, 1, 2, ... $B$KBP1~$E$1$i$l$F$$$k(B.
I_BOP, I_COP, I_AND, I_OR, I_NOT, I_CE,
I_PRESELF, I_POSTSELF,
I_FUNC, I_FUNC_OPT, I_IFUNC, I_MAP, I_RECMAP, I_PFDERIV,
I_ANS, I_PVAR, I_ASSPVAR,
I_FORMULA, I_LIST, I_STR, I_NEWCOMP, I_CAR, I_CDR, I_CAST,
I_INDEX, I_EV, I_TIMER, I_GF2NGEN, I_GFPNGEN, I_GFSNGEN,
I_LOP, I_OPT, I_GETOPT, I_POINT, I_PAREN, I_MINUS,
I_NARYOP
@end itemize
$B<!$NNc$G$O(B (x+1)+(x+2) $B$N3g8L$r$O$:$7$F(B x+1+x+2 $B$KJQ49$7$F$$$k(B.
@example
[0] ctrl("print_quote",1) $
[1] Q=quote((x+1)+(x+2));
[b_op,+,[u_op,(),[b_op,+,[internal,x],[internal,1]]],
[u_op,(),[b_op,+,[internal,x],[internal,2]]]]
[2] FA=quote_to_funargs(Q);
[0,<...quoted...>,
[u_op,(),[b_op,+,[internal,x],[internal,1]]],
[u_op,(),[b_op,+,[internal,x],[internal,2]]]]
[3] FA2=quote_to_funargs(FA[2])[1];
[b_op,+,[internal,x],[internal,1]]
[4] FA3=quote_to_funargs(FA[3])[1];
[b_op,+,[internal,x],[internal,2]]
[5] funargs_to_quote([FA[0],FA[1],FA2,FA3]);
[b_op,+,[b_op,+,[internal,x],[internal,1]],
[b_op,+,[internal,x],[internal,2]]]
@end example
$B<!$NNc$O(B OpenXM/asir-contrib $BHG$N(B asir $B$G<B9T(B.
@example
[1287] load("noro_simplify.rr");
1
[1293] noro_simplify.remove_paren(quote( f(1-(x))));
quote(f(1-x))
@end example
funargs_to_quote $B$rMQ$$$F4{B8$N(B quote $B$N;R6!$rCV$-49$($F(B
$B?7$7$$(B quote $B$r$D$/$j=P$;$k(B.
@example
[1184] R=quote_to_funargs(quote(a+(b+c)));
[0,<...quoted...>,<...quoted...>,<...quoted...>]
[1185] T=quote_to_funargs(quote(1+2));
[0,<...quoted...>,<...quoted...>,<...quoted...>]
[1186] funargs_to_quote([0,R[1],R[2],T[2]]);
quote(a+1)
@end example
@table @t
@item $B;2>H(B
@ref{quotetolist}
@end table
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$l$i$N4X?t$O(B 2004-7-8 $B$+$i3+H/$N$O$8$^$C$F$$$k(B quote $B$N(B simplification $B4XO"(B
$B$N<B83E*4X?t$G$"$k(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$OB?4t$K$o$?$k$N$G$^$@=q$+$J$$(B.
@item
$B3g8L$r<h$j5n$kLdBj$O(B OpenXM/fb $B$,C_$($F$$$k8x<0$r(B tex $B$Ge:No$KI=<($9$k$N$,F05!$N0l$D(B.
@item
2004-6-26 $B$N7W;;Be?t%;%_%J!<$K$*$$$F(B, $BCf@n$5$s$,(B simplifier $B$K$D$$$F$$$m$$$mLdBjDs5/(B
$B$r$7$?(B ($B7W;;Be?t%;%_%J!<%S%G%*;2>H(B).
@item parse/quote.c $B$N(B {\tt strcut fid_spec fid_spec_tab[] }
$B$NItJ,$K=q$$$F$"$k7A<0$K(B @code{funargs_to_quote} $B$OJQ49$9$k(B.
@end itemize
@node eval_quote,,, $B%/%*!<%H(B
@subsection @code{eval_quote}
@findex eval_quote
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item eval_quote(@var{Q});
:: quote $B7?%G!<%?(B @var{Q} $B$r(B asir $B$N%*%V%8%'%/%H$KJQ49$9$k(B.
@end table
@table @var
@item return
$B%*%V%8%'%/%H(B
@item Q
quote$B7?(B
@end table
@itemize @bullet
@item quote $B7?%G!<%?(B @var{Q} $B$r(B asir $B$N%*%V%8%'%/%H$KJQ49$9$k(B.
@item $B5U4X?t$O(B @code{objtoquote}
@end itemize
@example
ctrl("print_quote",2);
A=quote((x-1)^2+(x-1)+3);
$B=PNO(B: ((((x)-(1))^(2))+((x)-(1)))+(3)
eval_quote(A);
$B=PNO(B: x^2-x+3
print_input_form(A); /* asir-contrib */
$B=PNO(B: quote((x-1)^2+(x-1)+3)
@end example
@table @t
@item $B;2>H(B
@ref{objtoquote}, @ref{quotetolist}, @ref{eval_string},
@ref{quote_to_funargs}, @ref{funargs_to_quote}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item -----$B$^$@=q$$$F$J$$(B.
@end itemize
@node nqt_match,,, $B%/%*!<%H(B
@subsection @code{nqt_match}
@findex nqt_match
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item nqt_match(@var{Expr},@var{Pattern}[,@var{Mode}])
:: @var{Expr} $B$,(B @var{Pattern} $B$K%^%C%A(B($BE,9g(B)$B$9$k$H(B 1 $B$rLa$9(B. $B$7$J$$$H(B 0 $B$rLa$9(B.
@end table
@table @var
@item return
$B@0?t(B
@item Expr
quote$B7?(B
@item Pattern
quote$B7?(B
@item Mode
$B@0?t(B
@end table
@itemize @bullet
@item @var{Expr} $B$,(B @var{Pattern} $B$K%^%C%A(B($BE,9g(B)$B$9$k$H(B 1 $B$rLa$9(B. $B$7$J$$$H(B 0 $B$rLa$9(B.
@item $BE,9g$7$?>l9g(B, $BI{:nMQ$H$7$F(B, @var{Pattern} $B$K4^$^$l$k%W%m%0%i%`JQ?t(B($BBgJ8;z$G$O$8$^$kJQ?t(B)$B$KE,9g$7$?CM$,BeF~$5$l$k(B.
@item nqt $B$O(B normalized quote $B$NN,$G$"$j(B fnode$BI8=`7A$KJQ49$7$F$+$iE,9g8!::$r$9$k(B. fnode$BI8=`7A$K$D$$$F$O(B @ref{qt_normalize} $B$r8+$h(B.
@item @var{Mode} $B$K$h$jE83+J}K!$r;XDj$7(B, $B$=$NE83+J}K!$K$h$jF@$i$l$?(B @var{Expr} $B$N(B
fnode$BI8=`7A$H(B @var{Pattern} $B$rHf3S$9$k(B.
@end itemize
@example
ctrl("print_quote",2);
A=quote((x-y)*(x+y));
nqt_match(A,quote(P*Q));
[P,Q]
$B=PNO(B: [x-y, x+y]
nqt_match(A,quote(P*Q),1);
$B%^%C%A$7$J$$(B.
nqt_match(A,quote(P*Q),2);
$B%^%C%A$7$J$$(B.
qt_normalize(A,1);
$B=PNO(B: ((x)^(2))+((x)*(y))+((-1)*((y)^(2)))+((-1)*(y)*(x))
qt_normalize(A,2);
$B=PNO(B: ((x)*(x))+((x)*(y))+((-1)*(y)*(x))+((-1)*(y)*(y))
@end example
@table @t
@item $B;2>H(B
@ref{nqt_match_rewrite},
@ref{qt_rewrite}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item ----- $B$^$@=q$$$F$J$$(B.
@end itemize
@node nqt_match_rewrite,,, $B%/%*!<%H(B
@subsection @code{nqt_match_rewrite}
@findex nqt_match_rewrite
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item nqt_match_rewrite(@var{Expr},@var{Rule},@var{Mode})
:: @var{Expr} $B$r(B @var{Rule} $B$K=>$$=q$-49$($k(B.
@end table
@table @var
@item return
quote$B7?(B
@item Expr
quote$B7?(B
@item Rule
[@var{Pattern},@var{Action}] $B$+$^$?$O(B
[@var{Pattern},@var{Condition},@var{Action}].
$B$3$l$i$NMWAG$O$9$Y$F(B quote$B7?(B.
@item Mode
$B@0?t(B
@end table
@itemize @bullet
@item @var{Expr} $B$r(B @var{Rule} $B$K=>$$=q$-49$($k(B. @var{Pattern} $B$KE,9g$7$J$$>l9g$O(B
@var{Exprt} $B<+BN$rLa$9(B.
@item nqt $B$O(B normalized quote $B$NN,$G$"$j(B fnode$BI8=`7A$KJQ49$7$F$+$iE,9g8!::$r$9$k(B. fnode$BI8=`7A$K$D$$$F$O(B @ref{qt_normalize} $B$r8+$h(B.
@end itemize
@comment %%Doc: cfep/tests/2006-03-12-qt.rr
@example
ctrl("print_quote",2);
nqt_match_rewrite(`x*y*z,[`X*Y,`X+Y],1);
$B=PNO(B: (x)+((y)*(z))
A=`x*x;
nqt_match_rewrite(A,[`X*Y,`X+Y],1);
$B=PNO(B: x^2 ($B%^%C%A$7$F$$$J$$(B)
nqt_match_rewrite(A,[`X*Y,`X+Y],2);
$B=PNO(B: 2*x
$BE,9g$K$D$$$F$N%b!<%I$N0c$$$rM}2r$9$k$?$a$K<!$NNc$*$h$S(B fnode$BI8=`7A(B(qt_normalize) $B$r;2>H(B.
quotetolist(qt_normalize(`x*x,0));
$B=PNO(B: [b_op,^,[internal,x],[internal,2]]
quotetolist(qt_normalize(`x*x,1));
$B=PNO(B: [b_op,^,[internal,x],[internal,2]]
quotetolist(qt_normalize(`x*x,2));
$B=PNO(B: [n_op,*,[internal,x],[internal,x]]
@end example
@table @t
@item $B;2>H(B
@ref{nqt_match},
@ref{qt_rewrite},
@ref{qt_normalize}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item -----$B$^$@=q$$$F$J$$(B.
@end itemize
@node qt_normalize,,, $B%/%*!<%H(B
@subsection @code{qt_normalize}
@findex qt_normalize
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item qt_normalize(@var{Expr}[,@var{Mode}])
:: @var{Expr} $B$r(B fnode$BI8=`7A$KJQ49$9$k(B. @var{Mode}$B$K$h$jI8=`7A$X$NE83+%"%k%4%j%:%`$r;XDj$G$-$k(B.
@end table
@table @var
@item return
quote$B7?(B
@item Expr
quote$B7?(B
@item Mode
$B@0?t(B
@end table
fnode$B$O(B quote$B7?$N<BBN$G$"$k(B.
fnode $B$OLZ$G$"$j(B, $B7?(B id $B$*$h$S;R6!$+$i$J$k(B.
$B7?$*$h$S;R6!$r<h$j=P$94X?t$,(B funargs_to_quote $B$G$"$k(B.
$B$^$?(B fnode $B$r%j%9%H$KJQ49$9$k4X?t$,(B quotetolist $B$G$"$k(B.
fnode $B$NI8=`7A$O%Q%?!<%s%^%C%A%s%0(B, $B=q$-49$($rMF0W$K$*$3$J$&$?$a$KF3F~$5$l$?(B.
fnode $B$NI8=`7A$r(B fn $B$H=q$/$H$-(B, $BI8=`7A$N(B BNF$BIwI=8=$G$NDj5A$O0J2<$N$H$*$j(B.
@example
fn = formula | functor(nf [,...]) | sum_of_monom
fnode $B$NI8=`7A(B. functor $B$O4X?t$h$S$@$7$_$?$$$J$b$N(B.
sum_of_monom = monom [+ ...]
$B%b%N%_%"%k$NOB(B
monom = [formula *] nfpow [* ...]
$B%b%N%_%"%k(B
nfpow = nf | nf^(nf)
$BQQ>hItJ,$NI8=`7A(B
formula = Risa object
@end example
@itemize @bullet
@item @var{Expr} $B$r(B fnode$BI8=`7A$KJQ49$9$k(B. @var{Mode}$B$K$h$jI8=`7A$X$NE83+%"%k%4%j%:%`$r;XDj$G$-$k(B.
@item $BE83+$O:F5"E*$G$"$k(B.
@item $BF~NO$,(B fnode $B$KJQ49$5$l$?=i4|>uBV$G$O(B + $B$d(B * $B$O;R6!$,(B2$B?M$N(B binary operator
(b_op) $B$G$"$k$,(B, qt_normalize $B$r:nMQ$5$;$k$3$H$K$h$j(B, + $B$d(B * $B$OG$0U?M?t$N(B
$B;R6!$r;}$F$k(B n-ary operator $B$KJQ49$5$l$k(B.
@item n-ary operator $B$r4pAC$H$7$?(B fnode$BI8=`7A$rMQ$$$k$3$H$K$h$j(B, $B%Q%?!<%s%^%C%AMQ$N%Q%?!<%s$N?t$r8:$i$;$k$3$H$,7P83E*$K$o$+$C$F$$$k(B.
@item @var{Mode}=0. $BE83+$7$J$$(B. $B$3$l$,4{Dj$NF0:n(B.
@item @var{Mode}=1. $BE83+$9$k(B. $B$?$@$7(B x*x $BEy$r(B x^2 $BEy$KJQ49(B
@item @var{Mode}=2. $BE83+$9$k(B. $B$?$@$7(B x*x $BEy$r(B x^2 $BEy$KJQ49$7$J$$(B.
@end itemize
@var{Mode} $B$N0c$$$K$D$$$F$O0J2<$NNc$b;29M$K(B.
@comment %%cfep/tests/2006-03-12-qt.rr
@example
ctrl("print_quote",2);
A=quote((x-y)*(x+y));
$B=PNO(B: ((x)-(y))*((x)+(y))
B=qt_normalize(A,0);
$B=PNO(B: ((x)+((-1)*(y)))*((x)+(y)) Mode=0. $BE83+$O$5$l$J$$(B. +, * $B$O(B n_op (nary-op) $B$X(B.
quotetolist(B);
$B=PNO(B: [n_op,*,[n_op,+,[internal,x],[n_op,*,[internal,-1],[internal,y]]],[n_op,+,[internal,x],[internal,y]]]
B=qt_normalize(A,1);
$B=PNO(B: ((x)^(2))+((x)*(y))+((-1)*((y)^(2)))+((-1)*(y)*(x))
Mode=1. $BE83+$9$k(B. +, * $B$O(B n_op (nary-op) $B$X(B. $B6R$r$^$H$a$k(B.
quotetolist(B);
$B=PNO(B: [n_op,+,[b_op,^,[internal,x],[internal,2]],[n_op,*,[internal,x],[internal,y]],[n_op,*,[internal,-1],[b_op,^,[internal,y],[internal,2]]],[n_op,*,[internal,-1],[internal,y],[internal,x]]]
qt_normalize(A,2);
$B=PNO(B: ((x)*(x))+((x)*(y))+((-1)*(y)*(x))+((-1)*(y)*(y))
Mode=2. $BE83+$9$k(B. +, * $B$O(B n_op (nary-op) $B$X(B. $B6R$O;H$o$J$$(B.
quotetolist(B);
$B=PNO(B: [n_op,+,[b_op,^,[internal,x],[internal,2]],[n_op,*,[internal,x],[internal,y]],[n_op,*,[internal,-1],[b_op,^,[internal,y],[internal,2]]],[n_op,*,[internal,-1],[internal,y],[internal,x]]]
qt_normalize(`x^2,2);
$B=PNO(B: (x)*(x)
Mode=2. $B6R$O;H$o$J$$(B. n-ary $B$N(B * $B$X(B.
@end example
@table @t
@item $B;2>H(B
@ref{nqt_match},
@ref{nqt_match_rewrite},
@ref{quotetolist},
@ref{quote_to_funargs}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item -----$B$^$@=q$$$F$J$$(B.
@end itemize
@node qt_set_coef,,, $B%/%*!<%H(B
@subsection @code{qt_set_coef}
@findex qt_set_coef
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item qt_set_coef(@var{ParamList})
:: $B0J2<(B @var{ParamList} $B$K8=$l$kB?9`<0JQ?t$rJQ?t$H$9$kM-M}4X?tBN$r78?t$H$9$k(B
$BHs2D49B?9`<0$r07$&(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item ParamList
$B%j%9%H(B
@end table
@itemize @bullet
@item $B0J2<(B @var{ParamList} $B$K8=$l$kB?9`<0JQ?t$rJQ?t$H$9$kM-M}4X?tBN$r78?t$H$9$k(B
$BHs2D49B?9`<0$r07$&(B.
@item $B$3$N@k8@$r$7$J$$$H78?tBN$r?t$H$9$kHs2D49B?9`<0$H$7$F7W;;$9$k(B.
@item qt_normalize $B$*$h$S$=$N5!G=$rMQ$$$k4X?t$,$3$N5!G=$N1F6A$r<u$1$k(B.
@item qt_comp $B4X?t$,$3$N5!G=$N1F6A$r<u$1$k(B.
@end itemize
@example
ctrl("print_quote",2);
qt_set_coef([a]);
B=qt_normalize(quote((a*x+a)^2),2);
$B=PNO(B: ((a^2)*(x)*(x))+((2*a^2)*(x))+(a^2)
qt_normalize(B+B,2);
$B=PNO(B: ((2*a^2)*(x)*(x))+((4*a^2)*(x))+(2*a^2)
@end example
@table @t
@item $B;2>H(B
@ref{qt_normalize}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item -----$B$^$@=q$$$F$J$$(B.
@end itemize
@node qt_set_ord,,, $B%/%*!<%H(B
@subsection @code{qt_set_ord}
@findex qt_set_ord
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item qt_set_ord(@var{VarList})
:: @var{VarList} $B$rJQ?t=g=x$H$9$k(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item VarList
$B%j%9%H(B
@end table
@itemize @bullet
@item @var{VarList} $B$r<-=q<0$KMQ$$$?JQ?t=g=x$r0J2<;HMQ$9$k(B.
@item $B$3$N@k8@$r$7$J$$$H$"$kITDj85$K$D$$$F$N4{Dj$N<-=q<0=g=x(B-----$B$^$@=q$$$F$J$$(B---$B$rMQ$$$F9`$rHf3S$9$k(B.
@var{VarList} $B$K8=$l$J$$JQ?t$K$D$$$F$O$3$N=g=x$,E,MQ$5$l$k(B.
@item qt_normalize $B$*$h$S$=$N5!G=$rMQ$$$k4X?t$,$3$N5!G=$N1F6A$r<u$1$k(B.
@item qt_comp $B4X?t$,$3$N5!G=$N1F6A$r<u$1$k(B.
@end itemize
@example
ctrl("print_quote",2);
qt_normalize(quote(x+y),2);
$B=PNO(B: (x)+(y)
qt_set_ord([y,x]);
$B=PNO(B: [y,x,z,u,v,w,p,q,r,s,t,a,b,c,d,e,f,g, $B0J2<>JN,(B ]
qt_normalize(quote(x+y),2);
$B=PNO(B: (y)+(x)
@end example
@table @t
@item $B;2>H(B
@ref{qt_normalize},
@ref{nqt_comp}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item -----$B$^$@=q$$$F$J$$(B.
@end itemize
@node qt_set_weight,,, $B%/%*!<%H(B
@subsection @code{qt_set_weight}
@findex qt_set_weight
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item qt_set_weight(@var{WeightVector})
:: $BJQ?t$K$D$$$F(B weight $B%Y%/%H%k$r@_Dj$9$k(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item WeightVector
$B%j%9%H(B
@end table
fnode f $B$N(B weight w(f) $B$O<!$N<0$G7W;;$9$k(B.
@example
f $B$,MU$N>l9g$O86B'(B 0. qt_weight_vector $B$G(B weight $B$,M?$($i$l$F$$$kITDj85$K(B
$B$D$$$F$O$=$NCM(B.
f $B$,(Bnode$B$N>l9g$O<!$N5,B'$G:F5"E*$K$-$a$k(B.
w(f+g) = max(w(f),w(g))
w(f g) = w(f) + w(g)
w(f^n) = n w(f)
$B4X?t$K$D$$$F$O(B? -----$B$^$@=q$$$F$J$$(B.
@end example
@itemize @bullet
@item @var{WeightVector} $B$G$^$:=g=x$NHf3S$r$7$F(B, $B$=$l$+$i(B qt_set_order $B$K$h$k=g=x(B, $B:G8e$K4{Dj$N=g=x$GHf3S$9$k(B.
@var{WeightVector} $B$K8=$l$J$$JQ?t$K$D$$$F$N(B weight $B$O(B 0 $B$H$J$k(B.
@item qt_normalize $B$*$h$S$=$N5!G=$rMQ$$$k4X?t$,$3$N5!G=$N1F6A$r<u$1$k(B.
qt_normalize $B$G$NE83+$G$O(B, $B$3$N=g=x$rMQ$$$F9`$,%=!<%H$5$l$k(B.
@item qt_comp $B$*$h$S$=$N5!G=$rMQ$$$k4X?t$,$3$N5!G=$N1F6A$r<u$1$k(B.
@item weight $B%Y%/%H%k$K$h$k=g=xHf3S$K$D$$$F$O%0%l%V%J4pDl$N@a(B@ref{dp_gr_main}$B$b;2>H(B.
@end itemize
@example
ctrl("print_quote",2);
qt_set_weight([[x,-1],[y,-1]]);
$B7k2L(B: [[x,-1],[y,-1]]
qt_normalize(quote( 1+(x+y)+(x+y)^2),1);
$B7k2L(B: (1)+(y)+(x)+((y)^(2))+((y)*(x))+((x)^(2))+((x)*(y))
@end example
@table @t
@item $B;2>H(B
@ref{qt_normalize},
@ref{qt_set_ord},
@ref{qt_set_weight},
@ref{dp_gr_main}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item -----$B$^$@=q$$$F$J$$(B.
@end itemize
@node nqt_comp,,, $B%/%*!<%H(B
@subsection @code{nqt_comp}
@findex nqt_comp
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item nqt_cmp(@var{Expr1},@var{Exprt2})
:: @var{Expr1} $B$H(B @var{Expr2} $B$N=g=x$rHf3S$9$k(B.
@end table
@table @var
@item return
$B@0?t(B
@item Expr1, Expr2
quote$B7?(B
@end table
@itemize @bullet
@item @var{Expr1} $B$H(B @var{Expr2} $B$N=g=x$rHf3S$9$k(B.
@item @var{Expr1} > @var{Exprt2} $B$J$i(B 1.
@item @var{Expr1} < @var{Exprt2} $B$J$i(B -1.
@item @var{Expr1} = @var{Exprt2} ($B$*$J$8=g=x(B) $B$J$i(B 0.
@end itemize
@example
ctrl("print_quote",2);
qt_set_ord([y,x]); qt_set_weight([[x,-1],[y,-1]]);
[nqt_comp(`x,`y), nqt_comp(`y,`x), nqt_comp(`x,`x)];
$B=PNO(B: [-1,1,0]
@end example
@table @t
@item $B;2>H(B
@ref{qt_normalize},
@ref{qt_set_ord},
@ref{qt_set_weight}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$^$@=q$$$F$J$$(B.
@end itemize
@comment ****************************************************************
@node qt_is_var,,, $B%/%*!<%H(B
@subsection @code{qt_is_var}, @code{qt_is_coef}
@findex qt_is_var
@findex qt_is_coef
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item qt_is_var(@var{Expr})
:: @var{Expr} $B$,ITDj85$KBP1~$9$k(B quote $B$J$i(B 1 $B$rLa$9(B.
@item qt_is_coef(@var{Expr})
:: @var{Expr} $B$,78?t$NM-M}4X?tBN$KB0$9$k$H$-(B 1 $B$rLa$9(B.
@end table
@table @var
@item return
$B@0?t(B
@item Expr
quote$B7?(B
@end table
@itemize @bullet
@item @var{Expr} $B$,ITDj85$KBP1~$9$k(B quote $B$J$i(B 1 $B$rLa$9(B.
$B$=$&$G$J$$$H$-(B 0 $B$rLa$9(B.
@end itemize
@example
[qt_is_var(quote(x)), qt_is_var(quote(3/2))];
$B=PNO(B: [1,0]
@end example
@table @t
@item $B;2>H(B
@ref{qt_rewrite},
@ref{nqt_match_rewrite}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item -----$B$^$@=q$$$F$J$$(B.
@end itemize
@comment ****************************************************************
@node qt_rewrite,,, $B%/%*!<%H(B
@subsection @code{qt_rewrite}
@findex qt_rewrite
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item qt_rewrite(@var{Expr},@var{Rules},@var{Mode})
:: @var{Expr} $B$r5,B'=89g(B @var{Rules} $B$rMQ$$$F=q$-49$($k(B.
@end table
@table @var
@item return
quote$B7?(B
@item Expr
quote$B7?(B
@item Rules
$B%j%9%H(B
@item Mode
$B@0?t(B
@end table
@itemize @bullet
@item $B%f!<%68@8l$rMQ$$$FDj5A$5$l$?4X?t(B.
@code{import("noro_rewrite.rr")} $B$7$F$*$/$3$H(B.
(noro_rewrite.rr $B$,(B OpenXM/lib/asir-contrib $B$KB8:_$7$J$$>l9g(B
$B%=!<%9$N(B OpenXM/src/asir-contrib/testing/noro/new_rewrite.rr $B$r%3%T!<(B)
@item @var{Expr} $B$r5,B'=89g(B @var{Rules} $B$rMQ$$$F=q$-49$($k(B.
@item $B5,B'$NE,MQ$O(B fnode$BLZ$KBP$7$F:F5"E*$G$"$k(B.
$B0lJ}(B @code{nqt_match_rewrite} $B$G$O%H%C%W%l%Y%k$N$_$K5,B'$,E,MQ$5$l$k(B.
@item $B5,B'=89g(B @var{Rules} $B$N3FMWAG$N=q$-J}$O(B @code{nqt_match()} $B$N(B
@var{Pattern} $B$HF1$8=q$-J}(B.
$B$D$^$j(B [$B%Q%?!<%s(B, $B=q$-49$(7k2L(B] $B$^$?$O(B
[$B%Q%?!<%s(B, $B>r7o(B, $B=q$-49$(7k2L(B].
@item @var{Mode} $B$N0UL#$O(B @ref{qt_normalize} $B$N(B @var{Mode} $B$HF1MM(B.
$B%Q%?!<%s%^%C%A(B, $B=q$-49$($O(B @var{Mode} $B$G(B @code{qt_normalize()}
$B$5$l$F$+$i?k9T$5$l$k(B.
@end itemize
$BCm0U(B: $B?t3XE*$K$O(B X*Y=Y*X $B$,2D49@-$rM?$($k5,B'$@$,(B, $B$3$l$r$=$N$^$^5,B'$H$7$F(B
$BM?$($k$H=q$-49$($,Dd;_$7$J$$(B. $B<!$NNc$G$O(B, $B>e$NNc$N$h$&$K=g=xHf3S$7(B, $B$?$H$($P(B,
$B=g=x$,Bg$-$/$J$k>l9g$N$_$K=q$-49$($k$Y$-$G$"$k(B.
@example
import("noro_rewrite.rr");
R=[[`X*Y,`nqt_comp(Y*X,X*Y)>0, `Y*X]];
qt_rewrite(`(x-y)^2,R,2);
$B=PNO(B: quote(x*x+-2*x*y+y*y)
@end example
$B30@QBe?t$N7W;;(B (asir-contrib $B$r%m!<%I$7$?>uBV(B).
@example
import("noro_rewrite.rr");
Rext0=[quote(X*Y),quote(qt_is_var(X) && qt_is_var(Y) && nqt_comp(Y,X)>0),
quote(-Y*X)];
Rext1=[quote(X^N),quote(eval_quote(N)>=2),quote(0)];
Rext2=[quote(X*X),quote(0)];
Rext=[Rext0,Rext1,Rext2];
qt_rewrite(quote( (x+2*y)*(x+4*y) ), Rext,1);
$B=PNO(B: 2*x*y
qt_set_coef([a,b,c,d]);
qt_rewrite(quote((a*x+b*y)*(c*x+d*y)), Rext,1);
$B=PNO(B: (d*a-c*b)*x*y
@end example
$BHyJ,$N7W;;(B (asir-contrib $B$r%m!<%I$7$?>uBV(B).
@example
import("noro_rewrite.rr");
qt_set_coef([a,b]);
Rd1=[`d(X+Y), `d(X)+d(Y)];
Rd2=[`d(X*Y),`d(X)*Y+X*d(Y)];
Rd3=[`d(N), `qt_is_coef(N), `0];
Rd4=[`d(x),`1];
Rd=[Rd1,Rd2,Rd3,Rd4];
B=qt_rewrite( `d( (a*x+b)^3),Rd,2);
$B=PNO(B: quote(3*a^3*x*x+6*b*a^2*x+3*b^2*a)
fctr(eval_quote(B));
$B=PNO(B: [[3,1],[a,1],[a*x+b,2]]
@end example
@table @t
@item $B;2>H(B
@ref{nqt_match},
@ref{nqt_match_rewrite},
@ref{qt_normalize}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item qt $B7O$N4X?t$N867?$O(B OpenXM/src/asir-contrib/testing/tr.rr $B$G$"$k(B.
$B$3$N%f!<%68@8l$K$h$k3+H/$,(B 2005$BG/$N=U$^$G9T$o$l(B, $B$=$N$"$HAH$_9~$_4X?t<gBN$N(B
qt $B7O$N4X?t$,3+H/$5$l$?(B.
@item qt $B7O$N4X?t$K$D$$$F$N$=$NB>$N;29MJ88%(B:
OpenXM/doc/Papers/2005-rims-noro.tex $B$*$h$S(B
OpenXM/doc/Papers/2005-rims-noro.tm (TeXmacs$B$N5-;v(B).
@item Todo: qt $B7O$N4X?t$rMQ$$$?$*$b$7$m$$7W;;$r(B Risa/Asir $B%8%c!<%J%k$N5-;v$H$7$F=q$/(B.
@end itemize
@comment ****************************************************************
@node $BJ8;zNs=hM}(B,,, $B<B83E*;EMM$N4X?t(B
@section $BJ8;zNs=hM}(B
@comment --- $B"~"~"~"~(B $B4X?t(B copyright $B$N@bL@(B $B"~"~"~"~(B
@node copyright,,, $BJ8;zNs=hM}(B
@subsection @code{copyright}
@findex copyright
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item copyright()
:: Risa/Asir $B$N(B copyright $BI=<($rJ8;zNs$H$7$FLa$9(B.
@end table
@table @var
@item return
$BJ8;zNs(B
@end table
@itemize @bullet
@item
Risa/Asir $B$N(B copyright $BI=<($rJ8;zNs$H$7$FLa$9(B.
@end itemize
@example
[1150] copyright();
This is Risa/Asir, Version 20040312 (Kobe Distribution).
Copyright (C) 1994-2000, all rights reserved, FUJITSU LABORATORIES LIMITED.
Copyright 2000-2003, Risa/Asir committers, http://www.openxm.org/.
GC 6.2(alpha6) copyright 1988-2003, H-J. Boehm, A. J. Demers, Xerox, SGI, HP.
PARI 2.0.17, copyright 1989-1999, C. Batut, K. Belabas, D. Bernardi,
H. Cohen and M. Olivier.
@end example
@comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B texmacs $BMQ$K=q$+$l$?(B (2004-03).
@item OpenXM_contrib2/asir2000 $B$N2<$N0J2<$N%U%!%$%k$r$_$h(B. builtin/miscf.c 1.21,
parse/glob.c 1.47.
@end itemize
@comment --- $B"~"~"~"~(B $B4X?t(B string_to_tb, ... $B$N@bL@(B $B"~"~"~"~(B
@comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B ---
@node string_to_tb tb_to_string write_to_tb,,, $BJ8;zNs=hM}(B
@subsection @code{string_to_tb}, @code{tb_to_string}, @code{write_to_tb}
@findex string_to_tb
@findex tb_to_string
@findex write_to_tb
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item string_to_tb(@var{s})
@itemx tb_to_string(@var{tb})
@itemx write_to_tb(@var{s},@var{tb})
:: $BJ8;zNs2DJQD9G[Ns7?(B(text buffer)$B$N%G!<%?$N=hM}(B
@end table
@table @var
@item return
$BJ8;zNs2DJQD9G[Ns7?(B(string_to_tb), $BJ8;zNs7?(B(tb_to_string)
@item s
$BJ8;zNs(B
@item tb
$BJ8;zNs2DJQD9G[Ns7?(B
@end table
@itemize @bullet
@item
@code{string_to_tb(@var{s})} $B$O(B, $BJ8;zNs(B @var{s} $B$r$O$8$a$NMWAG$H$9$k(B
$BJ8;zNs2DJQD9G[Ns7?%*%V%8%'%/%H$r@8@.$9$k(B.
@item
@code{tb_to_string_(@var{tb})} $B$O(B,
$BJ8;zNs2DJQD9G[Ns7?%*%V%8%'%/%H(B @var{tb} $B$+$iDL>o$NJ8;zNs%*%V%8%'%/%H$r@8@.$9$k(B.
@item
@code{write_to_tb(@var{s},@var{tb})} $B$O(B, $BJ8;zNs(B @var{s} $B$r(B
$BJ8;zNs2DJQD9G[Ns7?%*%V%8%'%/%H(B @var{tb} $B$X=q$-=P$9(B.
@item @var{SS} $B$rJ8;zNsJQ?t$H$9$k$H$-(B,
@var{SS} += "$BJ8;zNs(B" $B$G(B @var{SS} $B$XJ8;zNs$r=q$-B-$7$F$$$/$3$H$,$G$-$k$,(B,
$BL5BL$J%a%b%j$rBgNL$K>CHq$9$k(B.
$BBe$j$K4X?t(B @code{write_to_tb} $B$rMQ$$$k$Y$-$G$"$k(B.
$BJ8;zNs2DJQD9G[Ns7?%*%V%8%'%/%H$OJ8;zNs$N2DJQD9$NG[Ns$G$"$j%a%b%j4IM}$KM%$7$$(B
$B%G!<%?9=B$$G$"$k(B.
@end itemize
@example
[219] T=string_to_tb("");
[220] write_to_tb("Hello",T);
0
[221] write_to_tb(" world!",T);
0
[222] tb_to_string(T);
Hello world!
@end example
@comment --- ChangeLog $B$r=q$/(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$N4X?t$O(B 2004-3 $B$K(B print_tex_form $B$r8zN(2=$9$k$?$a$K=q$+$l$?(B.
@item
OpenXM_contrib2/asir2000 $B$N2<$N0J2<$N%U%!%$%k$r8+$h(B.
io/ox_asir.c 1.52, builtin/strobj.c 1.12--1.13, 1.16,
engine/str.c 1.5, parse/quote.c 1.9.
@item
rtostr $B$,(B text buffer $B7?$N%G!<%?$K4X$7$F$*$=$+$C$?(B. $BB.EY$N2~A1$O(B
asir2000/io/pexpr_body.c 1.2, asir2000/parse/lex.c 1.32.
@end itemize
@node set_print_function,,, $BJ8;zNs=hM}(B
@subsection @code{set_print_function}
@findex set_print_function
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item set_print_function([@var{fname}])
:: $B2hLLI=<(MQ$N4X?t$rEPO?(B
@end table
@table @var
@item return
$B@0?t(B
@item fname
$BJ8;zNs(B
@end table
@itemize @bullet
@item
@code{set_print_function} $B$O(B @code{fname(F)} $B$rDL>o$N2hLLI=<(4X?t$NBe$o$j$K$h$V(B.
@code $B0z?t$,$J$$>l9g$O2hLLI=<(4X?t$r%G%U%)!<%k%H$XLa$9(B.
@code Asir-contrib $B$O$3$N4X?t$rMQ$$$F=PNO4X?t$r(B Asir-contrib $BMQ$KJQ99$7$F$$$k(B.
@end itemize
@example
[219] def my_output(F) @{
print("Out: ",0); print(rtostr(F));
@}
[220] set_print_function("my_output");
Out: 0
[221] 1+2;
Out: 3
@end example
@table @t
@item $B;2>H(B
@ref{rtostr}
@end table
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B 2001-9-4 $B$K(B asir-contrib $B$N$?$a$KF3F~$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/print.c 1.11 $B$G$"$k(B.
@end itemize
@node sprintf,,, $BJ8;zNs=hM}(B
@subsection @code{printf}, @code{fprintf}, @code{sprintf}
@findex sprintf
@table @t
@item printf(@var{format}[,@var{args}])
@item fprintf(@var{fd},@var{format}[,@var{args}])
@item sprintf(@var{format}[,@var{args}])
:: C $B$K;w$?%W%j%s%H4X?t(B
@end table
@table @var
@item return
$B@0?t(B(printf,fprintf), $BJ8;zNs(B(sprintf)
@item format
$BJ8;zNs(B
@item fd
$BHsIi@0?t(B($B%U%!%$%k5-=R;R(B)
@item args
$B%*%V%8%'%/%H(B
@end table
@itemize @bullet
@item
@code{printf} $B$O=q<0J8;zNs(B @var{format } $B$K$7$?$,$$(B, $B%*%V%8%'%/%H(B @var{args} $B$rI8=`=PNO$K=q$-=P$9(B.
@item
@code{fprintf} $B$O7k2L$r(B, $B%U%!%$%k5-=R;R(B @var{fd} $B$N;X$9%U%!%$%k$K=q$-=P$9(B.
@item
@code{sprintf} $B$O7k2L$rJ8;zNs$GJV$7(B, $BI8=`=PNO$K$O=q$-=P$5$J$$(B.
@item
$B=q<0J8;zNs$NCf$G(B @code{%a} (any) $B$,MxMQ2DG=(B.
@var{args} $B$N8D?t$O=q<0J8;zNs$NCf$N(B @code{%a} $B$N8D?t$KEy$7$/$9$k$3$H(B.
@item
$B%U%!%$%k5-=R;R$O(B, @code{open_file} $B4X?t$rMQ$$$FF@$k$3$H(B.
@end itemize
@example
[0] printf("%a: rat = %a\n",10,x^2-1)$
10: rat = x^2-1
[1] S=sprintf("%a: rat = %a",20,x^2-1)$
[2] S;
20: rat = x^2-1
[3] Fd=open_file("hoge.txt","w");
0
[4] fprintf(Fd,"Poly=%a\n",(x-1)^3)$
[5] close_file(Fd)$
[6] quit;
$ cat hoge.txt
Poly=x^3-3*x^2+3*x-1
@end example
@table @t
@item $B;2>H(B
@ref{rtostr},@ref{open_file},@ref{close_file}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item
$B4X?t(B sprintf$B$O(B 2004-7-13 $B$K%3%_%C%H$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/strobj (1.50) $B$G$"$k(B.
@item
$B4X?t(B printf$B$O(B 2007-11-8 $B$K%3%_%C%H$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/print.c (1.23) $B$G$"$k(B.
@item
$B4X?t(B fprintf$B$O(B 2008-11-18 $B$K%3%_%C%H$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/file.c (1.25) $B$G$"$k(B.
@item
@code{%a} $B$O(B Maple $B$N(B sprintf $B$N??;w$+(B.
@end itemize
@node $B%0%l%V%J!<4pDl(B,,, $B<B83E*;EMM$N4X?t(B
@section $B%0%l%V%J!<4pDl(B
@comment --- $B"~"~"~"~(B $B4X?t(B dp_gr_main $B$N@bL@(B $B"~"~"~"~(B
@comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B ---
@node dp_gr_main,,, $B%0%l%V%J!<4pDl(B
@subsection @code{dp_gr_main}
@findex dp_gr_main
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item dp_gr_main(@var{f} | v=@var{vv}, order=@var{oo}, homo=@var{n}, matrix=@var{m}, block=@var{b}, sugarweight=@var{sw})
:: dp_gr_main $B$N?7$7$$%$%s%?%U%'!<%9(B.
@end table
@table @var
@item return
$B%j%9%H(B ($B%0%l%V%J4pDl(B. $B:F5"I=8=B?9`<0$+J,;6I=8=B?9`<0$N%j%9%H(B)
@item f
$B%j%9%H(B ($BF~NOB?9`<07O(B. $B:F5"I=8=B?9`<0$+J,;6I=8=B?9`<0$N%j%9%H(B)
@item vv
$B%j%9%H(B ($BJQ?t$N%j%9%H(B)
@item oo
$B%j%9%H(B ($B=g=x$r$"$i$o$9%j%9%H(B)
@item n
0 $B$+(B1 (homogenization $B$r$9$k$+(B)
@item m
$B=g=x$r(B matrix $B$GI=8=$9$k>l9g(B (cf. dp_ord).
@item b
???
@item sw
Sugar strategy $B$rE,MQ$9$k$H$-$N(B weight vector. $BA4$F$NMWAG$OHsIi(B.
@end table
@itemize @bullet
@item
@code{dp_gr_main(@var{f})} $B$O(B, @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B.
$B%0%l%V%J4pDl$O=g=x$rJQ$($k$H$=$N7A$,JQ$o$k(B. asir $B$G$O$$$^$^$G=g=x$N;XDjJ}K!$,(B
$B7OE}$@$C$F$$$J$+$C$?(B.
dp_gr_main $B$N?7$7$$%$%s%?%U%'!<%9$G$O=g=x$r$"$kJ8K!$K=>$$;XDj$9$k(B.
@comment ~taka/this03/misc-2003/A2/dp
@item $B=g=x(B order $B$O<!$NJ8K!$GDj5A$9$k(B. @{, @} $B$O(B 0 $B2s0J>e$N7+$jJV$7$r0UL#$9$k(B.
@example
order : '[' orderElement @{ ',' orderElement @} ']'
orderElement : weightVec | builtinOrder
weightVec : '[' weightElement @{ ',' weightElement @} ']'
builtiniOrder : '[' orderName ',' setOfVariables ']'
weightElement : NUMBER | setOfVariables ',' NUMBER
setOfVariables: V | range(V,V)
orderName : @@grlex | @@glex | @@lex
@end example
$B$3$3$G(B @code{V} $B$O(B $BJQ?tL>(B, @code{NUMBER} $B$O@0?t$r$"$o$i$9(B.
$BNc(B1: @code{v=[x,y,z,u,v], order=[[x,10,y,5,z,1],[@@grlex,range(x,v)]]}
$B$O(B @code{x},@code{y},@code{z} $B$,$=$l$>$l(B weight 10, 5, 1 $B$r$b$D(B
$B=g=x$GHf3S$7$?$"$H(B, @code{[x,y,z,u,v]} $B$K$D$$$F$N(B
graded reverse lexicographic order $B$r(B tie-breaker $B$H$7$FMQ$$$k$3$H$r0UL#$9$k(B.
$B;29M=q(B: B.Sturmfels: Gr\"obner Bases and Convex Polytopes (1995).
M.Saito, B.Sturmfels, N.Takayama:
Gr\"obner Deformations of Hypergeometric Differential Equations (2000).
@item
$B=g=xMWAG(B (orderElement) $B$N;XDjJ}K!$O(B
(1) $BJQ?tL>$^$?$O(B range$B$G;XDj$5$l$?JQ?t$N=89g$H=E$_$NCM$N7+$jJV$7(B
(2) $B=E$_$NCM$rJQ?t%j%9%H$N=gHV$KJB$Y$kJ}K!(B
(3) $BJQ?tL>$^$?$O(B range$B$G;XDj$5$l$?JQ?t$N=89g$H=g=xL>$NAH(B
$B$N;0DL$j$N4pACE*J}K!$,$"$k(B.
$B;w$?;XDjJ}K!$,(B Macaulay, Singular, CoCoA, Kan/sm1 $BEy$N4DO@%7%9%F%`$G(B
$B;HMQ$5$l$F$$$?(B. Risa/Asir $B$N;XDjJ}K!$O$3$l$i$N%7%9%F%`$N;XDjJ}K!$r;29M$K(B
$B$5$i$K2~NI$r2C$($?$b$N$G=@Fp@-$,9b$$(B.
@item
order $B$N(B tie-breaker $B$O(B grlex $B$,%G%U%)!<%k%H(B.
@item
$BJ,;6I=8=B?9`<0$r0z?t$H$7$?$H$-$O7k2L$bJ,;6I=8=B?9`<0$H$7$FLa$k(B.
order $B;XDj$K$b$A$$$k%G%U%)!<%k%H$NJQ?tL>$O$3$N$H$-(B x0, x1, x2, ... $B$H$J$k(B.
@item
$B%*%W%7%g%s$NCM$O(B option_list $B%-!<%o!<%I$rMQ$$$F%j%9%H$GM?$($F$b$h$$(B.
$B2<$NNc$r;2>H(B.
@end itemize
@example
[218] load("cyclic");
[219] V=vars(cyclic(4));
[c0,c1,c2,c3]
[220]dp_gr_main(cyclic(4) | v=V, order=[[c0,10,c1,1],[c2,5],[@@grlex,range(c0,c3)]]);
[ 10 1 0 0 ]
[ 0 0 5 0 ]
[ R R R R ]
[(-c3^6+c3^2)*c2^2+c3^4-1,c3^2*c2^3+c3^3*c2^2-c2-c3,
(c3^4-1)*c1+c3^5-c3,(c2-c3)*c1+c3^4*c2^2+c3*c2-2*c3^2,-c1^2-2*c3*c1-c3^2,
c0+c1+c2+c3]
[1151] F=map(dp_ptod,katsura(4), vars(katsura(4)));
[(1)*<<1,0,0,0,0>>+(2)*<<0,1,0,0,0>>+ ... ]
[1152] dp_gr_main(F | order=[[range(x0,x3),1]]);
[ 1 1 1 1 0 ]
[ R R R R R ]
[(47774098944)*<<0,0,0,0,13>>+ ... ]
[1153] Opt=[["v",[x,y]], ["order",[[x,5,y,1]]]];
[[v,[x,y]],[order,[[x,5,y,1]]]]
[1154] dp_gr_main([x^2+y^2-1,x*y-1] | option_list=Opt);
[ 5 1 ]
[ R R ]
[-y^4+y^2-1,x+y^3-y]
@end example
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B 2003-12 $B$+$i(B 2004-2 $B$N;O$a$KBg$-$J=$@5$,9T$o$l$?(B.
@item
@code{setOfVariables}$B$NI=8=$N$?$a$K(B range $B%*%V%8%'%/%H$,F3F~$5$l$?(B.
@item
$B%0%l%V%J4pDl$O=g=x$rJQ$($k$H$=$N7A$,JQ$o$k(B. asir $B$G$O$$$^$^$G=g=x$N;XDjJ}K!$,(B
$B7OE}$@$C$F$$$J$+$C$?(B.
dp_gr_main $B$N?7$7$$%$%s%?%U%'!<%9$G$O=g=x$r$"$kJ8K!$K=>$$;XDj$9$k(B.
@item
OpenXM_contrib2/asir2000 $B$N2<$N<!$N3F%U%!%$%k$,=$@5$r$&$1$?(B.
builtin/gr.c 1.56--1.57,
builtin/dp-supp.c 1.27--1.31 (create_composite_order_spec),
builtin/dp.c 1.46--1.48 (parse_gr_option),
engine/Fgfs.c 1.20,
engine/dist.c 1.27--1.28
engine/nd.c 1.89,
include/ca.h 1.42--1.43,
io/pexpr.c 1.28,
io/sexpr.c 1.26,
parse/arith.c 1.11,
parse/glob.c 1.44-1.45,
parse/lex.c 1.29,
parse/parse.h 1.23--1.26
@item
Todo: return $B%-!<%o!<%I$GLa$jCM$N%G!<%?$r(B quote $B$N%j%9%H$K$G$-$k$h$&$K(B.
attribute, ring $B9=B$BN(B.
@end itemize
@comment --- $B"~"~"~"~(B $B4X?t(B dp_gr_main $B$N@bL@(B $B"~"~"~"~(B
@node dp_weyl_gr_main,,, $B%0%l%V%J!<4pDl(B
@subsection @code{dp_weyl_gr_main}
@findex dp_weyl_gr_main
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item dp_weyl_gr_main(@var{f} | v=@var{vv}, order=@var{oo}, homo=@var{n}, matrix=@var{m}, block=@var{b}, sugarweight=@var{sw})
:: dp_weyl_gr_main $B$N?7$7$$%$%s%?%U%'!<%9(B. dp_gr_main $B$HF1$87A<0$G$"$k(B.
@end table
@table @var
@item return
$B%j%9%H(B ($B%0%l%V%J4pDl(B. $B:F5"I=8=B?9`<0$+J,;6I=8=B?9`<0$N%j%9%H(B)
@item f
$B%j%9%H(B ($BF~NOB?9`<07O(B. $B:F5"I=8=B?9`<0$+J,;6I=8=B?9`<0$N%j%9%H(B)
@item vv
$B%j%9%H(B ($BJQ?t$N%j%9%H(B)
@item oo
$B%j%9%H(B ($B=g=x$r$"$i$o$9%j%9%H(B)
@item n
0 $B$+(B1 (homogenization $B$r$9$k$+(B). [$B%F%9%H$^$@(B]
@item m
$B=g=x$r(B matrix $B$GI=8=$9$k>l9g(B (cf. dp_ord). [$B%F%9%H$^$@(B]
@item b
???
@item sw
Sugar strategy $B$rE,MQ$9$k$H$-$N(B weight vector. $BA4$F$NMWAG$OHsIi(B. [$B%F%9%H$^$@(B]
@end table
@itemize @bullet
@item
@code{dp_weyl_gr_main(@var{f})} $B$O(B, @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B.
$B%0%l%V%J4pDl$O=g=x$rJQ$($k$H$=$N7A$,JQ$o$k(B. asir $B$G$O$$$^$^$G=g=x$N;XDjJ}K!$,(B
$B7OE}$@$C$F$$$J$+$C$?(B.
dp_weyl_gr_main $B$N?7$7$$%$%s%?%U%'!<%9$G$O=g=x$r$"$kJ8K!$K=>$$;XDj$9$k(B.
$B;XDjJ}K!$K$D$$$F$O(B dp_gr_main $B$N%^%K%e%"%k$r;2>H(B.
@item
$BJ,;6I=8=B?9`<0$N3F%b%N%_%"%k$ND9$5$,6v?t$N$H$-$O%o%$%kBe?t(B
K[x_1, ..., x_n, d_1, ..., d_n]
$B$G7W;;$,$*$3$J$o$l$k(B. $B%o%$%kBe?t$G$O(B x_i $B$H(B d_i $B$OHs2D49$J3]$1;;5,B'(B
d_i x_i = x_i d_i +1 $B$r$_$?$7(B, x_i $B$H(B x_j $B$d(B d_i $B$H(B d_j $B$O2D49$G$"$k(B.
$B$^$?(B i $B$H(B j $B$,0[$J$k>l9g$O(B x_i $B$H(B d_j $B$b2D49$G$"$k(B.
@item
$BJ,;6I=8=B?9`<0$N3F%b%N%_%"%k$ND9$5$,4q?t$N$H$-$OF1<!2=%o%$%kBe?t(B
K[x_1, ..., x_n, d_1, ..., d_n, h]
$B$G7W;;$,$*$3$J$o$l$k(B. $BF1<!2=%o%$%kBe?t$G$O(B x_i $B$H(B d_i $B$OHs2D49$J3]$1;;5,B'(B
d_i x_i = x_i d_i + h^2
$B$r$_$?$7(B, h $B$OG$0U$N85$H2D49(B, $B$=$NB>$NJQ?t$b%o%$%kBe?t$HF1MM$J2D49@-$N5,B'$r$_$?$9(B.
$B>\$7$/$O(B dp_gr_main $B$G;2>H$7$?(B Saito, Sturmfels, Takayama $B$N652J=q$r$_$h(B.
@end itemize
@example
[1220] F=sm1.gkz([ [[1,1,1,1],[0,1,3,4]], [0,0]]); /* Command in asir-contrib*/
[[x4*dx4+x3*dx3+x2*dx2+x1*dx1,4*x4*dx4+3*x3*dx3+x2*dx2,-dx1*dx4+dx2*dx3,-dx2^2*dx4+dx1*dx3^2,dx1^2*dx3-dx2^3,-dx2*dx4^2+dx3^3],[x1,x2,x3,x4]]
[1221] V=[x1,x2,x3,x4,dx1,dx2,dx3,dx4]$
[1222] dp_weyl_gr_main(F[0] | v=V, order=[[dx1,1,dx2,1,dx3,1,dx4,1]]);
...
[1238] FF=map(dp_ptod,F[0],V);
[(1)*<<1,0,0,0,1,0,0,0>>+(1)*<<0,1,0,0,0,1,0,0>>+(1)*<<0,0,1,0,0,0,1,0>>+(1)*<<0,0,0,1,0,0,0,1>>,(1)*<<0,1,0,0,0,1,0,0>>+(3)*<<0,0,1,0,0,0,1,0>>+(4)*<<0,0,0,1,0,0,0,1>>,0,0,0,0]
[1244] FF=map(dp_ptod,F[0],V);
[(1)*<<1,0,0,0,1,0,0,0>>+(1)*<<0,1,0,0,0,1,0,0>>+(1)*<<0,0,1,0,0,0,1,0>>+(1)*<<0,0,0,1,0,0,0,1>>,(1)*<<0,1,0,0,0,1,0,0>>+(3)*<<0,0,1,0,0,0,1,0>>+(4)*<<0,0,0,1,0,0,0,1>>,(1)*<<0,0,0,0,0,1,1,0>>+(-1)*<<0,0,0,0,1,0,0,1>>,(1)*<<0,0,0,0,1,0,2,0>>+(-1)*<<0,0,0,0,0,2,0,1>>,(-1)*<<0,0,0,0,0,3,0,0>>+(1)*<<0,0,0,0,2,0,1,0>>,(1)*<<0,0,0,0,0,0,3,0>>+(-1)*<<0,0,0,0,0,1,0,2>>]
dp_weyl_gr_main(FF | v=V, order=[[0,0,0,0,1,1,1,1]]);
[1246] dp_weyl_gr_main(FF | v=V, order=[[dx1,1,dx2,1,dx3,1,dx4,1]]);
[ 0 0 0 0 1 1 1 1 ]
[ R R R R R R R R ]
...
@end example
@table @t
@item $B;2>H(B
@ref{dp_gr_main}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item dp_gr_main $B$N%$%s%?%U%'!<%9$,(B dp_weyl_gr_main $B$X$bF3F~$5$l$?(B.
@item
OpenXM_contrib2/asir2000 $B$N2<$N<!$N3F%U%!%$%k$,=$@5$r$&$1$?(B.
builtin/dp-supp.c 1.32--1.33
builtin/dp.c 1.49--1.50
@end itemize
@comment --- $B"~"~"~"~(B $B4X?t(B dp_initial_term $B$N@bL@(B $B"~"~"~"~(B
@node dp_initial_term,,, $B%0%l%V%J!<4pDl(B
@subsection @code{dp_initial_term}
@findex dp_initial_term
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item dp_initial_term(@var{f} | v=@var{vv}, order=@var{oo})
:: dp_initial_term $B$OM?$($i$l$?(B weight $B$KBP$9$k@hF,9`$NOB$rLa$9(B.
@end table
@table @var
@item return
$BJ,;6I=8=B?9`<0$^$?$OJ,;6I=8=B?9`<0$N%j%9%H(B.
@item f
$BJ,;6I=8=B?9`<0$+J,;6I=8=B?9`<0$N%j%9%H(B.
@item vv
$B%j%9%H(B ($BJQ?t$N%j%9%H(B)
@item oo
$B%j%9%H(B ($B=g=x$r$"$i$o$9%j%9%H(B)
@end table
@itemize @bullet
@item
dp_initial_term $B$OM?$($i$l$?(B weight w $B$KBP$9$k@hF,9`$NOB$rLa$9(B.
$B$3$l$OB?$/$N652J=q$G(B @tex ${\rm in}_w(f)$ @end tex
$B$H=q$+$l$F$$$k(B.
@item
$B=g=x$rI=$9%j%9%H$O(B dp_gr_main $B$GDj5A$7$?J8K!$K=>$&(B.
$B$3$N%j%9%H$N@hF,$,(B weight vector $B$GL5$$>l9g$O%(%i!<$H$J$k(B.
$B$?$H$($P(B order=[[@@lex,...]] $B$O%(%i!<$H$J$k(B.
@item
$B7k2L$OM?$($i$l$?=g=x$K4X$7$F%=!<%H$5$l$F$k$o$1$G$O$J$$(B.
@end itemize
@example
[1220] F=<<2,0,0>>+<<1,1,0>>+<<0,0,1>>;
(1)*<<2,0,0>>+(1)*<<1,1,0>>+(1)*<<0,0,1>>
[1220] dp_initial_term(F | order=[[1,1,1]]);
[ 1 1 1 ]
[ R R R ]
(1)*<<2,0,0>>+(1)*<<1,1,0>>
[1221] dp_initial_term(F | v=[x,y,z], order=[[x,1]]);
[ 1 0 0 ]
[ R R R ]
(1)*<<2,0,0>>
@end example
@table @t
@item $B;2>H(B
@ref{dp_gr_main}, @ref{dp_weyl_gr_main}, @ref{dp_order}, @ref{dp_hm}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item
OpenXM_contrib2/asir2000 $B$N2<$N<!$N3F%U%!%$%k$,=$@5$r$&$1$?(B.
builtin/dp-supp.c 1.32
builtin/dp.c 1.49
@end itemize
@comment --- $B"~"~"~"~(B $B4X?t(B dp_order $B$N@bL@(B $B"~"~"~"~(B
@node dp_order,,, $B%0%l%V%J!<4pDl(B
@subsection @code{dp_order}
@findex dp_order
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item dp_order(@var{f} | v=@var{vv}, order=@var{oo})
:: dp_order $B$OM?$($i$l$?(B weight $B$KBP$9$k<!?t$N:GBgCM$rLa$9(B.
@end table
@table @var
@item return
$B?t$+?t$N%j%9%H(B
@item f
$BJ,;6I=8=B?9`<0$+J,;6I=8=B?9`<0$N%j%9%H(B.
@item vv
$B%j%9%H(B ($BJQ?t$N%j%9%H(B)
@item oo
$B%j%9%H(B ($B=g=x$r$"$i$o$9%j%9%H(B)
@end table
@itemize @bullet
@item
$B=g=x$rI=$9%j%9%H$O(B dp_gr_main $B$GDj5A$7$?J8K!$K=>$&(B.
$B$3$N%j%9%H$N@hF,$,(B weight vector $B$GL5$$>l9g$O%(%i!<$H$J$k(B.
$B$?$H$($P(B order=[[@@lex,...]] $B$O%(%i!<$H$J$k(B.
@item
dp_order $B$OM?$($i$l$?(B weight w $B$KBP$9$k<!?t$N:GBgCM$rLa$9(B.
$B$3$l$r(B @tex ${\rm ord}_w(f)$ @end tex
$B$H=q$/O@J8$d652J=q$b$"$k(B.
@item
$B0z?t$,%j%9%H$N>l9g3FMWAG$N<!?t$,7W;;$5$l$k(B.
@end itemize
@example
[1220] F=<<2,0,0>>+<<1,1,0>>+<<0,0,1>>;
(1)*<<2,0,0>>+(1)*<<1,1,0>>+(1)*<<0,0,1>>
[1222] dp_order(F | order=[[1,1,1]]);
[ 1 1 1 ]
[ R R R ]
2
[1223] dp_order(F | v=[x,y,z], order=[[x,1]]);
[ 1 0 0 ]
[ R R R ]
@end example
@table @t
@item $B;2>H(B
@ref{dp_gr_main}, @ref{dp_weyl_gr_main}, @ref{dp_initial_term}, @ref{dp_hm}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item
OpenXM_contrib2/asir2000 $B$N2<$N<!$N3F%U%!%$%k$,=$@5$r$&$1$?(B.
builtin/dp-supp.c 1.32
builtin/dp.c 1.49
@end itemize
@node nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module),,, $B%0%l%V%J!<4pDl(B
@subsection @code{nd_gr}, @code{nd_gr_trace} ($B2C72(B)
@findex nd_gr (module)
@findex nd_gr_trace (module)
@findex nd_weyl_gr (module)
@findex nd_weyl_gr_trace (module)
@comment --- nd_gr, nd_gr_trace $B$K$*$1$k2C72$N%0%l%V%J!<4pDl7W;;(B ---
@table @t
@item nd_gr(@var{gen},@var{vars},@var{char},@var{ord})
@itemx nd_gr_trace(@var{gen},@var{vars},@var{homo},@var{char},@var{ord})
@item nd_weyl_gr(@var{gen},@var{vars},@var{char},@var{ord})
@itemx nd_weyl_gr_trace(@var{gen},@var{vars},@var{homo},@var{char},@var{ord})
:: $BItJ,2C72$N%0%l%V%J!<4pDl$N7W;;(B
@end table
@table @var
@item gen
$B%j%9%H$N%j%9%H(B
@item ord
@var{[IsPOT,Ord]} $B$J$k%j%9%H(B
@item return
$B%j%9%H$N%j%9%H(B
@end table
@itemize @bullet
@item $BB?9`<04D$"$k$$$O%o%$%kBe?t>e$N<+M32C72$NItJ,2C72$N%0%l%V%J!<4pDl(B
$B$r7W;;$9$k(B. $B7k2L$O%j%9%H$N%j%9%H$G$"$k(B. $B3FMWAG%j%9%H$O(B, $B<+M32C72$N(B
$B85$G$"$k%Y%/%H%k$H$_$J$9(B.
@item @var{ord} $B$H$7$F(B @var{[IsPOT,Ord]} $B$H$$$&(B2$BMWAG%j%9%H$,;XDj$5$l$?(B
$B>l9g(B, $B2C72$N%0%l%V%J!<4pDl7W;;$r<B9T$9$k(B. $B$3$N>l9g(B, @var{gen} $B$O(B, $BB?9`<0(B
$B$N%j%9%H$N%j%9%H$H$7$FM?$($kI,MW$,$"$k(B.
@item @var{IsPOT} $B$,(B 1 $B$N>l9g(B, POT (position over term), 0 $B$N(B
$B>l9g(B TOP (term over position) $B$GHf3S$9$k(B. $B4pAC4D$G$N9`Hf3S$O(B @var{Ord}
$B$G9T$&(B.
@item $B@bL@$5$l$F$$$J$$0z?t$O(B, $B%$%G%"%k$N>l9g$N2r@b$r;2>H$N$3$H(B.
@end itemize
@example
[0] Gen=[[x,y,z],[y^2+x,x^2,z],[y^2,z^3+x,x+z]];
[[x,y,z],[x+y^2,x^2,z],[y^2,x+z^3,x+z]]
[1] nd_gr(Gen,[x,y,z],0,[0,0]);
[[x,y,z],[y^2,x^2-y,0],[y^2,x+z^3,x+z],[y^3+z^3*y^2,y^3*x-y^3,
-x^3-z*x^2+(z*y^2+y)*x-z*y^2+z*y],[0,0,x^4+z*x^3+(-z*y^2-y)*x^2
+(-y^3+z*y^2-z*y)*x+z^4*y^2]]
@end example
@table @t
@item $B;2>H(B
@ref{nd_gr}, @ref{nd_gr_trace}
@end table
@node nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option),,, $B%0%l%V%J!<4pDl(B
@subsection @code{nd_gr}, @code{nd_gr_trace} (option)
@findex nd_gr (option)
@findex nd_gr_trace (option)
@findex nd_weyl_gr (option)
@findex nd_weyl_gr_trace (option)
@comment --- nd_gr, nd_gr_trace $B$N%*%W%7%g%s(B ---
@table @t
@item nd_gr(@var{...}[|@var{opt},@var{opt},@dots{}])
@itemx nd_gr_trace(@var{...}[|@var{opt},@var{opt},@dots{}])
@itemx nd_weyl_gr(@var{...}[|@var{opt},@var{opt},@dots{}])
@itemx nd_weyl_gr_trace(@var{...}[|@var{opt},@var{opt},@dots{}])
:: $B%0%l%V%J!<4pDl7W;;$K4X$9$k<o!9$N%*%W%7%g%s$N@bL@(B
@end table
@table @var
@item opt
@var{key=value} $B$J$k%*%W%7%g%s@_Dj(B
@item return
$B%*%W%7%g%s$K$h$j0[$J$k(B
@end table
@itemize @bullet
@item $B%0%l%V%J!<4pDl7W;;$r%*%W%7%g%s$K$h$j@)8f$9$k(B.
@item $B8=>u$G$O<!$N(B 3 $B$D$N%*%W%7%g%s$r<u$1IU$1$k(B.
@table @var
@item gentrace
@var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B%0%l%V%J!<4pDl$N7W;;7P2a>pJs$r=PNO$9$k(B.
@item gentsyz
@var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B7W;;$5$l$?%0%l%V%J!<4pDl$KBP$9$k(B syzygy $B$N@8@.7O$r=PNO$9$k(B.
@item nora
@var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B:G=*%9%F%C%W$GAj8_4JLs$r9T$o$J$$(B.
@end table
@item @var{gentrace} $B$,;XDj$5$l$?>l9g(B, $B=PNO$O(B,
@var{[GB,Homo,Trace,IntRed,Ind,InputRed,SpairTrace]} $B$J$k%j%9%H$G$"$k(B. $B3FMWAG$N0UL#$O(B
$B<!$NDL$j$G$"$k(B.
@table @var
@item GB
$B%0%l%V%J!<4pDl(B
@item Homo
$BCf4V4pDl$,@F<!2=$5$l$F$$$k>l9g(B 1, $B$=$&$G$J$$>l9g(B 0.
@item Trace
$BA4Cf4V4pDl$KBP$9$k7W;;7P2a>pJs(B
@item IntRed
$BAj8_4JLs$KBP$9$k7W;;7P2a>pJs(B
@item Ind
$B4JLs%0%l%V%J!<4pDl$N3FMWAG$N(B, $BA4Cf4V4pDl$N$K$*$1$k%$%s%G%C%/%9(B
@item InputRed
$B3FF~NOB?9`<0$r%0%l%V%J!<4pDl$G4JLs$7$F>jM>(B 0 $B$rF@$k$^$G$N7W;;7P2a>pJs(B
(@var{gensyz} $B$,;XDj$5$l$?>l9g(B)
@item SpairTrace
$B4JLs%0%l%V%J!<4pDl$KBP$9$k(B S $BB?9`<0$r4JLs$7$F>jM>(B 0 $B$rF@$k$^$G$N7W;;7P2a>pJs(B
(syzygy $B2C72$N@8@.7O$NMWAG$N$_(B; @var{gensyz} $B$,;XDj$5$l$?>l9g(B)
@end table
@item $B>\:Y$O(B, $BF~NOB?9`<0=89g$H%0%l%V%J!<4pDl$NAj8_JQ499TNs(B, $B$*$h$S(B syzygy $B7W;;(B
$B4X?t$N9`$G@bL@$9$kM=Dj(B.
@end itemize
@example
[0] C=[c3*c2*c1*c0-1,((c2+c3)*c1+c3*c2)*c0+c3*c2*c1,...]
[1] D=nd_gr_trace(C,[c0,c1,c2,c3,c4],0,1,0|gentrace=1,gensyz=1)$
[2] D[0];
[c0+c1+c2+c3,-c1^2-2*c3*c1-c3^2,...]
[3] D[2];
[[[0,0,1],[1,1,1],[2,2,1],[3,3,1]],[4,[[1,2,(1)*<<0,0,0,0>>,1],...]
[4] D[6];
[[-1,[[1,0,(1)*<<0,0,2,4>>,1],[1,6,(-1)*<<1,0,0,0>>,1],...]
@end example
@table @t
@item $B;2>H(B
@ref{nd_gr}, @ref{nd_gr_trace}
@end table
@node $B%7%9%F%`(B,,, $B<B83E*;EMM$N4X?t(B
@section $B%7%9%F%`(B
@comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B
@comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B ---
@node asir-install.sh,,, $B%7%9%F%`(B
@subsection @code{asir-port.sh}, @code{asir-install.sh}
@findex asir-port.sh
@findex asir-install.sh
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item asir-install.sh
@itemx asir-port.sh
:: $B$3$l$O(B asir $B$NFbIt%3%^%s%I$G$O$J$$(B. asir $B$r%M%C%H%o!<%/$+$i%@%&%s%m!<%I$+$D<B9T$9$k%7%'%k%9%/%j%W%H(B
@end table
@itemize @bullet
@item
asir-port.sh $B$O(B knoppix $B@lMQ$G$"$k(B.
$B$3$N%3%^%s%I$O(B asir $B$N%P%$%J%j$*$h$S(B FLL $B$GG[I[$G$-$J$$ItJ,$r(B
ftp.math.kobe-u.ac.jp $B$h$j%@%&%s%m!<%I$7$F(B
/home/knoppix/.asir-tmp $B$X%;!<%V$7$F(B, $B<B9T$9$k(B.
.asirrc $B$*$h$S(B .TeXmacs/plugins/ox/progs/init-ox.scm $B$b%@%&%s%m!<%I$9$k(B.
@item
asir-install.sh $B$O(B Debian GNU Linux / openxm-binary*.deb $B@lMQ$G$"$k(B.
asir-install.sh $B$O(B asir $B$r%@%&%s%m!<%I$7$F(B /usr/local/OpenXM/bin $B$*$h$S(B
/usr/local/OpenXM/lib/asir $B$X%$%s%9%H!<%k$9$k(B.
@end itemize
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$l$i$N%7%'%k%9%/%j%W%H$O(B knoppix/math $B$N$?$a$K(B 2004/2, 3 $B7n$K=q$+$l$?(B.
@item
knoppix/math $B$OJ!2,Bg3X$N_@ED$5$s$,Cf?4$H$J$j3+H/$5$l$F$$$k(B.
@item
OpenXM/misc/packages/Linux/Debian $B$N2<$NA4$F$N%U%!%$%k(B (2004-2-22 $B$+$i(B
2004-3 $B$NKv$^$G(B). ( ~taka/this03/misc-2003/A3/knoppix-03-05 ($B%W%i%$%Y!<%H%U%!%$%k(B) $B$b8+$h(B.)
OpenXM/src/asir-port $B$N2<$N<!$N3F%U%!%$%k(B.
Makefile 1.1--1.8, asir-install.sh 1.1--1.2, asir-port.sh 1.1--1.6.
@end itemize
@node asirgui.hnd,,, $B%7%9%F%`(B
@subsection @code{asirgui.hnd}
@findex asirgui.hnd
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item asirguid.hnd
:: asirgui $B$N(B main window $B$N%O%s%I%kHV9f$rJ];}$9$k%U%!%$%k(B
@end table
@comment ****************************************************************
@itemize @bullet
@item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B asirgui.exe $B$N$"$k%U%)%k%@$*$h$S(B $B4D6-JQ?t(B TEMP $B$,Dj5A$5$l$F$$$l$P$3$N%U%!%$%k$,:n@.$5$l$k(B.
@item $BCf?H$O#1#0?J@0?t$G(B, asirgui $B$N(B main window $B$N%O%s%I%k$G$"$k(B. $B$3$N%O%s%I%k$"$F$K(B PostMessage $B$r$9$l$P(B, asuirgui $B$K%-!<%\!<%I$+$iF~NO$7$?$N$HF1MM$J8z2L$,F@$i$l$k(B.
@item text editor $B$G:n@.(B, $BJ]B8$7$?%U%!%$%k$r(B text editor $BB&$+$i(B asirgui $B$KFI$_9~$^$;$?$j$9$k$?$a$KMxMQ2DG=(B.
@item http://www.math.kobe-u.ac.jp/Asir/Add-ons $B$K$F(B winfep.exe $B$rG[I[$7$F$$$k(B. winfep $B$G$O$"$i$+$8$a%U%!%$%k$KF~NO%9%/%j%W%H$r=q$$$F$*$$$F(B, asirgui $B$G0l9T$E$D<B9T$5$;$k$3$H$,$G$-$k(B. winfep $B$O%W%l%<%s%F!<%7%g%sMQ$N%=%U%H%&%(%"$G$"$k(B. $B$3$l$O(B asirgui.hnd $B$rMxMQ$7$F$$$k(B.
@end itemize
@example
// cl test.c user32.lib
#include <windows.h>
#include <stdlib.h>
#include <stdio.h>
#include <process.h>
int main()
@{
HWND hnd;
FILE *fp = fopen("c:/Program Files/asir/bin/asirgui.hnd","r");
fscanf(fp,"%d",&hnd);
fclose(fp);
while (1) @{
int c;
c = getchar();
if ( c == '#' ) break;
PostMessage(hnd,WM_CHAR,c,1);
@}
return 0;
@}
@end example
@table @t
@item $B;2>H(B
@ref{xyz_abc}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N5!G=$O(B 2006-12-5, 2007-02-13 $B$K2C$($i$l$?(B.
@item @code{OpenXM_contrib2/windows/asir32gui/asir32gui.clw} 1.11
@item @code{OpenXM_contrib2/windows/asir32gui/asir32guiview.cpp} 1.15, 1.1.6
@item winfep $B$O(B 2010-01-20 $B:"$KBh0lHG$,(B commit $B$5$l$?(B.
@item @code{OpenXM_contrib2/windows/winfep} 1.1
@end itemize
@comment ****************************************************************
@node chdir,,, $B%7%9%F%`(B
@subsection @code{chdir}, @code{pwd}
@findex chdir
@findex pwd
@comment --- $B%G%#%l%/%H%jA`:n(B ---
@table @t
@item chdir(@var{directory})
@item pwd()
:: $B%7%'%k%3%^%s%I(B cd $B$H(B pwd $B$KBP1~$9$kA`:n(B.
@end table
@table @var
@item return
$BJ8;zNs(B(@code{pwd}), $B@0?t(B(@code{chdir})
@item dirctory
$BJ8;zNs(B
@end table
@itemize @bullet
@item
@code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B.
@item
@code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B. $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B.
@item
$B$3$l$i$N4X?t$O(B UNIX $BHG$K$N$_<BAu$5$l$F$$$k(B.
@end itemize
@example
[0] S=pwd();
/home/ohara
[1] chdir(".../taka");
-1
[2] chdir("/usr/bin");
0
@end example
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$l$i$N4X?t$O(B 2008-8-27 $B$K%3%_%C%H$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/miscf.c (1.27) $B$G$"$k(B.
@end itemize
@node dcurrenttime,,, $B%7%9%F%`(B
@subsection @code{dcurrenttime}
@findex dcurrenttime
@comment --- $B8=:_;~9o$r<hF@(B ---
@table @t
@item dcurrenttime()
:: $B8=:_;~9o$r<hF@(B.
@end table
@table @var
@item return
$BIbF0>.?tE@?t(B
@end table
@itemize @bullet
@item
$BJV$jCM$O(B1970$BG/(B1$B7n(B1$BF|(B0$B;~(B0$BJ,(B0$BIC$+$i$N7P2aIC?t$G$"$k(B.
@end itemize
@example
[0] ctrl("real_digit", 16);
16
[1] dcurrenttime();
1226390851.34476
[2] currenttime();
1226390854
@end example
@table @t
@item $B;2>H(B
@ref{currenttime}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$N4X?t$O(B 2008-9-12 $B$K%3%_%C%H$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/time.c (1.6) $B$G$"$k(B.
@end itemize
@comment ****************************************************************
@node $B8@8l(B,,, $B<B83E*;EMM$N4X?t(B
@section $B8@8l(B
@node get_struct_name,,, $B8@8l(B
@subsection @code{get_struct_name}, @code{get_element_names}, @code{get_element_at}, @code{put_element_at}
@findex get_struct_name
@findex get_element_names
@findex get_element_at
@findex put_element_at
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item get_struct_name(@var{s})
@itemx get_element_names(@var{s})
@itemx get_element_at(@var{s},@var{key})
@itemx put_element_at(@var{s},@var{key},@var{obj})
:: $B9=B$BN(B @var{s} $B$KBP$9$kA`:n(B
@end table
@table @var
@item return
$BJ8;zNs(B (get_struct_name),
$BJ8;zNs$N%j%9%H(B (get_element_names),
$B%*%V%8%'%/%H(B (get_element_at),
$B%*%V%8%'%/%H(B (put_element_at)
@item s
$B9=B$BN(B
@item key
$BJ8;zNs(B
@item obj
$B%*%V%8%'%/%H(B
@end table
@itemize @bullet
@item
@code{get_struct_name(s)} $B$O(B, $B9=B$BN(B @var{s} $B$NL>A0$rLa$9(B.
@item
@code{get_element_names(s)} $B$O(B, $B9=B$BN$N%a%s%P!<$NL>A0$N%j%9%H$rLa$9(B.
@item
@code{get_element_at(s,key)} $B$O9=B$BN(B s $B$N%a%s%P!<(B key $B$NCM$rLa$9(B.
@item
@code{put_element_at(s,key,obj)} $B$O9=B$BN(B s $B$N%a%s%P!<(B key $B$NCM$r(B obj $B$K@_Dj$9$k(B.
@end itemize
@example
[219] struct point @{ x, y, color@};
[220] P = newstruct(point);
@{0,0,0@}
[221] P->x = 10$ P->y=5$ P->color="red"$
[222] get_element_names(P);
[x,y,color]
[223] put_element_at(P,"color","blue");
blue
[224] P->color;
bule
@end example
@table @t
@item $B;2>H(B
@ref{newstruct}, @ref{struct}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B9=B$BN$NDj5A$rCN$i$:$K9=B$BN$r07$&%f!<%64X?t$r=q$/$H$-$KJXMx(B.
asir-contrib $B$N(B noro_print.rr $B$r8+$h(B.
@item OpenXM_contrib2/asir2000/builtin/compobj.c 1.8.
@end itemize
@comment mapat
@node mapat,,, $B8@8l(B
@subsection @code{mapat}
@findex mapat
@table @t
@item mapat(@var{fname},@var{pos}[,@var{arg0}, @var{arg1}, ...])
:: @var{pos} $B$KBP$9$k(B map $B4X?t(B
@end table
@table @var
@item return
$B%*%V%8%'%/%H(B
@item pos
$B@0?t(B
@item arg0, arg1, arg2, ...
$B%*%V%8%'%/%H(B
@end table
@itemize @bullet
@item
@code{map} $B4X?t$O(B 0 $BHVL\$N0z?t$KBP$7$F$7$+F0:n$7$J$$$,(B, @code{mapat}
$B4X?t$O;XDj$7$?HV9f$N0z?t$KBP$7$F(B @code{map} $B4X?t$r<B9T$9$k(B.
@item
@code{mapat(fname,0,A0,A1,...)} $B$O(B
@code{map(fname,A0,A1,...)} $B$KEy2A$G$"$k(B.
@item
$B<!$NI{:nMQ$,$"$k(B. $B$^$@=q$$$F$J$$(B.
@end itemize
@example
[219] mapat(deg,1,x^2+y^3+x+y,[x,y]);
[2,3]
[220] mapat(subst,1,x+y+z,[x,y,z],2);
[y+z+2,x+z+2,x+y+2]
@end example
@table @t
@item $B;2>H(B
@ref{map}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B 2004-6-22 $B$K%3%_%C%H$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/pf.c, subst.c $B$G$"$k(B.
@end itemize
@comment list
@node list,,, $B8@8l(B
@subsection @code{list}
@findex list
@table @t
@item list([@var{arg0}, @var{arg1}, ...])
:: list $B$r@8@.$9$k(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item arg0, arg1, arg2, ...
$B%*%V%8%'%/%H(B
@end table
@itemize @bullet
@item
@var{arg0}, @var{arg1}, ... $B$rMWAG$H$9$k%j%9%H$r@8@.$9$k(B.
@end itemize
@example
[219] list(1,2,3);
[1,2,3]
[220] list(1,2,[3,4]);
[1,2,[3,4]]
@end example
@table @t
@item $B;2>H(B
@ref{cons}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B 2004-6-22 $B$K%3%_%C%H$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/list.c $B$G$"$k(B.
@end itemize
@node assoc,,, $B8@8l(B
@subsection @code{assoc}
@findex assoc
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item assoc(@var{a},@var{b})
:: $BO"A[%j%9%H$r$D$/$k(B
@end table
@table @var
@item return
List
@item a
List
@item b
List
@end table
@itemize @bullet
@item $B%j%9%H(B @var{a}, @var{b} $B$h$j(B
[[@var{a}[0],@var{b}[0]], [@var{a}[1],@var{b}[1]], ...]
$B$J$k?7$7$$%j%9%H$r@8@.$9$k(B.
@end itemize
$B2<$NNc$G$O(B @code{A} $B$KF0J*$NL>A0$,(B,
@code{B} $B$KB-$NK\?t$,F~$C$F$$$k(B.
@code{assoc(A,B)} $B$GF0J*$HB-$NK\?t$r%Z%"$K$7$?%j%9%H$r@8@.$9$k(B.
@example
[1192] A=["dog","cat","snake"];
[dog,cat,snake]
[1193] B=[4,4,0];
[4,4,0]
[1194] assoc(A,B);
[[dog,4],[cat,4],[snake,0]]
@end example
@table @t
@item $B;2>H(B
@ref{cons}, @ref{append}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item
$B$3$N4X?t$O(B 2004-6-28 $B$K=q$+$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B
builtin/list.c 1.9
parse/eval.c 1.35,
parse/parse.h 1.31,
parse/quote.c 1.14--1.16.
@end itemize
@node set_secure_flag,,, $B8@8l(B
@subsection @code{set_secure_flag}, @code{set_secure_mode}
@findex set_secure_flag
@findex set_secure_mode
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item set_secure_flag(@var{fname},@var{m})
@itemx set_secure_mode(@var{m})
:: $B4X?t$N<B9T8"8B$r@_Dj$9$k(B. (web $B%5!<%S%9MQ(B)
@end table
@table @var
@item return
$B@0?t(B
@item fname
$BJ8;zNs(B
@item m
$B@0?t(B
@end table
@itemize @bullet
@item @code{set_secure_flag}, @code{set_secure_mode} $B$O(B
asir $B$r(B web $B%5!<%PEy$G8x3+$9$k$?$a$K2C$($i$l$?4X?t(B.
@code{set_secure_flag} $B$G8x3+$9$k4X?t$r;XDj$9$k(B.
@code{secure_mode} $B$,(B 1 $B$N>l9g$O(B @code{set_secure_flag} $B$G;XDj$5$l$?(B
$B4X?t$7$+<B9T$G$-$J$$(B.
$B4X?t$N<B9TESCf$G$O(B @code{secure_mode} $B$,(B 0 $B$H$J$C$F$$$k$N$G(B,
$BG$0U$N4X?t$r<B9T$G$-$k(B.
$B$^$?%(%i!<$N;~Ey$O(B, @code{secure_mode} $B$O(B 1 $B$K<+F0E*$KI|5"$9$k(B.
$B$?$@$7(B @code{def} $B$O<B9T$G$-$J$$(B.
$B8x3+$9$k4X?t$G$O(B, $B$=$N=hM}Cf$OG$0U$N4X?t$,<B9T$G$-$k$N$G(B,
security $B$K==J,Cm0U$7$?<BAu$r$9$kI,MW$,$"$k(B.
@item
@code{set_secure_flag} $B$O(B, @var{fname} $B$N(B secure flag $B$r(B @var{m}
$B$K$9$k(B.
$B8x3+$9$kL?Na$O(B 1 $B$K@_Dj$9$k(B.
@item
@var{set_secure_mode(1)} $B$G(B @code{secure_mode} $B$,(B 1 $B$H$J$j(B,
$B8x3+$5$l$?4X?t$7$+<B9T$G$-$J$/$J$k(B.
quit $BEy$b<B9T$G$-$J$$$N$GCm0U(B.
@item @code{ timer } $B$N0z?t$H$7$F(B secure_flag $B$r@_Dj$7$F$$$J$$4X?t$r(B
$B;XDj$7$F<B9T$7$F$b%(%i!<$,I=<($5$l$J$$(B.
$B$3$N$H$-$O(B, @code{ ctrl("error_in_timer",1) } $B$r<B9T$7$F$*$/(B.
@end itemize
@example
[1194] set_secure_flag("print_input_form_",1);
1
[1195] set_secure_flag("fctr",1);
1
[220] set_secure_mode(1);
1
[1197] fctr((x-1)^3);
[[1,1],[x-1,3]]
[1198] fctr(shell("ls"));
evalf : shell not permitted
return to toplevel
@end example
@table @t
@item $B;2>H(B
@ref{timer}
@end table
@noindent
ChangeLog
@itemize @bullet
@item @code{set_secure_flag}, @code{set_secure_mode} $B$O(B asir $B$r(B
web $B%5!<%PEy$G8x3+$9$k$?$a$K2C$($i$l$?4X?t(B.
sm1 $B$NF1MM$J4X?t(B RestrictedMode $B$G:NMQ$5$l$?J}K!$rMQ$$$F$$$k(B.
$B$D$^$j(B, @code{set_secure_flag} $B$G8x3+$9$k4X?t$r;XDj$9$k(B.
@code{secure_mode} $B$,(B 1 $B$N>l9g$O(B @code{set_secure_flag} $B$G;XDj$5$l$?(B
$B4X?t$7$+<B9T$G$-$J$$(B.
v$B4X?t$N<B9TESCf$G$O(B @code{secure_mode} $B$,(B 0 $B$H$J$C$F$$$k$N$G(B,
$BG$0U$N4X?t$r<B9T$G$-$k(B.
@item $B$3$N4X?t$O(B 2004-10-27 $B$+$i(B 2004-11-22 $B$K$+$1$F3+H/$5$l$?(B.
@item cgiasir.sm1, cgi-asir.sh $B$HAH$_9g$o$;$F(B cgi $B%5!<%S%9$rDs6!$9$k$?$a$K(B
$BMxMQ$9$k(B.
cgi-asir.sh $B$G$O(B
@code{CGI_ASIR_ALLOW} $B4D6-JQ?t$G8x3+$9$k%3%^%s%I$r;XDj$9$k(B.
@item
1.24--1.25 OpenXM_contrib2/asir2000/builtin/miscf.c
@item
1.36--1.38 OpenXM_contrib2/asir2000/parse/eval.c
@item
1.6--1.7 OpenXM_contrib2/asir2000/parse/function.c
@item
1.33 OpenXM_contrib2/asir2000/parse/parse.h
@end itemize
@node initialize_static_variable,,, $B8@8l(B
@subsection @code{initialize_static_variable}
@findex initialize_static_variable
@comment --- $B@bL@(B ---
@table @t
@item static $BJQ?t$N=i4|2=$NLdBjE@(B. $B=i4|2=$N;~$K(B segmentation fault $B$,$*$-$k(B.
@end table
@itemize @bullet
@item static $BJQ?t$N<h07(B.
$B2<$NNc$r;2>H$N$3$H(B.
@end itemize
@example
if (1) @{
module abc;
static A;
A=1;
endmodule;
@} else @{ @};
end$
$B$r(B t.rr $B$H$9$k$H$-(B,
[6] load("./t.rr");
1
internal error (SEGV)
$B$H$J$k(B.
t.rr $B$r(B
if (1) @{
module abc;
static A;
localf initA;
localf foo;
def initA() @{
A=1;
@}
initA();
def foo() @{
return A;
@}
endmodule;
@} else @{ @};
end$
$B$H$9$k$H@5$7$/=i4|2=$5$l$k(B.
@end example
@comment --- ChangeLog
@noindent
ChangeLog
@itemize @bullet
@item oxasir-win.rr $B$N<h07$GLdBjE@$H$7$FIb>e(B. 2005.07.25.
@item oxasir-win.rr $B$N<h07$G(B double quote $B$N<h$j07$$$KLdBj$,$"$C$?$,(B, $B$3$l$O(B asir2000/io/ox_asir.c, 1.58, $B$GLdBjE@2r7h(B.
@item ox_asir $B$K7W;;$r0MMj$9$k;~$O(B if (1) @{ ... @}$B$G0O$`(B.
@end itemize
@comment ****************************************************************
@node $B?tO@!&Be?t(B,,, $B<B83E*;EMM$N4X?t(B
@section $B?tO@!&Be?t(B
@node small_jacobi,,, $B?tO@!&Be?t(B
@subsection @code{small_jacobi}
@findex small_jacobi
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item small_jacobi(@var{a},@var{m})
:: Jacobi $B5-9f$N7W;;(B
@end table
@table @var
@item return
$B@0?t(B
@item arg1, arg2
$B@0?t(B
@end table
@itemize @bullet
@item
@var{m} $B$,AG?t$N$H$-$O(B Legendre $B5-9f$H$h$P$l(B,
x^2 = @var{a} mod @var{m} $B$K2r$,$"$k$H$-(B 1, $B2r$,$J$$$H$-(B -1 $B$r$b$I$9(B.
@item
Jacobi $B5-9f$O(B Legendre $B5-9f$N@Q$GDj5A$5$l$k(B ($B=iEy@0?tO@$NK\;2>H(B).
@item
$B$3$N4X?t$O(B machine int $B$NHO0O$G(B jacobi $B5-9f$r7W;;$9$k(B.
@end itemize
@example
[1286] small_jacobi(2,3);
-1
[1287] small_jacobi(2,7);
1
@end example
@table @t
@item $B;2>H(B
http://members.jcom.home.ne.jp/yokolabo/asirlib/
$B$b8+$F$M(B.
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$NM3Mh$OITL@(B.
@end itemize
@node noro_matrix.rr,,, $B?tO@!&Be?t(B
@subsection @code{noro_matrix.rr}
@findex noro_matrix.rr
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item linalg.unit_mat(@var{arg1})
@item linalg.random_rmat(@var{arg1}, @var{arg2}, @var{arg3})
@item linalg.minipoly_mat(@var{arg1})
@item linalg.compute_kernel(@var{arg1})
@item linalg.compute_image(@var{arg1})
@item linalg.jordan_canonical_form(@var{arg1})
@end table
@itemize @bullet
@item $B4JC1$J2r@b$*$h$S<BNc$O(B http://www.math.kobe-u.ac.jp/HOME/taka/2007/knx/noro_matrix-ja.txt $B$r;2>H(B.
@end itemize
@example
load("noro_matrix.rr");
A=newmat(4,4,[[2,0,0,0],[3,5,1,0],[-9,-9,-1,0],[-5,0,0,1]]);
B=linalg.jordan_canonical_form(A);
@end example
@table @t
@item $B;2>H(B
@ref{invmat}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B 2004-04 $B:"$+$i@~7ABe?t(BIII $B$N9V5A$r$7$J$,$i=q$+$l$?(B.
@item $B%=!<%9(B: OpenXM/src/asir-contrib/packages/src/noro_matrix.rr
@end itemize
@node f_res,,, $B?tO@!&Be?t(B
@subsection @code{f_res}
@findex f_res
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item f_res
@end table
@itemize @bullet
@item f_res $B$O3F<o$N=*7k<0$r7W;;$9$k%b%8%e!<%k$G$"$k(B. ox_grep("f_res"); $B$G(B online manual $B$r1\Mw2DG=$G$"$k(B.
@end itemize
@table @t
@item $B;2>H(B
@ref{}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N%b%8%e!<%k$O(B Fujiwara $B7/$N=$;NO@J8$,85$K$J$j(B, $B$=$l$r2~B$$7$?$b$N$G$"$k(B.
@item OpenXM/src/ox_cdd, OpenXM/src/asir-contrib/packages/src/f_res.rr
@end itemize
@node D $B2C72$N@)8B$K4X$9$k4X?t(B,,, $B<B83E*;EMM$N4X?t(B
@section D $B2C72$N@)8B$K4X$9$k4X?t(B
@node nk_restriction.restriction,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
@subsection @code{nk_restriction.restriction}
@comment --- $B:w0zMQ%-!<%o!<%I(B
@findex nk_restriction.restriction
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item nk_restriction.restriction(@var{Id}, @var{VL}, @var{DVL}, @var{W})
:: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9!#(B
@end table
@comment --- $B0z?t$N4JC1$J@bL@(B ---
@table @var
@item Id
$B%$%G%"%k$N@8@.85$N%j%9%H(B
@item VL
$BJQ?t$N%j%9%H(B
@item DVL
$BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
@item W
$B=E$_%Y%/%H%k$rI=$9%j%9%H(B
@end table
@itemize @bullet
@item
@var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
@item
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B
$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
x,y $B$K$D$$$F@)8B$r9T$&!#(B
@end itemize
$B0J2<$O!"%$%G%"%k(B
@iftex
@tex
$I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $
@end tex
$B$N(B
@tex
$x$
@end tex
@end iftex
@ifinfo
I = D . @{ x dx -1, y dy - 1 @} $B$N(B x
@end ifinfo
$B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k!#(B
@example
[1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);
-- generic_bfct_and_gr :0.001sec(0.001629sec)
generic bfct : [[1,1],[s-1,1]]
S0 : 1
B_@{S0@} length : 2
-- fctr(BF) + base :0.000999sec(0.0005109sec)
[[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]
@end example
@node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
@subsection @code{nk_restriction.restriction_ideal}
@comment --- $B:w0zMQ%-!<%o!<%I(B
@findex nk_restriction.restriction_ideal
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})
:: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B%$%G%"%k$rJV$9!#(B
@end table
@comment --- $B0z?t$N4JC1$J@bL@(B ---
@table @var
@item Id
$B%$%G%"%k$N@8@.85$N%j%9%H(B
@item VL
$BJQ?t$N%j%9%H(B
@item DVL
$BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
@item W
$B=E$_%Y%/%H%k$rI=$9%j%9%H(B
@end table
@itemize @bullet
@item
@var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
@item
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B
$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
x,y $B$K$D$$$F@)8B$r9T$&!#(B
@end itemize
$B0J2<$O!"%$%G%"%k(B
@iftex
@tex
$I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $
@end tex
$B$N(B
@tex
$x$
@end tex
@end iftex
@ifinfo
I = D . @{ x dx -1, y dy - 1 @} $B$N(B x
@end ifinfo
$B$K$D$$$F$N@)8B%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B
@example
[1346] nk_restriction.restriction_ideal([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);
-- generic_bfct_and_gr :0.002sec(0.001652sec)
generic bfct : [[1,1],[s-1,1]]
S0 : 1
B_@{S0@} length : 2
-- fctr(BF) + base :0sec(0.000566sec)
-- restriction_ideal_internal :0.001sec(0.0007441sec)
[-1]
@end example
@node nk_restriction.integration,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
@subsection @code{nk_restriction.integration}
@comment --- $B:w0zMQ%-!<%o!<%I(B
@findex nk_restriction.integration
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W})
:: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9!#(B
@end table
@comment --- $B0z?t$N4JC1$J@bL@(B ---
@table @var
@item Id
$B%$%G%"%k$N@8@.85$N%j%9%H(B
@item VL
$BJQ?t$N%j%9%H(B
@item DVL
$BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
@item W
$B=E$_%Y%/%H%k$rI=$9%j%9%H(B
@end table
@comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
@comment --- @bullet $B$O9uE@IU$-(B ---
@itemize @bullet
@item
@var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
@item
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B
$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
x,y $B$K$D$$$F@QJ,$r9T$&!#(B
@end itemize
$B0J2<$O!"%$%G%"%k(B
@iftex
@tex
$I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $
@end tex
$B$N(B
@tex
$t$
@end tex
@end iftex
@ifinfo
I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t
@end ifinfo
$B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])
@example
[1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],
[dt,dx],[1,0]);
-- generic_bfct_and_gr :0.001sec(0.001796sec)
generic bfct : [[1,1],[s,1],[s-1,1]]
S0 : 1
B_@{S0@} length : 2
-- fctr(BF) + base :0.001sec(0.0006731sec)
[[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]]
@end example
@node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
@subsection @code{nk_restriction.integration_ideal}
@comment --- $B:w0zMQ%-!<%o!<%I(B
@findex nk_restriction.integration_ideal
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})
:: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,%$%G%"%k$rJV$9!#(B
@end table
@comment --- $B0z?t$N4JC1$J@bL@(B ---
@table @var
@item Id
$B%$%G%"%k$N@8@.85$N%j%9%H(B
@item VL
$BJQ?t$N%j%9%H(B
@item DVL
$BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
@item W
$B=E$_%Y%/%H%k$rI=$9%j%9%H(B
@end table
@comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
@comment --- @bullet $B$O9uE@IU$-(B ---
@itemize @bullet
@item
@var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B
($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
@item
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B
$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
x,y $B$K$D$$$F@QJ,$r9T$&!#(B
@end itemize
$B0J2<$O!"%$%G%"%k(B
@iftex
@tex
$I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $
@end tex
$B$N(B
@tex
$t$
@end tex
@end iftex
@ifinfo
I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t
@end ifinfo
$B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])
@example
[1431] nk_restriction.integration_ideal([2*t*dx+dt,t*dt+2*x*dx+2],[t,x],
[dt,dx],[1,0]);
-- generic_bfct_and_gr :0.002999sec(0.002623sec)
generic bfct : [[1,1],[s,1],[s-1,1]]
S0 : 1
B_@{S0@} length : 2
-- fctr(BF) + base :0.001sec(0.001091sec)
-- integration_ideal_internal :0.002sec(0.001879sec)
[2*x*dx+1]
[1432]
@end example
@node nk_restriction,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option)
@subsection @code{nk_restriction (option)}
@comment --- $B:w0zMQ%-!<%o!<%I(B
@findex nk_restriction (option)
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@table @t
@item nk_restriction.restriction(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
@item nk_restriction.restriction_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
@item nk_restriction.integration(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
@item nk_restriction.integration_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
:: D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N%*%W%7%g%s$N@bL@(B
@end table
@comment --- $B0z?t$N4JC1$J@bL@(B ---
@table @var
@item @var{n}
0 $B$^$?$O(B 1
@item @var{p}
$B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B)
@item @var{m}
$B@0?t(B
@end table
@comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
@comment --- @bullet $B$O9uE@IU$-(B ---
@itemize @bullet
@item @var{n} $B$,(B 0 $B$G$J$$$H$-(B, $BHs@F<!ItJ,$N7W;;$r9T$&(B.
restriction_ideal (integration_ideal) $B$K4X$7$F$O(B, $B%$%G%"%k(B @code{I} $B$N(B
@code{M} $BJQ?t$K$D$$$F$N@)8B(B($B@QJ,(B)$B%$%G%"%k(B @code{J} $B$H(B
@iftex
@tex
{\tt J[K]-(1/IH[K][1])(IH[K][0][0][0]IH[K][0][0][1]+...+IH[K][0][M][0]IH[K][0][M][1])} $\in$ {\tt I}
@end tex
@end iftex
@ifinfo
J[K]-(1/IH[K][1])(IH[K][0][0][0]IH[K][0][0][1]+...+IH[K][0][M][0]IH[K][0][M][1]) \in I
@end ifinfo
$B$rK~$?$9Hs@F<!ItJ,$r9=@.$9$k>pJs(B @code{IH} $B$H$N%Z%"(B @code{[J,IH]} $B$r=PNO$9$k(B.
$B>\$7$$=PNO$N8+J}$K$D$$$F$O(B, $B2<$NNc$d%=!<%9$N(B @code{inhomo_part} $B$N(B
$B%3%a%s%H$r;2>H(B.
restriction, integration $B$KBP$9$k(B @code{inhomo} $B%*%W%7%g%s$O(B
restriction_ideal, integration_ideal $B$N%5%V%k!<%A%s$H$7$F$N<B9TMQ$J$N$G(B,
$B%f!<%6$,L@<(E*$K;HMQ$9$k$3$H$O$J$$(B.
@item @var{param} $B$K;XDj$5$l$?JQ?t$O78?tBN$KB0$9$k$b$N$H$_$J$5$l$F7W;;$,9T$o$l$k(B.
$B$^$?(B, ``generic'' $B$G$"$k$3$H$,2>Dj$5$l$k(B.
$B$D$^$j(B, $B$3$l$i$NJQ?t$K0MB8$9$k$h$&$J(B generic b-$B4X?t$N:,$O(B,
$B:GBg@0?t:,$G$J$$$H$$$&$3$H$G$"$k(B.
@item @var{param} $B$,;XDj$5$l$k$H(B, generic b-$B4X?t$N7W;;$O(B noro $B$K$h$k(B
$B9bB.%"%k%4%j%:%`$G$O$J$/(B, $B>C5nK!$,MQ$$$i$l$k(B.
@var{param} $B$K6u%j%9%H$r;XDj$9$k$3$H$G(B, b-$B4X?t$N7W;;J}K!$N%U%i%0$H$7$F$b(B
$BMxMQ$G$-$k(B.
@item @var{m} $B$,Ii$G$J$$$H$-(B, $B7W;;$r9T$o$:$K(B s-m $B$r(B generic b-$B4X?t$H$7$F(B
$B@)8B(B, $B@QJ,Ey$N7W;;$r9T$&(B.
@end itemize
$B0J2<$O(B,
@iftex
@tex
$ t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a} $
@end tex
$B$N(B annihilator
@tex
$I = D \cdot \{ x(1-x) \partial_x^2+((1-t) \partial_t-(a+b+1)x+c-1)
\partial_x-ab, (1-t)x \partial_x+t(1-t) \partial_t+(2-c)t+b-1,
(xt-1) \partial_x+at \}$
@end tex
$B$N(B
@tex
$t$
@end tex
$B$K$D$$$F$N@QJ,%$%G%"%k(B
@tex
$J$
@end tex
$B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3])
@end iftex
@ifinfo
t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a}
$B$N(B annihilator
I = D . @{ x(1-x)dx^2+((1-t)dt-(a+b+1)x+c-1)dx-ab,
(1-t)x dx+t(1-t)dt+(2-c)t+b-1, (xt-1)dx+at @}
$B$N(B t $B$K$D$$$F$N@QJ,%$%G%"%k(B J
$B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3])
@end ifinfo
@example
[1555] A=ndbf.ann_n([t,1-t,1-x*t])$
[1556] I=map(subst,A,s0,b-1,s1,c-b-1,s2,-a);
[(x^2-x)*dx^2+((t-1)*dt+(a+b+1)*x-c+1)*dx+b*a,(-t+1)*x*dx+(t^2-t)*dt+(-c+2)*t+b-1,(t*x-1)*dx+a*t]
[1557] J=nk_restriction.integration_ideal(I,[t,x],[dt,dx],[1,0]|inhomo=1, param=[a,b,c]);
-- nd_weyl_gr :0sec(0.001875sec)
-- weyl_minipoly_by_elim :0.008001sec(0.006133sec)
-- generic_bfct_and_gr :0.008001sec(0.006181sec)
generic bfct : [[-1,1],[s,1],[s-a+c-1,1]]
S0 : 0
B_{S0} length : 1
-- fctr(BF) + base :0sec(0.003848sec)
-- integration_ideal_internal :0sec(0.07707sec)
[[(x^2-x)*dx^2+((a+b+1)*x-c)*dx+b*a],[[[[dt,(-t+1)*dx]],1]]]
@end example
@iftex
$B$3$N=PNO$O(B
@tex
$\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \}
- 1/1 \{ \partial_t (-t+1) \partial_x \} \in I$
@end tex
$B$G$"$k$3$H$r0UL#$9$k(B.
@end iftex
@ifinfo
$B$3$N=PNO$O(B
@{(x^2-x)dx^2+((a+b+1)x-c)dx+ab @} - 1/1 @{ dt (-t+1)dx @} \in I
$B$G$"$k$3$H$r0UL#$9$k(B.
@end ifinfo
@noindent
ChangeLog
@itemize @bullet
@item $B$3$l$i$N4X?t$O(B OpenXM/src/asir-contrib/packages/src/nk_restriction.rr $B$GDj5A$5$l$F$$$k(B. nk_restriction.rr, 1.1--1.6 $B$r8+$h(B.
@item 2010-02-05 $B$K(B 3 $B$D$N(B option (@code{inhomo}, @code{param}, @code{s0}) $B$,DI2C$5$l$?(B.
@end itemize
@node $B$=$NB>(B($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B
@section $B$=$NB>(B($BL$J,N`(B)
@node tk_pfn.rkn,,, $B<B83E*;EMM$N4X?t(B
@subsection @code{tk_pfn.rkn}
@findex tk_pfn.rkn
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item tk_pfn.rkn(@var{F},@var{X},@var{Y},@var{Xs},@var{Ys},@var{Ht},@var{H})
:: Pfaffian $BJ}Dx<0$KBP$9$k(B Runge-Kutta $BK!(B
@end table
@table @var
@item return
$B%j%9%H(B $BFHN)JQ?t$H2r$NAH(B
@item F, X, Y, Xs, Ys, Ht, H
@var{F} $B$O(B Pfaffian $BJ}Dx<0$N78?t9TNs%j%9%H(B.
@var{X} $B$OFHN)JQ?t%j%9%H(B.
@var{Y} $B$O=>B0JQ?t%j%9%H(B.
@var{Xs} $BFHN)JQ?t$N=PH/CM%j%9%H(B.
@var{Ys} $B$O=PH/;~$N=>B0JQ?t$NCM%j%9%H(B.
@var{Xt} $B$ODd;_$9$kFHN)JQ?t$NCM%j%9%H(B.
@var{H} $B$OHy>/?t(B.
@end table
@itemize @bullet
@item $B$3$N4X?t$OO"N)(BPfaffian$BJ}Dx<0(B dY/d X[i] = F[i] Y $B$r?tCME*$K2r$/(B.
@item $BG$0U$N(B holonomic system $B$O(B Pfaffian $BJ}Dx<0$KJQ49$G$-$k(B ([SST, Chap 1]).$B!!JQ49$K$O(B yang.rr $B%Q%C%1!<%8$rMQ$$$k(B.
@item d F[i]/d X[j] + F[i] F[j] = d F[j]/d X[i] + F[j] F[i] = 0 $B$,G$0U$N(B i, j $B$KBP$7$F@.N)$7$F$$$k$3$H$,2r$,B8:_$9$kI,MW==J,>r7o$G$"$k(B. $B$3$N>r7o$,@.N)$7$J$$$H$-$K$3$N4X?t$rMQ$$$F2r$r7W;;$7$F$b$=$N2r$O56J*$G$"$k(B.
@item X[i] $B$,F0$/HO0O$O<B?t$G$J$$$H$$$1$J$$(B.
@item Xs[i] <= X[i] <= Xt[i] $B$^$?$O(B Xt[i] <= X[i] <= Xs[i] $B$G$"$k(B.
@item $B0z?t$NM?$(J}$NNc$O%=!<%9%3!<%I(B (@code{OpenXM/lib/asir-contrib/tk_pfn.rr} )$B$N(B @code{tk_pfn.test1}, @code{tk_pfn.test2} $B$r;2>H(B.
@item $B2<$NNc$N=PNO$O(B X=(1,3) $B$G$NCM$,(B Y=(-8,2,-6) $B$G$"$k$3$H$r0UL#$9$k(B.
@item $B;29M(B. taka_runge_kutta.rr, yang.rr
@end itemize
@example
[1355] import("tk_pfn.rr");
[1590] tk_pfn.test1();
Value at (3,0.1)[8.99,6,-0.2]
Value at (1,3)[-8,2,-6]
[[[1,3],-8,2,-6],
[[1,2.9],-7.41,2,-5.8],
--- snip ---
[[3,0.1],8.99,6,-0.2]]
@end example
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B 2009-12 $B$+$i(B 2010-01 $B$K$+$1$F:G=i$NHG$,=q$+$l$?(B.
@item @code{OpenXM/src/asir-contrib/packages/src/tk_pfn.rr} 1.1, 1.2
@item $B$3$N%b%8%e!<%k$NA0?H$O(B @code{tk_pf2.rr} $B$G$"$k(B. $B$3$l$OFHN)JQ?t$,(B 2 $B8D$N>l9g$G$"$k(B.
@end itemize
@node fj_simp.simplify,,, $B<B83E*;EMM$N4X?t(B
@subsection @code{fj_simp.simplify}
@findex fj_simp.simplify
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item fj_simp.simplify(@var{arg1})
:: arg1 $B$r4JC12=$9$k(B.
@end table
@table @var
@item return
$BB?9`<0(B, $BM-M}<0(B $B$^$?$O(B quote
@item arg1
$BB?9`<0(B $B$^$?$O(B $BM-M}<0(B
@end table
@itemize @bullet
@item
$B8=:_$N%P!<%8%g%s$G$O(B fj_simp.simplify $B$G$J$/(B, $BC1$K(B simplify $B$H$h$V(B.
@item
$B$3$N4X?t$O(B
Joel S. Cohen, Computer Algebra and Symbolic Computation,
http://web.cs.du.edu/~jscohen/MathematicalMethods/index.htm
$B$K5-=R$5$l$F$$$k(B Automatic simplification algorithm $B$H(B
B.F.Caviness, R.J.Fateman, Simplification of Radical Expressions (1976)
$B$K5-=R$5$l$F$$$k(B radcan $B%"%k%4%j%:%`$N<BAu$G$"$k(B.
@item
$BJ#AGB?CM4X?t$H$7$F$O(B (x*y)^a = x^a*x^b $B$O0lHL$K$O@.N)$7$J$$$N$G(B, $B7k2L$rJ#AG4X?t$K;H$&$H$-$O(B
$BCm0U$,I,MW$G$"$k(B. (x^a = exp(a*log(x)) $B$J$N$G(B)
@end itemize
@example
load("fj_simplify.rr");
[1434] simplify((x^(1/2))^3);
((x)^(3/2))
[1435] simplify((2^(1/2))^2);
2
[1436] simplify((2+2^(1/2))^3);
14*((2)^(1/2))+20
[1437] simplify(exp(x)*exp(-x+y));
((@@e)^(y))
@end example
@table @t
@item $B;2>H(B
@ref{quote}
@end table
@noindent
ChangeLog
@itemize @bullet
@item
$B>-MhE*$K$O(B module $B2=$7$F(B fj_simp module $B$K4^$a$kM=Dj(B.
poly_simplify $B$+$i(B fj_simp.simplify $B$r8F$V(B.
@item
Todo: exp $B0J30$NFC<l4X?t$K$D$$$F$N(Bsimplification $B$N5!G=(B.
@item
$B$3$N4X?t$O(B 2010.01 $B$K(B M.Fujimoto $B$K$h$j:G=i$NHG$,=q$+$l$?(B.
OpenXM/src/asir-contrib/packages/src/fj_simplify.rr
@end itemize
@comment ----------- $B0J2<$O8+K\(B. $B>C$9$J(B.
@comment ****************************************************************
@comment --- $B"~"~"~"~(B $B0J2<B>$N4X?t$K$D$$$F??;w$7$F5-=R$9$k(B. $B"~"~"~"~(B
@comment $B?7$7$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B.
@comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B
@comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B ---
@node xyz_pqr,,, $B<B83E*;EMM$N4X?t(B
@subsection @code{xyz_pqr}, @code{syz_stu}
@findex xyz_pqr
@findex xyz_stu
@comment --- $B4X?t$N4JC1$J@bL@(B ---
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
@table @t
@item xyz_pqr(@var{arg1},@var{arg2}[,@var{flag}])
@itemx xyz_stu(@var{arg1},@var{arg2})
:: xyz $B$K4X$9$kA`:n(B.
@end table
@table @var
@item return
$B@0?t(B
@item arg1, arg2
$B@0?t(B
@item flag
0 $B$^$?$O(B 1
@end table
@itemize @bullet
@item $B$3$N9`L\$O?7$7$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B.
@item
@code{xyz_pqr()} $B$O(B, @var{arg1}, @var{arg2} $B$r(B pqr $B$9$k(B.
@item
@var{flag} $B$,(B 0 $B$G$J$$$H$-(B, $B%b%8%e%i7W;;$r9T$&(B.
@item
@code{xyz_stu()} $B$O(B stu $B%"%k%4%j%:%`$rMQ$$$k(B.
@end itemize
@example
[219] xyz_pqr(1,2);
3
[220] xyz_pqr(1,2,1);
3
0
[221] xyz_stu(1,2);
3
@end example
@table @t
@item $B;2>H(B
@ref{xyz_abc}
@end table
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@item $B$3$N4X?t$O(B 2004-3-1 $B$+$i(B 2004-3-14 $B$K$+$1$F(B $B%"%k%4%j%:%`(B xyz ($BO@J8(B
http://www.afo.org/xyz.pdf ) $B$rMQ$$$F=q$-D>$5$l$?(B.
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B xxxyy.rr, ppp.c $B$G$"$k(B.
@item $B$3$N4X?t$O(B 2000 $B:"$K$O$8$a$F$N%P!<%8%g%s$,=q$+$l$?(B. $B%=!<%9$O(B ppp.c $B$G$"$k(B.
@end itemize
@comment --- $B$*$^$8$J$$(B ---
@node Index,,, Top
@unnumbered Index
@printindex fn
@printindex cp
@iftex
@vfill @eject
@end iftex
@summarycontents
@contents
@bye
@comment --- $B$*$^$8$J$$=*$j(B ---
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