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Up to [local] / OpenXM / src / asir-contrib / testing

1. qt.input_form, qt.hop,
   qt.hc_etov(Q,V),  Q is a monomial in quote. It returns the leading
coefficient and the exponent vector of Q.

$Id: tr.oxt,v 1.39 2005/05/11 03:32:56 taka Exp $
$OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.9 2005/05/11 06:40:10 takayama Exp $

$BCm0U(B: testing/tr.rr $B$G$O(B quote $B$r(B quotetolist $B$G(B list $B$KJQ49$7$F07$&$?$a(B,
      $B2<$N;EMM$H$O$3$H$J$j(B, list $B7?$G%G!<%?$rLa$9>l9g$bB?$$(B.
      $B%f!<%68@8l$G=q$$$F$$$k4X78>e(B pn(x) $B$r(B pn("x") $B$H$7$F$$$k(B. 
      $BB>$K$bF1MM$J4X?t$,$"$j(B.

$B$3$N%U%!%$%k$+$i(B texi $B%U%!%$%k$r:n@.$9$k$K$O0J2<$N$h$&$KF~NO$7$F2<$5$$(B.
oxgentexi $B$O(B OpenXM/src/util $B$N2<$K$"$j$^$9(B.

nkf -e tr.oxt | oxgentexi --noSorting --title 'Term rewriting functions for Risa/Asir' --author 'Nobuki Takayama' >t.texi

begin: AAA01|

$B8=:_$N%5%s%W%k<BAu$K$O(B bug $B$,Bt;3$G$+$D(B,
$B%5%s%W%k<BAu$O8zN($b0-$$(B.
$B$4Cm0U(B!

@c ---------------------------------------------------------
@section $BJQ?t%Q%?!<%s$H4X?t%Q%?!<%s(B


$BJQ?t%Q%?!<%s(B
@itemize @bullet
@item pn(x),             $BG$0U$N$b$N$K%^%C%A(B. $B%^%C%A$7$?$b$N$r(B x $B$K(B bind.
@item pn(x,qt.is_integer(x)),  x $B$,(B @code{qt.is_integer(x)} $B$r$_$?$;$P%^%C%A(B.

@item Todo; $B4X?t$K%^%C%A$9$k(B fn $B$OB?J,$$$i$J$$(B. qt.is_function(x) $B$G(B OK.
@end itemize

$B%Q%?!<%s$O(B quote $B$GM?$($k(B.
$BM=Ls8l(B  tr.and, tr.or, tr.not  $B$O%Q%?!<%s$N%^%C%A$K4X$7$FO@M}1i;;$r$*$3$J$&(B.
$B$?$H$($P(B
quote(tr.and(pn(x,qt.is_integer(x)),pn(x,qt.is_non_negative(x)))
$B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.

end:

begin: AAA011|

@c ---------------------------------------------------------
@section $B<BAu$N$?$a$NJd=u4X?t(B

@itemize @bullet
@item @code{quotetolist}, @code{listtoquote}, @code{listtoquote_str} ;
   quote $B$H(B list $B$N4V$NJQ49(B.
@item @code{quote_to_funargs}, @code{funargs_to_quote}, @code{get_function_name} ;
  quote $B$H(B funarg $B7A<0$NJQ49(B. $B<B83E*4X?t$N%^%K%e%"%k$r;2>H(B.
@item @code{quotetoobj}, @code{eval_quote} ;
   quote $B$H(B object $B$N4V$NJQ49(B.
@item @code{quote_input_form}, @code{ctrl("print_quote",1)} ;
   quote $B$HJ8;zNs$N4V$NJQ49(B.
@item @code{quote_flatten} ;
   $B:87k9gE*$K:n$jJQ$($k(B. $B<B83E*4X?t$N%^%K%e%"%k$r;2>H(B.
@end itemize

end:

begin: AAA02|

@section quote $B$KBP$9$k4pK\4X?t(B  (module qt $B$N4X?t(B)

end:


begin: qt.node(Q)
 quote $B%G!<%?(B {Q} $B$N(B node $B$r<h$j=P$9(B.
 example: qt.node(quote(1+2*3))     
        ["b_op","+"]  ($B8=:_$N<BAu$G$O$3$l$,La$k(B)
end:


begin: qt.nchild(Q)
 quote $B%G!<%?(B {Q} $B$N(B $B;R6!$N?t$rLa$9(B.
 example: qt.nchild(quote(1+2*3))     2 $B$rLa$9(B.
end:


begin: qt.child(Q,K)
 quote $B%G!<%?(B {Q} $B$N(B {K} $BHVL\$N;R6!$rLa$9(B.
 example: qt.child(quote(1+2*3),1)     quote(2*3) $B$rLa$9(B.
 example: qt.child(quote(1+2*3),0)     quote(1) $B$rLa$9(B.
end:

begin: hoge|
@c --------------------------------------------------------------------
@section quote $B$KBP$9$k=R8l(B
end:

begin: qt.is_integer(Q)
 quote $B%G!<%?(B {Q} $B$,@0?t$J$i(B 1
 example: qt.is_integer(quote(0))     
end:

begin: qt.is_dependent(Q,x)
 quote $B%G!<%?(B {Q} $B$,ITDj85(B {x} $B$r4^$`$H(B 1, $B4^$^$J$$$H(B 0.
 example: qt.is_dependent(quote(1+1/x),x)
end:

begin: qt.is_function(Q)
 quote $B%G!<%?(B {Q} $B$,4X?t$N$H$-(B 1, $B$=$&$G$J$$$H$-(B 0.
 example: qt.is_function(f(x,y));
end:

begin: qt.is_minus(Q)
 quote $B%G!<%?(B {Q} $B$,7A<0E*$K(B -1 $B$h$j;O$^$k$H$-(B 1.
 example: qt.is_minus(quote(-1/x));
 ref: qt.add_paren, qt.add_paren0
end:

begin: qt.is_rational(Q)
 quote $B%G!<%?(B {Q} $B$,7A<0E*$KM-M}?t$N;~(B 1.
 example: qt.is_rational(quote(1/2));
 example: 
   [1321] qt.is_rational(quote(1/2+4));
   1
 ref: qt.cancel_number
end:

begin: hoge2|
@c --------------------------------------------------------------------
@section quote $B$KBP$9$k%3%s%9%H%i%/%?(B
end:

begin: qt.zero()
 quote 0 $B$rLa$9(B.
end:

begin: qt.id(Qobj)
 quote object {Qobj} $B$r$=$N$^$^La$9(B.
end:

begin: qt.replace(Qobj,[[x,Valuex],[y,Valuey],...])
   quote object {Qobj} $B$NCf$N(B x $B$r(B Valuex, y $B$r(B Valuey, ... $B$KCV$-49$($?(B
   quote object $B$rLa$9(B.
   description:
    $B2]Bj(B; x, y $B$OBgJ8;z$b5v$9$+(B? @var{Qobj} $B$b85!94^$^$l$F$$$kBgJ8;z$rI>2A$7$FCV$-49$($k(B
    $B4X?t$bI,MW$+(B?

   example: qt.replace(quote(sin(x*@pi)), [[x,quote( (2*t+3) )]])
end:

   qt.replace $B$O(B asir-contrib $B$N(B base_replace $B$H;w$?5!G=(B.
   quote $B$NFbIt$KBgJ8;z$G$O$8$^$kJQ?t(B($BI>2A$9$k(B)$B$,=q$1$J$$$?$a(B.

begin: qt.parenthesis(Qobj)
   quote object {Qobj} $B$NCf$N3g8L$,B-$j$J$$$H$-$K$OJd$$(B, $BB?$$$H$-$K$O<h$j5n$C$?(B
   quote object $B$r:n$k(B.
   +, *, /, ^, - $BEy$K$D$$$F(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
  description:
  $B;29M(B;  
   @itemize
   @item $B$^$@<BAu$7$F$J$$(B.
   @item noro_simplify.rr  $B$N(B @code{noro_simplify.remove_paren()} 
      $B$,$9$G$K<B8=$E$_(B?
        ($B2C$($kJ}$O$@$a$_$?$$(B)
         @code{flatten()} $B$d(B @code{quote_to_funargs()} $B$rMxMQ$7$F$kLOMM(B.
   @item $B<B83E*4X?t%^%K%e%"%k$N(B @code{quote_flatten} $B$b;2>H(B ($B$3$N4X?t$J$$(B).
   @end itemize

end:

begin: qt.eval(Qobj,type)
   Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
  description:
   @code{eval_quote()} $B$,$9$G$K<B8=$E$_(B.
   $B<BAu$7$F$J$$(B.

end:

begin: qt.qt(Obj)
   asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.  
   description:
     @code{objtoquote()} $B$,$9$G$K<B8=$E$_(B.  $B<BAu$7$F$J$$(B.

end:

begin: qt.cancel_number(Q)
   Quote {Q} $B$NCf$GM-M}?t$,$"$l$PDLJ,$9$k(B.
 example:
   [1320] qt.cancel_number(quote(2/4));
   quote(1/2)
 changelog:
   @itemize @bullet
   @item 2005.05.04, the initial version. Taylor $BE83+$N78?t$N4JLs$N$?$a$K:n@=(B.
   @end itemize
 ref: qt.is_rational
end:

begin: qt.add_paren(Q)
  +- $B$,$"$l$P(B ( ) $B$r2C$($k(B. $B$^$@(B bug $B$$$j(B.
  description: Taylor $BE83+$r7W;;$9$k$?$a$K:n$C$?(B.
end:

begin: qt.add_paren0(Q)
  $BL5>r7o$K(B {Q} $B$r(B ({Q}) $B$K$9$k(B.
end:

begin: qt.map_arg(F,Q)
 $B4X?t(B F $B$r(B quote $B%G!<%?(B {Q} $B$N(B $B$9$Y$F$N%N!<%I$K:F5"E*$K(B
 apply $B$7$?(B quote $B%G!<%?$rLa$9(B.
 example: qt.map_arg(nn,quote(sin(@pi)+2/3))
           nn(nn(sin(nn(@pi)))+nn(nn(2)/nn(3)))
end:

begin: qt.sin_int(Q)
  {Q} $B$,@0?t$J$i(B quote(0) $B$rLa$9(B.
  {Q} $B$,@0?t$G$J$$$J$i(B quote(sin(Q*@@pi)) $B$rLa$9(B.
description:
  @itemize @bullet
  @item $B=q$-49$(5,B'$N1&JUMQ$N4X?t(B.
  @item tr.simp_sin (sin$B$r4^$`<0$N4JC12=$N%5%s%W%k<BAu(B)$B$d(B
  $BNc$N%W%m%0%i%`$GMxMQ$5$l$F$$$k(B.
  @end itemize
changelog:
  @itemize @bullet
  @item  2005.04.02 $B$N=i4|HG$+$iB8:_$9$k4X?t$J$N$G;EMM$,8E$$(B. list $B$rLa$9(B.
  @item  2005.05.08 quote $B$rLa$9$h$&$K=q$-49$($?(B. $BL>A0$b$h$/$J$$$+$b(B, $B$7$+$7(B
         $B$H$j$"$($:$3$N$^$^(B.
  @end itemize
ref: tr.simp_sin
end:

begin: qt.sin_int2(Q)
ref: qt.sin_int
end:

begin: qt0021|
@c --------------------------------------------------------------------
@section qt, quote $B$rJL$N$b$N$KJQ49$9$k(B.
end:

begin: qt.input_form(Q)
 {Q} $B$rJ8;zNs$KJQ49$9$k(B.
 {Q} $B$,%j%9%H(B, $B%Y%/%H%k(B, $B9TNs$N>l9g$K$O$=$NMWAG$rJ8;zNs$KJQ49$9$k(B.
changelog:
 @itemize @bullet
 @item 2005.05.08, the initial version. 
   qt.hc_etov $B$N7k2LI=<($K(B. quote_input_form $B$O(B Q $B$,%j%9%H$N>l9gITJX(B.
 @end itemize
ref: quote_input_form,
     qt.hc_etov
end:


begin: qt003|
@c --------------------------------------------------------------------
@section qt, quote $B$GJ,;6B?9`<0(B, $BQQ5i?t$r<B8=$9$k$?$a$NJd=u4X?t(B.
end:

begin: qt.gtlex(f,g)
{f} $B$O(B {g} $B$h$j(B quote tree $B$N(B lex order $B$GBg$-$$(B.
description:
  quote tree $B$N(B lex order $B$O<!$N$h$&$K7h$a$k(B.  
  @itemize @bullet
  @item Todo; $B$^$@<BAu$7$F$J$$(B.
@c 4/15 $BLk(B.  $B<BAu$OL@F|9V5A$N=`Hw$N=*N;8e$+(B?
  @item $BITDj85$OITDj85$N=g=x(B.
  @item $BITDj85$h$j(B +, - , *, /, ^ $BEy$N(B node $B$OBg$-$$(B.
        $B$?$H$($P(B x < power(x,2)  (power(x,2) $B$O(B x^2 $B$N0UL#(B)
  @item $B$"$H$O:F5"E*(B. times(x,y) < power(x,y) $B$@$,(B,
        times(x,y) $B$H(B times(p,q) $B$O(B x $B$H(B p $B$NHf3S(B,  $B$3$l$G$-$^$i$J$$$J$i(B,
        y, q $B$NHf3S(B.
  @end itemize

end:

begin: qt.dtoq(F,V)
$BJ,;6I=8=B?9`<0(B {F} $B$r(B quote $B$KJQ49$9$k(B.
{V} $B$OJQ?t%j%9%H(B.
description:
 @itemize @bullet
 @item $BJQ?t%j%9%H$,6u$N$H$-$O(B x_1, x_2, ... $B$rMQ$$$k(B.
 @end itemize
example:
  F=dp_ptod((x-y-z)^3,[x,y]);
  qt.dtoq(F,[]);
  quote(x_1^3+(-3)*x_1^2*x_2+3*x_1*x_2^2+(-1)*x_2^3+(-3*z)*x_1^2
       +6*z*x_1*x_2+(-3*z)*x_2^2+3*z^2*x_1+(-3*z^2)*x_2+(-z^3))
changelog: 
 @itemize @bullet 
 @item 2005/4/21,  the initial version.
 @end itemize
ref: qt.qtod 
end:

begin: qt.qtod(F,V)
quote {F} $B$r(B $BJ,;6I=8=B?9`<0$KJQ49$9$k(B.
{V} $B$OJQ?t%j%9%H(B.
description:
 @itemize @bullet
 @item $BJQ?t%j%9%H$,6u$N$H$-$O(B x_1, x_2, ... $B$rMQ$$$k(B.
 @item $B$^$@<BAu$7$F$J$$(B.
 @end itemize
ref: qt.qtod 
end:


begin: qt.vars(Q)
 {Q} $B$K8=$l$kJQ?t$rLa$9(B.
 description: @code{vars(Obj)} $B$N(B qt $BHG(B.
 example:
  [2306] qt.vars(objtoquote((x-y-1)^4/z+y^q));
  [x,y,z,q]
end:

begin: qt.etov_pair(Q)
 {Q} $B$K(B p^q $B$N7A$N85$rC5$7$F(B [p,q] $B$r%j%9%H$K$7$FLa$9(B.
 description:  
   @itemize  @bullet
   @item $B$3$N4X?t$OLZ9=B$$NCf$N(B p^q $B$N7A$N85$r$9$Y$FC5:w$9$k(B.
   @end itemize 
 example:
[2410] ctrl("print_quote",1);
1
[2411]  qt.etov_pair(quote(3*x^4*y^(-3)));
[[[internal,y],[u_op,(),[u_op,-,[internal,3]]]],[[internal,x],[internal,4]]]
 changelog:
  @itemize @bullet
  @item 2005.05.04, dp_etov $B$K;w$?4X?t$r(B qt $B$G:n$k$?$a$N=`Hw(B.
  @end itemize 
 ref: qt.vars
end:

begin: qt.hm(Q)
 {Q} $B$NF,9`$rLa$9(B.
 example:
    [1314] Q=qt.dtoq(-4/3*<<1,4,5>>,[x,y,z]);
    quote((-4/3)*x*y^4*z^5)
    [1315] qt.hm(Q);
    quote((-4/3))
    [1316] qt.hop(Q);
    *
    [1317] QQ=qt.rest(Q);
    quote(x*y^4*z^5)
    [1318] qt.hm(QQ);
    quote(x)
    [1319] qt.rest(QQ);
    quote(y^4*z^5)
    [1320] qt.hm(qt.rest(QQ));
    quote(y^4)
 ref: qt.rest, qt.hop
end:

begin: qt.rest(Q)
  {Q}$B$,(B a+b+c+... $B$N;~(B b+c+...$B$rLa$9(B. dp_rest $B$N$^$M(B.
  description:
  @itemize @bullet
  @item I_BOP $B$N;~$KBh#20z?t$r(B flatten_quote $B$7$F$+$iLa$9(B.
  @end itemize
  example:
    [1667] load("taka_series.rr")$
    [1668] Q=tkseries.expand1(cos(x),x,0,5);
     quote(1+(-1/2)*x^2+1/24*x^4+oO(x, 6))
    [1769] qt.hm(qt.rest(Q));
      quote((-1/2)*x^2)
    [1770] QQ=qt.rest(Q);
      quote((-1/2)*x^2+1/24*x^4+oO(x, 6))
  changelog:
  @itemize @bullet
  @item 2005.05.04, tkseries.expand $B$N7k2L$KBP$7$F(B,
              $BKh2s(B flatten_quote $B$r$d$i$J$$$H:87k9gE*$K$J$i$J$$$N$O2?8N$+(B?
              BUG $B0BDjE*$KF0:n$9$k$+$I$&$+IT0B(B.
  @item 2005.05.04, $B$$$h$$$h(B $B78?t$H(B exponet $B%Y%/%H%k$N<h$j=P$7$r=q$/=`Hw$,40N;(B.
  @item 2005.05.05, Q=a*b $B$J$i(B qt.rest(Q) = b $B$H$J$k$h$&$KJQ99(B. 
            $B78?t$N<h$j=P$7(B, exponent $B%Y%/%H%k$N<h$j=P$7$K$O$3$l$,JXMx(B.
  @end itemize
  ref: qt.hm, qt.hop, qt.dtoq, dp_hm, dp_rest
end:

begin: qt.hop(Q)
  {Q} $B$NF,@a$,(B binary operator (I_BOP) $B$N;~(B binary operator $B$NL>A0$rLa$9(B.
  changelog:
  @itemize @bullet
  @item 2005.05.05, $B;O$a$F$NHG(B.
  @end itemize
end:

begin: hc_etov(Q,V)
  quote {Q} $B$rJQ?t%j%9%H(B {V} $B$N%b%N%_%"%k$H$_$F(B, hc (leading coefficient)
  $B$H(B exponet $B%Y%/%H%k$r(B quote $B7?$GLa$9(B.
 description:
  Q = hc*p1*p2* ... $B$J$k7A$r2>Dj(B. $B$3$l0J30$N7A$G$OF0:nJ]>Z$J$7(B.
 example:
  [1967] R=qt.hc_etov(quote(-3/2*x*z^3),[x,y,z]);
  [<...quoted...>,[ <...quoted...> 0 <...quoted...> ]]
  [1968] qt.input_form(R);
  [quote(1*(-1)*3/2),[ quote(1) 0 quote(3) ]]
 changelog:
  @itemize @bullet
  @item 2005.05.05, 
    qt.hc_etov(quote(-3/2*x*z^3),[x,y,z]);  $B$G%F%9%H$9$k$b$^$@F0:n$X$s(B. 
  @item if (A[0] == I_MINUS) $B$NItJ,$r$D$1$F2r7h(B. 05 $BLk(B. 
        $B$^$@(B bug $B$,;D$k$+$b$7$l$:(B.
  @item Todo; qtodl (distributed poly in quote $B$r(B list $B7A<0$G(B).
  @item Todo; quote $B$N(B distributed poly $B$NHf3S(B.
  @item Todo; $BB?JQ?t$N%F%$%i!<E83+(B. $B%F%$%i!<E83+$N@Q(B.
  @item Todo; Asir $B%I%j%k$N(B 10 $B9T(B Buchberger $B%"%k%4%j%:%`$N<BAu$r$3$3$G(B
   $BDj5A$7$?(B quote $B4X?t$G=q$/(B.
  @end itemize
end:


begin: tr|

@c --------------------------------------------------------------------
@section tr (term rewriting) $B$N%H%C%W%l%Y%k$N4X?t(B (module tr $B$N4X?t(B)

end:

begin: tr.match0(Qobj,P)
 quote $B%G!<%?(B {Qobj} $B$,(B $B%Q%?!<%s(B {P} $B$KE,9g$9$l$P(B 1 $B$rLa$7(B, $B$=$&$G$J$1$l$P(B 0
 $B$rLa$9(B. 
 example: tr.match0(quote(1+2*3),quote(pn(x)+pn(y)))        
                 x $B$K(B quote(1), y $B$K(B quote(2*3)           
          tr.match0(quote(1+2*3),quote(pn(x)+pn(y,qt.is_integer(y))));
                 qt.is_integer(quote(2*3)) $B$O(B 0 $B$J$N$G(B y $B$K$O%^%C%A$7$J$$(B.
 example:
  [2991]   tr.match0(quote(1),quote(pn(c,qt.is_dependent(c,x))));
  0
  [2992]   tr.match0(quote(x^3+1),quote(pn(c,qt.is_dependent(c,x))));
  1
end:

begin: pn(X)
  pn(x) $B$OG$0U$N(B quote object $B$K%^%C%A$7(B, $BL>A0(B x $B$r$D$1$k(B.
  quote $B$NCf$G;H$&FCJL$J4X?t5-9f(B.
  pn $B$O(B variable PatterN ($BJQ?t%Q%?!<%s(B)$B$NN,(B.
description:
  tr.match0(quote(1+2*3),quote(pn(x)+pn(y)))  $B$O(B 1 $B$rLa$9$,(B,
  tr.match0(quote(1+2*3),quote(pn(x)+pn(y,tr.is_integer(y)))) $B$O(B 0 $B$r$b$I$9(B.
  2*3 $B$O(B integer $B$+$i:n$i$l$?(B fnode $B$G$O$"$k$,(B integer $B$G$O$J$$$N$G(B qt.is_integer
  $B$,(B 0 $B$rLa$9$?$a(B.
end:


begin: tr.apply_rule1(Qobj,P,Act)
 quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B, 
 $B%Q%?!<%s(B {P} $B$KE,9g$9$k$b$N$,$"$k$H$-$O(B {Act} $B$r8F$S=P$7$=$NCM$rLa$9(B.
 $B$D$^$j(B top node $B$,(B {P} $B$KE,9g$9$k$+D4$Y(B, $BE,9g$7$J$$>l9g$O$=$N;R6!$K(B
  tr.apply_rule1 $B$rE,MQ$9$k(B ($B$3$3$,(B tr.match_act $B$H$O0[$J$k(B). 
 $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).

description:
 $B$3$3$G(B qt.sin_int(X) $B$O(B X $B$,(B integer $B$N;~$O(B quote(0) $B$rLa$7(B,
 $B$=$&$G$J$$$H$-$O(B quote(sin(X*@@pi)) $B$rLa$9(B.
 $B?<$5M%@h$G=q$-49$($r$9$k$K$O(B $B4X?t(B qt.sin_int $B$NCf$G$^$?(B 
 tr.apply_rule1 $B$r8F$S=P$;$P$h$$(B.

 example: 
   [2215] tr.apply_rule1(quote(1+sin(2*@pi)),quote(sin(pn(x)*@pi)),
            ["qt.sin_int",x]);

    quote(1+0)
end:


begin: tr.apply_or_rules(Qobj,Rules)
 quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B, 
 $B%k!<%k(B {Rules} $B$KE,9g$9$k$b$N$,$"$k$H$-$O%k!<%k$K5-=R$5$l$?(B action $B$r(B
 $B8F$S=P$9(B. {Rules} $B$K$OJ#?t$N%k!<%k$r=q$/$3$H$,0l$D$G$bE,MQ2DG=$J%k!<%k$,(B
 $B$"$l$P:F5"E*$K8F$S=P$5$l$k(B.

end:

begin: hoge4|
@section tr $BFbIt4X?t(B
end:

begin: tr.apply_function0(Qobj,BindingTable)
end:

begin: tr.rp(Qobj,P,A)
end:

begin: tr.make_binding(Qobj,P)
end:

begin: hoge41|
@section tr $B4JC12=4X?t$N%5%s%W%k<BAu(B

@itemize @bullet
@item 2005.05.08 $B4JC12=4X?t$OCm0U?<$/<BAu$7$J$$$H(B, $BL58B%k!<%W$K$*$A$$$C$?$j(B,
$B4JC12=$N$d$j$N$3$7$,$G$?$j$9$k(B.
$B$H$j$"$($:$^$H$a$F$*$/$,(B, $B$3$l$i$N<BAu$O$^$@$^$@$G$"$k(B.
@end itemize

end:

begin: tr.simp_zero(Q)
 $B<0(B {Q} $B$NCf$+$i(B 0 $B$d(B 1 $B$r$1$9(B. $B$?$H$($P(B 1*x $B$O(B x $B$X(B. 0*1 $B$O(B 0 $B$X(B.
 x+0 $B$O(B 0 $B$X(B. 
changelog:
 @itemize @bullet
 @item 2005.04 $B$N$*$o$j$K(B initial version? tkseries.expand1 $BMQ(B.
 @end itemize
end:

begin: tr.simp_unary(Q)
 "-"$B$r>C$9$h$&$K$9$k(B. $B$?$H$($P(B +-x $B$O(B -x $B$X(B. -(-x) $B$O(B x $B$X(B.
changelog:
 @itemize @bullet
 @item 2005.04 $B$N$*$o$j$K(B initial version? tkseries.expand1 $BMQ(B.
 @end itemize
end:

begin: tr.simp_sin(Q)
  $B<0(B {Q} $B$NCf$N(B sin($B@0?t(B @@pi) $B$r(B 0 $B$K$9$k(B.
example:
 [2217] tr.simp_sin(quote(sin(2*@pi)+sin(@pi/2)));    
 quote(sin(@pi()/2))
changelog:
 @itemize @bullet
 @item 2005.04 $B$N$*$o$j$K(B initial version? tkseries.expand1 $BMQ(B.
 @item 2005.05.08 tr.simp_sin(quote(sin(2*sin((1/2)*@@pi)))); $B$OL58B%k!<%W(B bug.
      $B$^$@D>$7$F$J$$(B.
 @end itemize
end:

begin: zzz00|

@section $BNcBj(B

end:

begin: zzz01|
$BNcBj(B  sin($B@0?t(B*@@pi) $B$r(B 0 $B$K(B.
example:
   /* $B=`Hw(B */
   extern P,A;
   P=quote(sin(pn(x)*@pi));  /* $B%Q%?!<%s(B */
   A=["sin_int",x];          /* action, action $B4X?t(B */ 
   def sin_int(X) {
     X = tr.apply_rule1(X,P,A); /* $B;R6!$K(B [P,A] $B$r:F5"E*$KE,MQ(B */  
     if (qt.is_integer(X)) return qt.zero();
     else qt.replace(quote(sin(y*@pi)),[[y,X]]);  
       /* sin(x*@pi) $B$r$=$N$^$^La$9(B.*/ 
   }

   /* $B7W;;(B */
   Qobj=quote(1+sin(sin(2*@pi)*@pi)*sin((1/2)*@pi));
   tr.apply_rule1(Qobj,P,A);
example_description:
  $B%U%!%$%k$K%;!<%V$7$F<B9T$N$3$H(B.  @code{Debug=1;} $B$H$9$k$HJQ7A$NMM;R$,$o$+$k(B.
end:
   
@c ------------------------------------------------------
@section $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.

begin: zzz02|
$BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
example:
    nn(sin(cos(@pi)+sqrt(2))) 
    --> nn(sin(nn(cos(nn(@pi)))+nn(sqrt(nn(2)))))
   Prog; test1-tr.rr $B$N(B test4().

  qt.map_arg $B4X?t$rMQ$$$k(B.
  def test4() {
    Rule=[quote(nn(pn(f))),["qt.map_arg",nn,f]];
    /* nn $B$G0O$^$l$?$b$N$,$"$l$P(B, nn $B$r$=$NFbIt$K:F5"E*$K(B apply $B$9$k(B */
    R0 = quote(nn(sin(1/2)*cos(1/3)));
    print(print_input_form(R0));
    R=tr.apply_rule1(R0,Rule[0],Rule[1]);
    return R;
  }

end:

@c ---------------------------------------------------------
@section $BNcBj(B  $BITDj@QJ,(B

begin: zzz03|
$BNcBj(B  $BITDj@QJ,(B
example:
   /* integral(f+g) => integral(f)+integral(g) */
   S1=[quote(integral(pn(f)+pn(g))),
       [int_linear1,f,g]];
   def int_linear1(X,Y) {
      return qt.replace(quote(integral(f)+integral(g)),[[f,X],[g,Y]]);
   }

   /* integral(c*f) => c*integral(f) */
   def is_independent(F,X) { return !qt.is_dependent(F,X); }
   S2=[quote(integral(pn(c,is_independent(c,x))*f)),
       [int_linear2,c,f]];
   def int_linear2(X,Y) {
      return qt.replace(quote(c*integral(f)),[[c,X],[f,Y]]);
   }

   tr.apply_or_rules(quote(integral(a*x^2+x+2/x)),[S1,S2]);
   $B$3$l$r$3$l0J>e=q$-49$($,5/$-$J$$$^$G7+$jJV$9(B.
   $B$3$N%k!<%k$N>l9gEz$($O(B
   a*integral(x^2)+integral(x)+integral(2/x);   

   quote(integral(x^pn(n))) --> x^(n+1)/(n+1) or log(x) $B$r=q$/(B.
example:
 tr.match0(quote(c*x),quote(pn(c,is_independent(c,x))*f));
example_description:
 2005.05.08, Todo; Bug. $B$3$NNc$,@5$7$/F0$$$F$/$l$J$$(B.

end:

@c ---------------------------------------------------------
@section $BNcBj(B  $B4JC1$J9=J82r@O(B

begin: zzz04|sortKey: zzz04
description:
---------------------  5/8 $B$3$3$^$G=$@5(B. ----------------------

$BNcBj(B  $B4JC1$J9=J82r@O(B

example:
   todo; $B$3$NNc$O$^$@%A%'%C%/$7$F$J$$(B.
   $B<0(B(expression) $B$O(B $B<0(B+$B<0(B | $B<0(B*$B<0(B | ($B<0(B) | $B@0?t(B

   extern R1,R2,R3,R4,S1,S2,S3,S4;
   /* $BJ8K!$rK~$?$9$+$I$&$+$N(B check $BMQ(B. Action $BIt$O(B 1 $B$+(B 0 */
   R1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), 1];
   R2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), 1];
   R3=[quote((pn(x,is_expression(x)))), 1];
   R4=[quote(pn(x,qt.is_integer(x))), 1];
   def is_expression(Qobj) {
     R = [R1,R2,R3,R4];
     A = apply_or_match0(Qobj,R);
     if (A == 0) return 0; else return 1;
   }

   /* $B7W;;MQ(B. R1,R2,R3,R4 $B$H:8$O6&DL(B. */
   S1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), [myadd,x,y]];
   S2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), [mymul,x,y]];
   S3=[quote((pn(x,is_expression(x)))), ["qt.id",x]];
   S4=[quote(pn(x,qt.is_integer(x))), ["qt.id",x]]; 

   def eval_expression(Qobj) {
     S = [S1,S2,S3,S4];
     return apply_or_rules(Qobj,S);
   }

   def myadd(X,Y) {
     return qt.qt(qt.eval(X,1)+qt.eval(Y,1));
   }

   def mymul(X,Y) {
     return qt.qt(qt.eval(X,1)*qt.eval(Y,1));
   }

   /* $B7W;;(B */
   tr.eval_expression(quote(1+2*(3+15)));
end:

begin: misc|

@section $B9M$(J}$K$D$$$F$N35@b(B

 $B%H%C%W%l%Y%k$N4X?tC#(B.  (stylesheet $B$N9M$($K;w$F$k(B.)

  iterator $B$N0l<o(B.

  yacc $B$K;w$F$k(B.

@section $B%G%P%C%,!<(B

  $BA*Br$9$Y$-%k!<%k$,Bt;3$"$k$H$-$O(B, $B7Y9p$9$k5!G=(B.

  $BL58B%k!<%W$N(B|$B8!=P(B.

end:

begin: hoge001|
@section Talor $BE83+(B (taka_series.rr $B$N2r@b(B)

end:

begin: tkseries.expand1(Q,X,A,N)
{Q} $B$r(B $BJQ?t(B {X} $B$K4X$7$F(B, {X}={A} $B$N6aK5$G(B {N} $B<!$^$G(B
Taylor $BE83+$9$k(B.

description:
@itemize @bullet
@item qt $B%Q%C%1!<%8$H(B tr $B%Q%C%1!<%8$NNcBj$H$7$F=q$$$F$$$k(B.
@item Bug $B$@$i$1$G$9(B.
@item Todo; $BB?JQ?t$N(B Taylor $BE83+(B.
@end itemize

example:
[1258] load("tr.rr");
1
[1359] load("taka_series.rr");
1
[1373] tkseries.expand1(cos(x),x,0,6);
quote(1+(-1/2)*x^2+1/24*x^4+(-1/720)*x^6+oO(x, 7))
example_description:
 cos $B$NCM$N7W;;$K(B tr.simp_sin $B$rMQ$$$F$$$k(B. 
 Bug; $B$3$N4X?t$OIT40A4$J$N$G(B, $B78?t$N7W;;$O$&$^$/9T$+$J$$>l9g$bB?$$(B.

example:
[1374] tkseries.expand1(quote(f(x)),x,0,3);
quote(f(0)+calc_diff(f(0), 0)/1*x^1
  +calc_diff(calc_diff(f(0), 0), 0)/2*x^2
  +calc_diff(calc_diff(calc_diff(f(0), 0), 0), 0)/6*x^3+oO(x, 4))
example_description:
 Todo; f $B$NHyJ,$K(B 0$B$rBeF~$7$?$b$N$O(B f(0), f_1(0),  f_2(0), ...
  ($B$=$l$>$l(B f(0), f'(0), f''(0), ... $B$N0UL#(B)
 $B$H$7$?J}$,$$$$$@$m$&(B.

changelog:
@itemize @bullet
@item 2005.04 $B$O$8$a$F$NHG(B.
@end itemize

end:

begin: hoge002|

@section $B5-9fHyJ,(B (taka_qtdiff.rr $B$N2r@b(B)

$B$^$@<BAu$7$F$J$$(B.

end:

begin: exp|

@c ------------------------------------------------
@section $B<B83E*4X?t(B

end:


begin: todo|

@section  Todo

@subsection $B%f!<%6Dj5A$NCfCV1i;;;R(B

   tfb $B$N=q$-J}$rF3F~(B.

@subsection $B?t3X$h$j$NNcBj(B

$B?t3XE*$K$*$b$7$m$$NcBj$r$J$k$Y$/Bt;3MQ0U$9$k(B.
$B$3$l$i$NNcBj$KBP$7$F(B tr $B$,;n:nIJ$r:n$k$N$KM-8z$G$"$k$H$$$&$3$H$r$$$&(B.

 $BNc(B; gcd $B7W;;$NB?9`<0(B reduction $B$r(B tr $B$G<B8=(B.

 $BNc(B; $BQQ5i?t$N7W;;$r(B quote $B$G<B8=(B.
        sort $B$d(B expand $B$OAH$_9~$_$G(B.

 $BNc(B; Mathematica $B$N(B Expand[], Toghether[] $BAjEv$N$b$N(B.

 $BNc(B; D $B$N3]$1;;$r(B $B%Q%?!<%s%^%C%A$G<B8=(B.  
    holonomic $B4X?t$r78?t$H$9$kHyJ,:nMQAG4D$G$N7W;;(B.

 $BNc(B; (x^(1/n))^n --> x $BEy(B.

 $BNc(B; $B5-9fHyJ,$HHyJ,4D$G$N7W;;(B.
       y''+xy=0,  y''=y^2+x $BEy(B.  index $BIU$-$NJQ?t@8@.$,I,MW(B. idxtov

 $BNc(B; QE, $BO@M}<0(B.

 $BNc(B; $B30@QBe?t(B. 

 $BNc(B; $B4dGH(B, $B1~MQ?t3X(B, $B?@J]$N%=%j%H%s$NK\$K$"$k$h$&$J(B fermion $BEy$NNc(B.


 $BNc(B;
   Bergman, George M.
   The diamond lemma for ring theory.
   Advances in Math. 29 (1978), no. 2, 178--218.
   $B$K$"$k$h$&$JHs2D49Be?t$NNc(B.

end:

begin: new-functions|

@section   $B$^$@%9%1%C%A$N$_$N4X?t;EMM(B

  qt.ltor, qt.rtol ; $BLZ$N9=B$$NJQ49(B; $BNc(B (x*y)*z --> x*(y*z)

end:

begin: idx|

@subsection Index $B$D$-JQ?t(B

end:

begin: idxtov(X,I)
  idxtov({X},{I}) $B$OJQ?t(B {X}_{I} $B$rLa$9(B.
  {I} $B$O%9%+%i!<$+%j%9%H(B.
 example:
  idxtov(x,i)  $B$O(B x_i $B$rLa$9(B. 
 description:
  idxtov(x,[i,j])  $B$O(B x_i_j $B$r@8@.(B.  x_i_i $B$N(B index (idx) $BB0@-(B $B$r(B [i,j] $B$K(B. 

  @code{util_v()} $B$H$[$\F1$8(B.

  x_i $B$N(B index (idx) $BB0@-(B $B$r(B i $B$K(B. 
  base_name $BB0@-$r(B  x $B$K(B.
  $BITDj85$NB0@-$rMxMQ$9$k$3$H$K$h$j9bB.$K(B index $B$r$H$j$@$;$F(B index $B$D$-JQ?t$N(B
  $BBe$j$,$G$-$k(B.

end:

begin: vtoidx(X)
  vtoidx(x_i) $B$O(B [x,i] $B$rLa$9(B. 
description:
  @code{util_index()} $B$H$[$\F1MM(B.
  
 $BB0@-$N8!:w$J$N$G9bB.(B. idx $BB0@-$,L5$$>l9g$O(B i $B$r@_Dj(B.

  idxtov $B4X?t$O(B $B4X?tL>$K$b;H$($k$h$&$K$9$k(B? --> $BHyJ,4DBP1~(B.

  qt.function($BL>A0(B, $B0z?t(B) --> quote($BL>A0(B($B0z?t(B)) $B$r@8@.(B.  
   index $BIU$-4X?t$OHyJ,4D$N<h07$KI,MW(B.
end:

begin: powerSeries|

@subsection $BQQ5i?t(B, dp $B$N(B pretty print.

  $B6R5i?t$N<h07(B, dp $B$N(B pretty print $B$N$?$a(B.
  qt.qttodp(Qobj | vlist,  order?)  quote $B$+$i(B dp $B$r:n$k(B. 
   exponent $B$,?t$G$J$$$H:n$l$:(B.

  qt.expand, qt.sort, qt.ht, qt.rest, qt.mtov $B$b4pAC4X?t$H$7$FM_$7$$(B.

end:

begin: monomialSimplifier00|

@section $B%b%N%_%"%k$rI8=`7A$X(B (builtin$B$G(B? Monomial $B$N(B simplifier)

changelog;
@quotation
Monomial simplifier $B$rDL$7$F$+$i(B,
$B%Q%?!<%s%^%C%A$r$7$J$$$H>l9g$o$1$,B?$9$.$k(B.
$B$3$l$OI,?\$@$m$&(B.
@end quotation

Example;
@example
  x^1 --> x   
  (x*y)*(z*t) --> x*y*z*t
  x*2*y*4     --> 8*x*y      ($B;XDj$7$?JQ?t0J30$O2D49$H$9$k(B)
  x*x^3       --> x^4
  x*(-y)*z    --> -x*y*z
  ((x))       --> x   $B$3$l$O(B noro_simplify.rr noro_simplify.remove_paren() $B$,BP1~(B
@end example 

end: