Annotation of OpenXM/src/asir-contrib/testing/tr-ja.oxt, Revision 1.8
1.8 ! takayama 1: $Id: tr.oxt,v 1.29 2005/05/04 05:42:12 taka Exp $
! 2: $OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.7 2005/04/21 10:54:50 takayama Exp $
1.1 takayama 3:
4: $BCm0U(B: testing/tr.rr $B$G$O(B quote $B$r(B quotetolist $B$G(B list $B$KJQ49$7$F07$&$?$a(B,
5: $B2<$N;EMM$H$O$3$H$J$j(B, list $B7?$G%G!<%?$rLa$9>l9g$bB?$$(B.
6: $B%f!<%68@8l$G=q$$$F$$$k4X78>e(B pn(x) $B$r(B pn("x") $B$H$7$F$$$k(B.
7: $BB>$K$bF1MM$J4X?t$,$"$j(B.
8:
1.5 takayama 9: $B$3$N%U%!%$%k$+$i(B texi $B%U%!%$%k$r:n@.$9$k$K$O0J2<$N$h$&$KF~NO$7$F2<$5$$(B.
10: oxgentexi $B$O(B OpenXM/src/util $B$N2<$K$"$j$^$9(B.
11:
12: nkf -e tr.oxt | oxgentexi --noSorting --title 'Term rewriting functions for Risa/Asir' --author 'Nobuki Takayama' >t.texi
13:
14: begin: AAA01|
15:
16: @c ---------------------------------------------------------
17: @section $BJQ?t%Q%?!<%s$H4X?t%Q%?!<%s(B
18:
19:
20: $BJQ?t%Q%?!<%s(B
21:
22: pn(x) $BG$0U$N$b$N$K%^%C%A(B. $B%^%C%A$7$?$b$N$r(B x $B$K(B bind.
23: pn(x,qt_is_integer(x))
24:
25: Todo; fn $B$OB?J,$$$i$J$$(B. qt_is_function(x) $B$G(B OK.
26: fn(f) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
27: fn(f,pn(x),pn(y)) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
28: f $B$N0z?t$r(B x, y $B$K(B bind
29:
30:
31: $B%Q%?!<%s$O(B quote $B$GM?$($k(B.
1.8 ! takayama 32: $BM=Ls8l(B tr.and, tr.or, tr.not $B$O%Q%?!<%s$N%^%C%A$K4X$7$FO@M}1i;;$r$*$3$J$&(B.
1.5 takayama 33: $B$?$H$($P(B
1.8 ! takayama 34: quote(tr.and(pn(x,"qt.is_integer"),pn(x,"qt.is_non_negative",x)))
1.5 takayama 35: $B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.
36:
37: end:
38:
1.8 ! takayama 39: begin: AAA011|
! 40:
! 41: @c ---------------------------------------------------------
! 42: @section $B<BAu$N$?$a$NJd=u4X?t(B
! 43:
! 44: @itemize @bullet
! 45: @item @code{quotetolist}, @code{listtoquote}, @code{listtoquote_str}
! 46: quote $B$H(B list $B$N4V$NJQ49(B.
! 47: @item @code{quote_to_funargs}, @code{funargs_to_quote}, @code{get_function_name}
! 48: quote $B$H(B funarg $B7A<0$NJQ49(B. $B<B83E*4X?t$N%^%K%e%"%k$r;2>H(B.
! 49: @item @code{quotetoobj}, @code{eval_quote}
! 50: quote $B$H(B object $B$N4V$NJQ49(B.
! 51: @item @code{quote_input_form}, @code{ctrl("print_quote",1)},
! 52: quote $B$HJ8;zNs$N4V$NJQ49(B.
! 53: @item @code{quote_flatten}
! 54: $B<B83E*4X?t$N%^%K%e%"%k$r;2>H(B.
! 55: @end itemize
! 56:
! 57: end:
! 58:
1.5 takayama 59: begin: AAA02|
1.4 takayama 60:
1.8 ! takayama 61: @section quote $B$KBP$9$k4pK\4X?t(B (module qt $B$N4X?t(B)
1.1 takayama 62:
1.5 takayama 63: end:
64:
65:
1.8 ! takayama 66: begin: qt.node(Q)
1.1 takayama 67: quote $B%G!<%?(B {Q} $B$N(B node $B$r<h$j=P$9(B.
1.8 ! takayama 68: example: qt.node(quote(1+2*3))
! 69: ["b_op","+"] ($B8=:_$N<BAu$G$O$3$l$,La$k(B)
1.4 takayama 70: end:
1.1 takayama 71:
72:
1.8 ! takayama 73: begin: qt.nchild(Q)
1.1 takayama 74: quote $B%G!<%?(B {Q} $B$N(B $B;R6!$N?t$rLa$9(B.
1.8 ! takayama 75: example: qt.nchild(quote(1+2*3)) 2 $B$rLa$9(B.
1.4 takayama 76: end:
1.1 takayama 77:
78:
1.8 ! takayama 79: begin: qt.child(Q,K)
1.1 takayama 80: quote $B%G!<%?(B {Q} $B$N(B {K} $BHVL\$N;R6!$rLa$9(B.
1.8 ! takayama 81: example: qt.child(quote(1+2*3),1) quote(2*3) $B$rLa$9(B.
! 82: example: qt.child(quote(1+2*3),0) quote(1) $B$rLa$9(B.
1.4 takayama 83: end:
1.1 takayama 84:
1.8 ! takayama 85: begin: hoge|
1.1 takayama 86: @c --------------------------------------------------------------------
1.8 ! takayama 87: @section quote $B$KBP$9$k=R8l(B
! 88: end:
1.1 takayama 89:
1.8 ! takayama 90: begin: qt.is_integer(Q)
1.1 takayama 91: quote $B%G!<%?(B {Q} $B$,@0?t$J$i(B 1
1.8 ! takayama 92: example: qt.is_integer(quote(0))
1.4 takayama 93: end:
1.1 takayama 94:
1.8 ! takayama 95: begin: qt.is_dependent(Q,x)
1.1 takayama 96: quote $B%G!<%?(B {Q} $B$,ITDj85(B {x} $B$r4^$`$H(B 1, $B4^$^$J$$$H(B 0.
1.8 ! takayama 97: example: qt.is_dependent(quote(1+1/x),x)
1.4 takayama 98: end:
99:
1.8 ! takayama 100: begin: qt.is_function(Q)
1.4 takayama 101: quote $B%G!<%?(B {Q} $B$,4X?t$N$H$-(B 1, $B$=$&$G$J$$$H$-(B 0.
1.8 ! takayama 102: example: qt.is_function(f(x,y));
1.4 takayama 103: end:
1.1 takayama 104:
1.8 ! takayama 105: begin: qt.is_minus(Q)
! 106: quote $B%G!<%?(B {Q} $B$,7A<0E*$K(B -1 $B$h$j;O$^$k$H$-(B 1.
! 107: example: qt.is_minus(quote(-1/x));
! 108: ref: qt.add_paren, qt.add_paren0
! 109: end:
! 110:
! 111: begin: qt.is_rational(Q)
! 112: quote $B%G!<%?(B {Q} $B$,7A<0E*$KM-M}?t$N;~(B 1.
! 113: example: qt.is_rational(quote(1/2));
! 114: ref: qt.cancel_number
! 115: end:
! 116:
! 117: begin: hoge2|
1.1 takayama 118: @c --------------------------------------------------------------------
1.8 ! takayama 119: @section quote $B$KBP$9$k%3%s%9%H%i%/%?(B
! 120: end:
1.1 takayama 121:
1.8 ! takayama 122: begin: qt.zero()
1.1 takayama 123: quote 0 $B$rLa$9(B.
1.4 takayama 124: end:
1.1 takayama 125:
1.8 ! takayama 126: begin: qt.id(Qobj)
1.1 takayama 127: quote object {Qobj} $B$r$=$N$^$^La$9(B.
1.4 takayama 128: end:
1.1 takayama 129:
1.8 ! takayama 130: begin: qt.replace(Qobj,[[x,Valuex],[y,Valuey],...])
1.1 takayama 131: quote object {Qobj} $B$NCf$N(B x $B$r(B Valuex, y $B$r(B Valuey, ... $B$KCV$-49$($?(B
132: quote object $B$rLa$9(B.
1.5 takayama 133: description:
134: $B2]Bj(B; x, y $B$OBgJ8;z$b5v$9$+(B? @var{Qobj} $B$b85!94^$^$l$F$$$kBgJ8;z$rI>2A$7$FCV$-49$($k(B
135: $B4X?t$bI,MW$+(B?
136:
1.8 ! takayama 137: example: qt.replace(quote(sin(x*@pi)), [[x,quote( (2*t+3) )]])
1.4 takayama 138: end:
1.1 takayama 139:
1.8 ! takayama 140: qt.replace $B$O(B asir-contrib $B$N(B base_replace $B$H;w$?5!G=(B.
1.3 takayama 141: quote $B$NFbIt$KBgJ8;z$G$O$8$^$kJQ?t(B($BI>2A$9$k(B)$B$,=q$1$J$$$?$a(B.
142:
1.8 ! takayama 143: begin: qt.parenthesis(Qobj)
1.1 takayama 144: quote object {Qobj} $B$NCf$N3g8L$,B-$j$J$$$H$-$K$OJd$$(B, $BB?$$$H$-$K$O<h$j5n$C$?(B
145: quote object $B$r:n$k(B.
1.3 takayama 146: +, *, /, ^, - $BEy$K$D$$$F(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
1.5 takayama 147: description:
1.8 ! takayama 148: $B;29M(B;
! 149: @itemize
! 150: @item $B$^$@=q$$$F$J$$(B.
! 151: @item noro_simplify.rr $B$N(B @code{noro_simplify.remove_paren()}
! 152: $B$,$9$G$K<B8=$E$_(B?
! 153: ($B2C$($kJ}$O$@$a$_$?$$(B)
! 154: @code{flatten()} $B$d(B @code{quote_to_funargs()} $B$rMxMQ$7$F$kLOMM(B.
! 155: @item $B<B83E*4X?t%^%K%e%"%k$N(B @code{quote_flatten} $B$b;2>H(B ($B$3$N4X?t$J$$(B).
! 156: @end itemize
1.5 takayama 157:
1.4 takayama 158: end:
1.1 takayama 159:
1.8 ! takayama 160: begin: qt.eval(Qobj,type)
1.2 takayama 161: Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
1.5 takayama 162: description:
163: @code{eval_quote()} $B$,$9$G$K<B8=$E$_(B.
1.8 ! takayama 164: $B<BAu$7$F$J$$(B.
1.5 takayama 165:
1.4 takayama 166: end:
1.2 takayama 167:
1.8 ! takayama 168: begin: qt.qt(Obj)
1.2 takayama 169: asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.
1.5 takayama 170: description:
1.8 ! takayama 171: @code{objtoquote()} $B$,$9$G$K<B8=$E$_(B. $B<BAu$7$F$J$$(B.
! 172:
! 173: end:
! 174:
! 175: begin: qt.cancel_number(Q)
! 176: Quote {Q} $B$NCf$GM-M}?t$,$"$l$PDLJ,$9$k(B.
! 177: ref: qt.is_rational
! 178: end:
! 179:
! 180: begin: qt.add_paren(Q)
! 181: +- $B$,$"$l$P(B ( ) $B$r2C$($k(B. $B$^$@(B bug $B$$$j(B.
! 182: description: Taylor $BE83+$r7W;;$9$k$?$a$K:n$C$?(B.
! 183: end:
1.5 takayama 184:
1.8 ! takayama 185: begin: qt.add_paren0(Q)
! 186: $BL5>r7o$K(B {Q} $B$r(B ( ) $B$9$k(B.
1.4 takayama 187: end:
1.2 takayama 188:
1.1 takayama 189:
1.8 ! takayama 190: begin: qt003|
! 191: @c --------------------------------------------------------------------
! 192: @section tr $B$=$NB>(B
! 193: end:
! 194:
! 195: begin: qt.vars(Q)
! 196: {Q} $B$K8=$l$kJQ?t$rLa$9(B.
! 197: description: @code{vars(Obj)} $B$N(B qt $BHG(B.
! 198: example:
! 199: [2306] qt.vars(objtoquote((x-y-1)^4/z+y^q));
! 200: [x,y,z,q]
! 201: end:
! 202:
! 203: begin: qt.etov_pair(Q)
! 204: {Q} $B$K(B p^q $B$N7A$N85$rC5$7$F(B [p,q] $B$r%j%9%H$K$7$FLa$9(B.
! 205: description:
! 206: @itemize @bullet
! 207: @item @code{dp_etov} $B$NN`;w$r:n$k$?$a$N=`Hw(B(2005/05/04).
! 208: @end itemize
! 209: example:
! 210: [2410] ctrl("print_quote",1);
! 211: 1
! 212: [2411] qt.etov_pair(quote(3*x^4*y^(-3)));
! 213: [[[internal,y],[u_op,(),[u_op,-,[internal,3]]]],[[internal,x],[internal,4]]]
! 214: end:
! 215:
1.5 takayama 216: begin: tr|
217:
1.1 takayama 218: @c --------------------------------------------------------------------
1.8 ! takayama 219: @section tr (term rewriting) $B$N%H%C%W%l%Y%k$N4X?t(B (module tr $B$N4X?t(B)
1.1 takayama 220:
1.5 takayama 221: end:
222:
1.8 ! takayama 223: begin: tr.match0(Qobj,P)
1.1 takayama 224: quote $B%G!<%?(B {Qobj} $B$,(B $B%Q%?!<%s(B {P} $B$KE,9g$9$l$P(B 1 $B$rLa$7(B, $B$=$&$G$J$1$l$P(B 0
225: $B$rLa$9(B.
1.8 ! takayama 226: example: tr.match0(quote(1+2*3),quote(pn(x)+pn(y)))
1.3 takayama 227: x $B$K(B quote(1), y $B$K(B quote(2*3)
1.8 ! takayama 228: tr.match0(quote(1+2*3),quote(pn(x)+pn(y,"qt.is_integer",y)))
! 229: qt.is_integer(2*3) $B$O(B 0 $B$J$N$G(B y $B$K$O%^%C%A$7$J$$(B.
1.4 takayama 230: end:
1.1 takayama 231:
1.4 takayama 232: begin: pn(X)
233: 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.
234: description:
1.8 ! takayama 235: tr.match0(quote(1+2*3),quote(pn(x)+pn(y))) $B$O(B 1 $B$rLa$9$,(B,
! 236: tr.match0(quote(1+2*3),quote(pn(x)+pn(y,tr.is_integer,x))) $B$O(B 0 $B$r$b$I$9(B.
! 237: 2*3 $B$O(B integer $B$+$i:n$i$l$?(B fnode $B$G$O$"$k$,(B integer $B$G$O$J$$$N$G(B qt.is_integer
1.4 takayama 238: $B$,(B 0 $B$rLa$9$?$a(B.
239: end:
1.1 takayama 240:
1.8 ! takayama 241: begin: tr.match0_act(Qobj,P,Act)
1.1 takayama 242: quote $B%G!<%?(B {Qobj} $B$,(B $B%Q%?!<%s(B {P} $B$KE,9g$9$l$P(B {Act} $B$r8F$S=P$7$=$NCM$rLa$9(B.
243: $B%Q%?!<%s(B {P} $B$K%^%C%A$7$J$$$H$-$O(B 0.
244:
1.8 ! takayama 245: example: tr.match0_act(quote(1+2*3),quote(pn(x)+pn(y)),[myadd,x,y])
1.4 takayama 246: end:
1.1 takayama 247:
1.8 ! takayama 248: begin: tr.or_match0_act(Qobj,Rules)
1.4 takayama 249: end:
1.1 takayama 250:
1.8 ! takayama 251: begin: tr.apply_rule1(Qobj,P,Act)
1.1 takayama 252: quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B,
253: $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.
254: $B$D$^$j(B top node $B$,(B {P} $B$KE,9g$9$k$+D4$Y(B, $BE,9g$7$J$$>l9g$O$=$N;R6!$K(B
1.8 ! takayama 255: tr.apply_rule1 $B$rE,MQ$9$k(B ($B$3$3$,(B tr.match_act $B$H$O0[$J$k(B).
1.1 takayama 256: $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).
257:
1.4 takayama 258: description:
1.3 takayama 259: $B$3$3$G(B sin_int(X) $B$O(B X $B$,(B integer $B$N;~$O(B quote(0) $B$rLa$7(B,
1.5 takayama 260: $B$=$&$G$J$$$H$-$O(B quote(sin(X*@@pi)) $B$rLa$9(B.
1.8 ! takayama 261: $B?<$5M%@h$G=q$-49$($r$9$k$K$O(B $B4X?t(B sin_int $B$NCf$G$^$?(B tr.apply_rule1 $B$r8F$S=P$;$P(B
1.1 takayama 262: $B$h$$(B.
263:
1.8 ! takayama 264: example: tr.apply_rule1(quote(1+sin(2*@pi)),quote(sin(pn(x)*@pi)),[sin_int,x])
1.4 takayama 265: end:
266:
267:
1.8 ! takayama 268: begin: tr.apply_or_rules(Qobj,Rules)
! 269: quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B,
! 270: $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
! 271: $B8F$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
! 272: $B$"$l$P:F5"E*$K8F$S=P$5$l$k(B.
! 273:
1.4 takayama 274: end:
1.1 takayama 275:
1.8 ! takayama 276: begin: hoge4|
! 277: @section tr $BFbIt4X?t(B
! 278: end:
1.2 takayama 279:
1.8 ! takayama 280: begin: tr.apply_function0(Qobj,BindingTable)
1.4 takayama 281: end:
1.2 takayama 282:
1.8 ! takayama 283: begin: tr.rp(Qobj,P,A)
1.4 takayama 284: end:
1.2 takayama 285:
1.8 ! takayama 286: begin: tr.make_binding(Qobj,P)
1.4 takayama 287: end:
1.2 takayama 288:
1.1 takayama 289:
1.5 takayama 290: begin: zzz00|
1.4 takayama 291:
1.5 takayama 292: @section $BNcBj(B
1.1 takayama 293:
1.4 takayama 294: end:
1.1 takayama 295:
1.5 takayama 296: begin: zzz01|
297: $BNcBj(B sin($B@0?t(B*@@pi) $B$r(B 0 $B$K(B.
1.4 takayama 298: example:
1.2 takayama 299: /* $B=`Hw(B */
300: extern P,A;
301: P=quote(sin(pn(x)*@pi)); /* $B%Q%?!<%s(B */
302: A=[sin_int,x] /* action, action $B4X?t(B */
303: def sin_int(X) {
1.8 ! takayama 304: X = tr.apply_rule1(X,P,A); /* $B;R6!$K(B [P,A] $B$r:F5"E*$KE,MQ(B */
! 305: if (qt.is_integer(X)) return qt.zero();
! 306: else qt.replace(sin(y*@pi),[[y,X]]); /* sin(x*@pi) $B$r$=$N$^$^La$9(B.*/
1.2 takayama 307: }
308:
309: /* $B7W;;(B */
310: Qobj=quote(1+sin(sin(2*@pi)*@pi)*sin((1/2)*@pi));
1.8 ! takayama 311: tr.apply_rule1(Qobj,P,A);
1.4 takayama 312: end:
1.2 takayama 313:
1.4 takayama 314: @c ------------------------------------------------------
315: @section $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
316:
1.5 takayama 317: begin: zzz02|
1.4 takayama 318: $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
319: example:
320: nn(sin(cos(@pi)+sqrt(2)))
321: --> nn(sin(nn(cos(nn(@pi)))+nn(sqrt(nn(2)))))
322: Prog; test1-tr.rr $B$N(B test4().
323:
1.8 ! takayama 324: qt.map_arg $B4X?t$rMQ$$$k(B.
1.4 takayama 325: def test4() {
1.8 ! takayama 326: Rule=[quote(nn(pn(f))),["qt.map_arg",nn,f]];
1.4 takayama 327: /* nn $B$G0O$^$l$?$b$N$,$"$l$P(B, nn $B$r$=$NFbIt$K:F5"E*$K(B apply $B$9$k(B */
328: R0 = quote(nn(sin(1/2)*cos(1/3)));
329: print(print_input_form(R0));
1.8 ! takayama 330: R=tr.apply_rule1(R0,Rule[0],Rule[1]);
1.4 takayama 331: return R;
332: }
333:
334: end:
1.1 takayama 335:
336: @c ---------------------------------------------------------
337: @section $BNcBj(B $BITDj@QJ,(B
338:
1.5 takayama 339: begin: zzz03|
1.4 takayama 340: $BNcBj(B $BITDj@QJ,(B
341: example:
1.2 takayama 342: /* integral(f+g) => integral(f)+integral(g) */
343: S1=[quote(integral(pn(f)+pn(g))),
344: [int_linear1,f,g]];
345: def int_linear1(X,Y) {
1.8 ! takayama 346: return qt.replace(quote(integral(f)+integral(g)),[[f,X],[g,Y]]);
1.2 takayama 347: }
348:
349: /* integral(c*f) => c*integral(f) */
1.8 ! takayama 350: def qt.independent(F,X) { return !qt.dependent(F,X); }
! 351: S2=[quote(integral(pn(c,"qt.independent",c,x))*f)),
1.2 takayama 352: [int_linear2,c,f]];
353: def int_linear2(X,Y) {
1.8 ! takayama 354: return qt.replace(quote(c*integral(f)),[[c,X],[f,Y]]);
1.2 takayama 355: }
356:
357: apply_or_rules(quote(integral(a*x^2+x+2/x)),[S1,S2]);
358: $B$3$l$r$3$l0J>e=q$-49$($,5/$-$J$$$^$G7+$jJV$9(B.
359: $B$3$N%k!<%k$N>l9gEz$($O(B
360: a*integral(x^2)+integral(x)+integral(2/x);
361:
362: quote(integral(x^pn(n))) --> x^(n+1)/(n+1) or log(x) $B$r=q$/(B.
1.4 takayama 363: end:
1.2 takayama 364:
1.1 takayama 365: @c ---------------------------------------------------------
366: @section $BNcBj(B $B4JC1$J9=J82r@O(B
367:
1.5 takayama 368: begin: zzz04|sortKey: zzz04
369: description:
370:
1.4 takayama 371: $BNcBj(B $B4JC1$J9=J82r@O(B
1.5 takayama 372:
1.4 takayama 373: example:
1.2 takayama 374: $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
375:
376: extern R1,R2,R3,R4,S1,S2,S3,S4;
377: /* $BJ8K!$rK~$?$9$+$I$&$+$N(B check $BMQ(B. Action $BIt$O(B 1 $B$+(B 0 */
378: R1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), 1];
379: R2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), 1];
380: R3=[quote((pn(x,is_expression(x)))), 1];
1.8 ! takayama 381: R4=[quote(pn(x,qt.is_integer(x))), 1];
1.2 takayama 382: def is_expression(Qobj) {
383: R = [R1,R2,R3,R4];
384: A = apply_or_match0(Qobj,R);
385: if (A == 0) return 0; else return 1;
386: }
387:
388: /* $B7W;;MQ(B. R1,R2,R3,R4 $B$H:8$O6&DL(B. */
389: S1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), [myadd,x,y]];
390: S2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), [mymul,x,y]];
1.8 ! takayama 391: S3=[quote((pn(x,is_expression(x)))), ["qt.id",x]];
! 392: S4=[quote(pn(x,qt.is_integer(x))), ["qt.id",x]];
1.2 takayama 393:
394: def eval_expression(Qobj) {
395: S = [S1,S2,S3,S4];
396: return apply_or_rules(Qobj,S);
397: }
398:
399: def myadd(X,Y) {
1.8 ! takayama 400: return qt.qt(qt.eval(X,1)+qt.eval(Y,1));
1.2 takayama 401: }
402:
403: def mymul(X,Y) {
1.8 ! takayama 404: return qt.qt(qt.eval(X,1)*qt.eval(Y,1));
1.2 takayama 405: }
406:
407: /* $B7W;;(B */
1.8 ! takayama 408: tr.eval_expression(quote(1+2*(3+15)));
1.4 takayama 409: end:
1.1 takayama 410:
1.5 takayama 411: begin: misc|
412:
413: @section $B9M$(J}$K$D$$$F$N35@b(B
414:
415: $B%H%C%W%l%Y%k$N4X?tC#(B. (stylesheet $B$N9M$($K;w$F$k(B.)
416:
417: iterator $B$N0l<o(B.
418:
419: yacc $B$K;w$F$k(B.
420:
421: @section $B%G%P%C%,!<(B
422:
423: $BA*Br$9$Y$-%k!<%k$,Bt;3$"$k$H$-$O(B, $B7Y9p$9$k5!G=(B.
424:
425: $BL58B%k!<%W$N(B|$B8!=P(B.
426:
427: end:
428:
429: begin: exp|
430:
431: @c ------------------------------------------------
432: @section $B<B83E*4X?t(B
433:
434: end:
435:
1.8 ! takayama 436: begin: qt.map_arg(F,Q)
1.5 takayama 437: $B4X?t(B F $B$r(B quote $B%G!<%?(B {Q} $B$N(B $B$9$Y$F$N%N!<%I$K:F5"E*$K(B
438: apply $B$7$?(B quote $B%G!<%?$rLa$9(B.
1.8 ! takayama 439: example: qt.map_arg(nn,quote(sin(@pi)+2/3))
1.5 takayama 440: nn(nn(sin(nn(@pi)))+nn(nn(2)/nn(3)))
441: end:
442:
443: begin: todo|
444:
445: @section Todo
446:
447: @subsection $B%f!<%6Dj5A$NCfCV1i;;;R(B
448:
449: tfb $B$N=q$-J}$rF3F~(B.
1.1 takayama 450:
1.5 takayama 451: @subsection $B?t3X$h$j$NNcBj(B
1.1 takayama 452:
1.5 takayama 453: $B?t3XE*$K$*$b$7$m$$NcBj$r$J$k$Y$/Bt;3MQ0U$9$k(B.
454: $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.
1.1 takayama 455:
1.5 takayama 456: $BNc(B; gcd $B7W;;$NB?9`<0(B reduction $B$r(B tr $B$G<B8=(B.
1.3 takayama 457:
1.4 takayama 458: $BNc(B; $BQQ5i?t$N7W;;$r(B quote $B$G<B8=(B.
1.3 takayama 459: sort $B$d(B expand $B$OAH$_9~$_$G(B.
460:
1.4 takayama 461: $BNc(B; Mathematica $B$N(B Expand[], Toghether[] $BAjEv$N$b$N(B.
1.3 takayama 462:
1.4 takayama 463: $BNc(B; D $B$N3]$1;;$r(B $B%Q%?!<%s%^%C%A$G<B8=(B.
1.5 takayama 464: holonomic $B4X?t$r78?t$H$9$kHyJ,:nMQAG4D$G$N7W;;(B.
1.3 takayama 465:
1.4 takayama 466: $BNc(B; (x^(1/n))^n --> x $BEy(B.
1.3 takayama 467:
1.4 takayama 468: $BNc(B; $B5-9fHyJ,$HHyJ,4D$G$N7W;;(B.
469: y''+xy=0, y''=y^2+x $BEy(B. index $BIU$-$NJQ?t@8@.$,I,MW(B. idxtov
1.3 takayama 470:
1.4 takayama 471: $BNc(B; QE, $BO@M}<0(B.
1.3 takayama 472:
1.5 takayama 473: $BNc(B; $B30@QBe?t(B.
474:
475: $BNc(B; $B4dGH(B, $B1~MQ?t3X(B, $B?@J]$N%=%j%H%s$NK\$K$"$k$h$&$J(B fermion $BEy$NNc(B.
1.3 takayama 476:
477:
1.5 takayama 478: $BNc(B;
479: Bergman, George M.
480: The diamond lemma for ring theory.
481: Advances in Math. 29 (1978), no. 2, 178--218.
482: $B$K$"$k$h$&$JHs2D49Be?t$NNc(B.
1.4 takayama 483:
484: end:
485:
1.5 takayama 486: begin: new-functions|
487:
1.3 takayama 488: @section $B$^$@%9%1%C%A$N$_$N4X?t;EMM(B
489:
1.8 ! takayama 490: qt.ltor, qt.rtol ; $BLZ$N9=B$$NJQ49(B; $BNc(B (x*y)*z --> x*(y*z)
1.5 takayama 491:
1.6 takayama 492: end:
493:
494: begin: idx|
1.5 takayama 495:
496: @subsection Index $B$D$-JQ?t(B
1.3 takayama 497:
1.6 takayama 498: end:
499:
500: begin: idxtov(X,I)
501: idxtov({X},{I}) $B$OJQ?t(B {X}_{I} $B$rLa$9(B.
502: {I} $B$O%9%+%i!<$+%j%9%H(B.
503: example:
504: idxtov(x,i) $B$O(B x_i $B$rLa$9(B.
505: description:
506: idxtov(x,[i,j]) $B$O(B x_i_j $B$r@8@.(B. x_i_i $B$N(B index (idx) $BB0@-(B $B$r(B [i,j] $B$K(B.
507:
508: @code{util_v()} $B$H$[$\F1$8(B.
509:
510: x_i $B$N(B index (idx) $BB0@-(B $B$r(B i $B$K(B.
511: base_name $BB0@-$r(B x $B$K(B.
512: $BITDj85$NB0@-$rMxMQ$9$k$3$H$K$h$j9bB.$K(B index $B$r$H$j$@$;$F(B index $B$D$-JQ?t$N(B
513: $BBe$j$,$G$-$k(B.
514:
515: end:
516:
517: begin: vtoidx(X)
518: vtoidx(x_i) $B$O(B [x,i] $B$rLa$9(B.
519: description:
520: @code{util_index()} $B$H$[$\F1MM(B.
521:
522: $BB0@-$N8!:w$J$N$G9bB.(B. idx $BB0@-$,L5$$>l9g$O(B i $B$r@_Dj(B.
1.3 takayama 523:
1.6 takayama 524: idxtov $B4X?t$O(B $B4X?tL>$K$b;H$($k$h$&$K$9$k(B? --> $BHyJ,4DBP1~(B.
1.3 takayama 525:
1.8 ! takayama 526: qt.function($BL>A0(B, $B0z?t(B) --> quote($BL>A0(B($B0z?t(B)) $B$r@8@.(B.
1.3 takayama 527: index $BIU$-4X?t$OHyJ,4D$N<h07$KI,MW(B.
1.6 takayama 528: end:
529:
530: begin: powerSeries|
1.3 takayama 531:
1.5 takayama 532: @subsection $BQQ5i?t(B, dp $B$N(B pretty print.
533:
1.3 takayama 534: $B6R5i?t$N<h07(B, dp $B$N(B pretty print $B$N$?$a(B.
1.8 ! takayama 535: qt.qttodp(Qobj | vlist, order?) quote $B$+$i(B dp $B$r:n$k(B.
1.3 takayama 536: exponent $B$,?t$G$J$$$H:n$l$:(B.
1.8 ! takayama 537: qt.dptoqt(Qobj | vlist) dp $B$+$i(B quote $B$r:n$k(B. vlist $B$OB0@-$GBP1~(B?
1.1 takayama 538:
1.8 ! takayama 539: qt.expand, qt.sort, qt.ht, qt.rest, qt.mtov $B$b4pAC4X?t$H$7$FM_$7$$(B.
1.5 takayama 540:
541: end:
1.1 takayama 542:
1.6 takayama 543: begin: MonomialSimplifier|
544:
545: @subsection $B%b%N%_%"%k$rI8=`7A$X(B (builtin$B$G(B?)
546:
547: example:
548: x^1 --> x
549: (x*y)*(z*t) --> x*y*z*t
550: x*2*y*4 --> 8*x*y ($B;XDj$7$?JQ?t0J30$O2D49$H$9$k(B)
551: x*x^3 --> x^4
552: x*(-y)*z --> -x*y*z
553: ((x)) --> x $B$3$l$O(B noro_simplify.rr noro_simplify.remove_paren() $B$,BP1~(B
554:
555:
556: end:
557:
558: 4/15 $BLk(B. $B<BAu$OL@F|9V5A$N=`Hw$N=*N;8e$+(B?
559: begin: qt.gtlex(f,g)
560: {f} $B$O(B {g} $B$h$j(B quote tree $B$N(B lex order $B$GBg$-$$(B.
561: description:
562: quote tree $B$N(B lex order $B$O<!$N$h$&$K7h$a$k(B.
563: @itemize
564: @item $BITDj85$OITDj85$N=g=x(B.
565: @item $BITDj85$h$j(B +, - , *, /, ^ $BEy$N(B node $B$OBg$-$$(B.
566: $B$?$H$($P(B x < power(x,2) (power(x,2) $B$O(B x^2 $B$N0UL#(B)
567: @item $B$"$H$O:F5"E*(B. times(x,y) < power(x,y) $B$@$,(B,
568: 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$$$J$i(B,
569: y, q $B$NHf3S(B.
570: @end itemize
571:
1.7 takayama 572: end:
573:
574: begin: qt.dtoq(F,V)
575: $BJ,;6I=8=B?9`<0(B {F} $B$r(B quote $B$KJQ49$9$k(B.
576: {V} $B$OJQ?t%j%9%H(B.
577: description:
1.8 ! takayama 578: @itemize @bullet
! 579: @item $BJQ?t%j%9%H$,6u$N$H$-$O(B x_1, x_2, ... $B$rMQ$$$k(B.
! 580: @item Changelog. 2005/4/21
! 581: @end itemize
1.7 takayama 582: example:
583: F=dp_ptod((x-y-z)^3,[x,y]);
584: qt.dtoq(F,[]);
1.8 ! takayama 585: 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
! 586: +6*z*x_1*x_2+(-3*z)*x_2^2+3*z^2*x_1+(-3*z^2)*x_2+(-z^3))
1.7 takayama 587: ref: qt.qtod
588: end:
589:
590: begin: qt.qtod(F,V)
591: quote {F} $B$r(B $BJ,;6I=8=B?9`<0$KJQ49$9$k(B.
592: {V} $B$OJQ?t%j%9%H(B.
593: description:
594: $BJQ?t%j%9%H$,6u$N$H$-$O(B x_1, x_2, ... $B$rMQ$$$k(B.
595: ref: qt.qtod
596: end:
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