Annotation of OpenXM/src/asir-contrib/testing/tr-ja.oxt, Revision 1.5
1.1 takayama 1: /*&generate-prologue
2: */
1.5 ! takayama 3: $Id: tr.oxt,v 1.17 2005/04/06 08:52:38 taka Exp $
! 4: $OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.4 2005/04/03 11:05:21 takayama Exp $
1.1 takayama 5:
6: $BCm0U(B: testing/tr.rr $B$G$O(B quote $B$r(B quotetolist $B$G(B list $B$KJQ49$7$F07$&$?$a(B,
7: $B2<$N;EMM$H$O$3$H$J$j(B, list $B7?$G%G!<%?$rLa$9>l9g$bB?$$(B.
8: $B%f!<%68@8l$G=q$$$F$$$k4X78>e(B pn(x) $B$r(B pn("x") $B$H$7$F$$$k(B.
9: $BB>$K$bF1MM$J4X?t$,$"$j(B.
10:
1.5 ! takayama 11: $B$3$N%U%!%$%k$+$i(B texi $B%U%!%$%k$r:n@.$9$k$K$O0J2<$N$h$&$KF~NO$7$F2<$5$$(B.
! 12: oxgentexi $B$O(B OpenXM/src/util $B$N2<$K$"$j$^$9(B.
! 13:
! 14: nkf -e tr.oxt | oxgentexi --noSorting --title 'Term rewriting functions for Risa/Asir' --author 'Nobuki Takayama' >t.texi
! 15:
! 16: begin: AAA01|
! 17:
! 18: @c ---------------------------------------------------------
! 19: @section $BJQ?t%Q%?!<%s$H4X?t%Q%?!<%s(B
! 20:
! 21:
! 22: $BJQ?t%Q%?!<%s(B
! 23:
! 24: pn(x) $BG$0U$N$b$N$K%^%C%A(B. $B%^%C%A$7$?$b$N$r(B x $B$K(B bind.
! 25: pn(x,qt_is_integer(x))
! 26:
! 27: Todo; fn $B$OB?J,$$$i$J$$(B. qt_is_function(x) $B$G(B OK.
! 28: fn(f) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
! 29: fn(f,pn(x),pn(y)) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
! 30: f $B$N0z?t$r(B x, y $B$K(B bind
! 31:
! 32:
! 33: $B%Q%?!<%s$O(B quote $B$GM?$($k(B.
! 34: $BM=Ls8l(B tr_and, tr_or, tr_not $B$O%Q%?!<%s$N%^%C%A$K4X$7$FO@M}1i;;$r$*$3$J$&(B.
! 35: $B$?$H$($P(B
! 36: quote(tr_and(pn(x,qt_is_integer),pn(x,qt_is_non_negative(x))))
! 37: $B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.
! 38:
! 39: end:
! 40:
! 41: begin: AAA02|
1.4 takayama 42:
1.1 takayama 43: @section quote $B$KBP$9$k4pK\4X?t(B
44:
1.5 ! takayama 45: end:
! 46:
! 47:
1.4 takayama 48: begin: qt_node(Q)
1.1 takayama 49: quote $B%G!<%?(B {Q} $B$N(B node $B$r<h$j=P$9(B.
50: example: qt_node(quote(1+2*3))
1.4 takayama 51: end:
1.1 takayama 52:
53:
1.4 takayama 54: begin: qt_nchild(Q)
1.1 takayama 55: quote $B%G!<%?(B {Q} $B$N(B $B;R6!$N?t$rLa$9(B.
56: example: qt_nchild(quote(1+2*3)) 2 $B$rLa$9(B.
1.4 takayama 57: end:
1.1 takayama 58:
59:
1.4 takayama 60: begin: qt_child(Q,K)
1.1 takayama 61: quote $B%G!<%?(B {Q} $B$N(B {K} $BHVL\$N;R6!$rLa$9(B.
62: example: qt_child(quote(1+2*3),1) quote(2*3) $B$rLa$9(B.
1.3 takayama 63: example: qt_child(quote(1+2*3),0) quote(1) $B$rLa$9(B.
1.4 takayama 64: end:
1.1 takayama 65:
66: @c --------------------------------------------------------------------
67: @subsection quote $B$KBP$9$k=R8l(B
68:
1.4 takayama 69: begin: qt_is_integer(Q)
1.1 takayama 70: quote $B%G!<%?(B {Q} $B$,@0?t$J$i(B 1
71: example: qt_is_integer(quote(0))
1.4 takayama 72: end:
1.1 takayama 73:
1.4 takayama 74: begin: qt_depend(Q,x)
1.1 takayama 75: quote $B%G!<%?(B {Q} $B$,ITDj85(B {x} $B$r4^$`$H(B 1, $B4^$^$J$$$H(B 0.
76: example: qt_depend(quote(1+1/x),x)
1.4 takayama 77: end:
78:
79: begin: qt_is_function(Q)
80: quote $B%G!<%?(B {Q} $B$,4X?t$N$H$-(B 1, $B$=$&$G$J$$$H$-(B 0.
81: example: qt_is_function(f(x,y));
82: end:
1.1 takayama 83:
84: @c --------------------------------------------------------------------
85: @subsection quote $B$KBP$9$k%3%s%9%H%i%/%?(B
86:
1.4 takayama 87: begin: qt_zero()
1.1 takayama 88: quote 0 $B$rLa$9(B.
1.4 takayama 89: end:
1.1 takayama 90:
1.4 takayama 91: begin: qt_id(Qobj)
1.1 takayama 92: quote object {Qobj} $B$r$=$N$^$^La$9(B.
1.4 takayama 93: end:
1.1 takayama 94:
1.4 takayama 95: begin: qt_replace(Qobj,[[x,Valuex],[y,Valuey],...])
1.1 takayama 96: quote object {Qobj} $B$NCf$N(B x $B$r(B Valuex, y $B$r(B Valuey, ... $B$KCV$-49$($?(B
97: quote object $B$rLa$9(B.
1.5 ! takayama 98: description:
! 99: $B2]Bj(B; x, y $B$OBgJ8;z$b5v$9$+(B? @var{Qobj} $B$b85!94^$^$l$F$$$kBgJ8;z$rI>2A$7$FCV$-49$($k(B
! 100: $B4X?t$bI,MW$+(B?
! 101:
1.3 takayama 102: example: qt_replace(quote(sin(x*@pi)), [[x,quote( (2*t+3) )]])
1.4 takayama 103: end:
1.1 takayama 104:
1.3 takayama 105: qt_replace $B$O(B asir-contrib $B$N(B base_replace $B$H;w$?5!G=(B.
106: quote $B$NFbIt$KBgJ8;z$G$O$8$^$kJQ?t(B($BI>2A$9$k(B)$B$,=q$1$J$$$?$a(B.
107:
1.4 takayama 108: begin: qt_parenthesis(Qobj)
1.1 takayama 109: quote object {Qobj} $B$NCf$N3g8L$,B-$j$J$$$H$-$K$OJd$$(B, $BB?$$$H$-$K$O<h$j5n$C$?(B
110: quote object $B$r:n$k(B.
1.3 takayama 111: +, *, /, ^, - $BEy$K$D$$$F(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
1.5 ! takayama 112: description:
! 113: $B;29M(B;
! 114: noro_simplify.rr $B$N(B @code{remove_paren()} $B$,$9$G$K<B8=$E$_(B?
! 115: @code{flatten()} $B$d(B @code{quote_to_funargs()} $B$rMxMQ$7$F$kLOMM(B.
! 116:
1.4 takayama 117: end:
1.1 takayama 118:
1.4 takayama 119: begin: qt_eval(Qobj,type)
1.2 takayama 120: Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
1.5 ! takayama 121: description:
! 122: @code{eval_quote()} $B$,$9$G$K<B8=$E$_(B.
! 123:
1.4 takayama 124: end:
1.2 takayama 125:
1.4 takayama 126: begin: qt_(Obj)
1.2 takayama 127: asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.
1.5 ! takayama 128: description:
! 129: @code{objtoquote()} $B$,$9$G$K<B8=$E$_(B.
! 130:
1.4 takayama 131: end:
1.2 takayama 132:
1.1 takayama 133:
1.5 ! takayama 134: begin: tr|
! 135:
1.1 takayama 136: @c --------------------------------------------------------------------
137: @section tr (term rewriting) $B$N%H%C%W%l%Y%k$N4X?t(B
138:
1.5 ! takayama 139: end:
! 140:
1.4 takayama 141: begin: tr_match0(Qobj,P)
1.1 takayama 142: 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
143: $B$rLa$9(B.
1.3 takayama 144: example: tr_match0(quote(1+2*3),quote(pn(x)+pn(y)))
145: x $B$K(B quote(1), y $B$K(B quote(2*3)
146: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,qt_is_integer,y)))
147: qt_is_integer(2*3) $B$O(B 0 $B$J$N$G(B y $B$K$O%^%C%A$7$J$$(B.
1.4 takayama 148: end:
1.1 takayama 149:
1.4 takayama 150: begin: pn(X)
151: pn(x) $B$OG$0U$N(B quote object $B$K%^%C%A$7(B, $BL>A0(B x $B$r$D$1$k(B.
152: description:
153: tr_match0(quote(1+2*3),quote(pn(x)+pn(y))) $B$O(B 1 $B$rLa$9$,(B,
154: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,tr_is_integer,x))) $B$O(B 0 $B$r$b$I$9(B.
155: 2*3 $B$O(B integer $B$+$i:n$i$l$?(B fnode $B$G$O$"$k$,(B integer $B$G$O$J$$$N$G(B qt_is_integer
156: $B$,(B 0 $B$rLa$9$?$a(B.
157: end:
1.1 takayama 158:
1.4 takayama 159: begin: tr_match0_act(Qobj,P,Act)
1.1 takayama 160: 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.
161: $B%Q%?!<%s(B {P} $B$K%^%C%A$7$J$$$H$-$O(B 0.
162:
1.4 takayama 163: example: tr_match0_act(quote(1+2*3),quote(pn(x)+pn(y)),[myadd,x,y])
164: end:
1.1 takayama 165:
1.4 takayama 166: begin: tr_or_match0_act(Qobj,Rules)
167: end:
1.1 takayama 168:
1.4 takayama 169: begin: tr_apply_rule1(Qobj,P,Act)
1.1 takayama 170: quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B,
171: $B%Q%?!<%s(B {P} $B$KE,9g$9$k$b$N$,$"$k$H$-$O(B {Act} $B$r8F$S=P$7$=$NCM$rLa$9(B.
172: $B$D$^$j(B top node $B$,(B {P} $B$KE,9g$9$k$+D4$Y(B, $BE,9g$7$J$$>l9g$O$=$N;R6!$K(B
1.3 takayama 173: 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 174: $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).
175:
1.4 takayama 176: description:
1.3 takayama 177: $B$3$3$G(B sin_int(X) $B$O(B X $B$,(B integer $B$N;~$O(B quote(0) $B$rLa$7(B,
1.5 ! takayama 178: $B$=$&$G$J$$$H$-$O(B quote(sin(X*@@pi)) $B$rLa$9(B.
1.1 takayama 179: $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
180: $B$h$$(B.
181:
1.4 takayama 182: example: tr_apply_rule1(quote(1+sin(2*@pi)),quote(sin(pn(x)*@pi)),[sin_int,x])
183: end:
184:
185:
186: begin: tr_apply_or_rules(Qobj,Rules)
187: end:
1.1 takayama 188:
1.2 takayama 189: @subsection $BFbIt4X?t(B
190:
1.4 takayama 191: begin: tr_apply_function0(Qobj,BindingTable)
192: end:
1.2 takayama 193:
1.4 takayama 194: begin: tr_rp(Qobj,P,A)
195: end:
1.2 takayama 196:
1.4 takayama 197: begin: tr_make_binding(Qobj,P)
198: end:
1.2 takayama 199:
1.1 takayama 200:
1.5 ! takayama 201: begin: zzz00|
1.4 takayama 202:
1.5 ! takayama 203: @section $BNcBj(B
1.1 takayama 204:
1.4 takayama 205: end:
1.1 takayama 206:
1.5 ! takayama 207: begin: zzz01|
! 208: $BNcBj(B sin($B@0?t(B*@@pi) $B$r(B 0 $B$K(B.
1.4 takayama 209: example:
1.2 takayama 210: /* $B=`Hw(B */
211: extern P,A;
212: P=quote(sin(pn(x)*@pi)); /* $B%Q%?!<%s(B */
213: A=[sin_int,x] /* action, action $B4X?t(B */
214: def sin_int(X) {
215: X = tr_apply_rule1(X,P,A); /* $B;R6!$K(B [P,A] $B$r:F5"E*$KE,MQ(B */
216: if (qt_is_integer(X)) return qt_zero();
217: else qt_replace(sin(y*@pi),[[y,X]]); /* sin(x*@pi) $B$r$=$N$^$^La$9(B.*/
218: }
219:
220: /* $B7W;;(B */
221: Qobj=quote(1+sin(sin(2*@pi)*@pi)*sin((1/2)*@pi));
222: tr_apply_rule1(Qobj,P,A);
1.4 takayama 223: end:
1.2 takayama 224:
1.4 takayama 225: @c ------------------------------------------------------
226: @section $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
227:
1.5 ! takayama 228: begin: zzz02|
1.4 takayama 229: $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
230: example:
231: nn(sin(cos(@pi)+sqrt(2)))
232: --> nn(sin(nn(cos(nn(@pi)))+nn(sqrt(nn(2)))))
233: Prog; test1-tr.rr $B$N(B test4().
234:
235: qt_map_arg $B4X?t$rMQ$$$k(B.
236: def test4() {
237: Rule=[quote(nn(pn(f))),[qt_map_arg,nn,f]];
238: /* nn $B$G0O$^$l$?$b$N$,$"$l$P(B, nn $B$r$=$NFbIt$K:F5"E*$K(B apply $B$9$k(B */
239: R0 = quote(nn(sin(1/2)*cos(1/3)));
240: print(print_input_form(R0));
241: R=tr_apply_rule1(R0,Rule[0],Rule[1]);
242: return R;
243: }
244:
245: end:
1.1 takayama 246:
247: @c ---------------------------------------------------------
248: @section $BNcBj(B $BITDj@QJ,(B
249:
1.5 ! takayama 250: begin: zzz03|
1.4 takayama 251: $BNcBj(B $BITDj@QJ,(B
252: example:
1.2 takayama 253: /* integral(f+g) => integral(f)+integral(g) */
254: S1=[quote(integral(pn(f)+pn(g))),
255: [int_linear1,f,g]];
256: def int_linear1(X,Y) {
257: return qt_replace(quote(integral(f)+integral(g)),[[f,X],[g,Y]]);
258: }
259:
260: /* integral(c*f) => c*integral(f) */
261: def qt_independent(F,X) { return !qt_dependent(F,X); }
262: S2=[quote(integral(pn(c,qt_independent(c,x))*f)),
263: [int_linear2,c,f]];
264: def int_linear2(X,Y) {
265: return qt_replace(quote(c*integral(f)),[[c,X],[f,Y]]);
266: }
267:
268: apply_or_rules(quote(integral(a*x^2+x+2/x)),[S1,S2]);
269: $B$3$l$r$3$l0J>e=q$-49$($,5/$-$J$$$^$G7+$jJV$9(B.
270: $B$3$N%k!<%k$N>l9gEz$($O(B
271: a*integral(x^2)+integral(x)+integral(2/x);
272:
273: quote(integral(x^pn(n))) --> x^(n+1)/(n+1) or log(x) $B$r=q$/(B.
1.4 takayama 274: end:
1.2 takayama 275:
1.1 takayama 276: @c ---------------------------------------------------------
277: @section $BNcBj(B $B4JC1$J9=J82r@O(B
278:
1.5 ! takayama 279: begin: zzz04|sortKey: zzz04
! 280: description:
! 281:
1.4 takayama 282: $BNcBj(B $B4JC1$J9=J82r@O(B
1.5 ! takayama 283:
1.4 takayama 284: example:
1.2 takayama 285: $B<0(B(expression) $B$O(B $B<0(B+$B<0(B | $B<0(B*$B<0(B | ($B<0(B) | $B@0?t(B
286:
287: extern R1,R2,R3,R4,S1,S2,S3,S4;
288: /* $BJ8K!$rK~$?$9$+$I$&$+$N(B check $BMQ(B. Action $BIt$O(B 1 $B$+(B 0 */
289: R1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), 1];
290: R2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), 1];
291: R3=[quote((pn(x,is_expression(x)))), 1];
292: R4=[quote(pn(x,qt_is_integer(x))), 1];
293: def is_expression(Qobj) {
294: R = [R1,R2,R3,R4];
295: A = apply_or_match0(Qobj,R);
296: if (A == 0) return 0; else return 1;
297: }
298:
299: /* $B7W;;MQ(B. R1,R2,R3,R4 $B$H:8$O6&DL(B. */
300: S1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), [myadd,x,y]];
301: S2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), [mymul,x,y]];
302: S3=[quote((pn(x,is_expression(x)))), [qt_id,x]];
303: S4=[quote(pn(x,qt_is_integer(x))), [qt_id,x]];
304:
305: def eval_expression(Qobj) {
306: S = [S1,S2,S3,S4];
307: return apply_or_rules(Qobj,S);
308: }
309:
310: def myadd(X,Y) {
311: return qt_(qt_eval(X,1)+qt_eval(Y,1));
312: }
313:
314: def mymul(X,Y) {
315: return qt_(qt_eval(X,1)*qt_eval(Y,1));
316: }
317:
318: /* $B7W;;(B */
319: tr_eval_expression(quote(1+2*(3+15)));
1.4 takayama 320: end:
1.1 takayama 321:
1.5 ! takayama 322: begin: misc|
! 323:
! 324: @section $B9M$(J}$K$D$$$F$N35@b(B
! 325:
! 326: $B%H%C%W%l%Y%k$N4X?tC#(B. (stylesheet $B$N9M$($K;w$F$k(B.)
! 327:
! 328: iterator $B$N0l<o(B.
! 329:
! 330: yacc $B$K;w$F$k(B.
! 331:
! 332: @section $B%G%P%C%,!<(B
! 333:
! 334: $BA*Br$9$Y$-%k!<%k$,Bt;3$"$k$H$-$O(B, $B7Y9p$9$k5!G=(B.
! 335:
! 336: $BL58B%k!<%W$N(B|$B8!=P(B.
! 337:
! 338: end:
! 339:
! 340: begin: exp|
! 341:
! 342: @c ------------------------------------------------
! 343: @section $B<B83E*4X?t(B
! 344:
! 345: end:
! 346:
! 347: begin: qt_map_arg(F,Q)
! 348: $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
! 349: apply $B$7$?(B quote $B%G!<%?$rLa$9(B.
! 350: example: qt_map_arg(nn,quote(sin(@pi)+2/3))
! 351: nn(nn(sin(nn(@pi)))+nn(nn(2)/nn(3)))
! 352: end:
! 353:
! 354: begin: todo|
! 355:
! 356: @section Todo
! 357:
! 358: @subsection $B%f!<%6Dj5A$NCfCV1i;;;R(B
! 359:
! 360: tfb $B$N=q$-J}$rF3F~(B.
1.1 takayama 361:
1.5 ! takayama 362: @subsection $B?t3X$h$j$NNcBj(B
1.1 takayama 363:
1.5 ! takayama 364: $B?t3XE*$K$*$b$7$m$$NcBj$r$J$k$Y$/Bt;3MQ0U$9$k(B.
! 365: $B$3$l$i$NNcBj$KBP$7$F(B tr $B$,;n:nIJ$r:n$k$N$KM-8z$G$"$k$H$$$&$3$H$r$$$&(B.
1.1 takayama 366:
1.5 ! takayama 367: $BNc(B; gcd $B7W;;$NB?9`<0(B reduction $B$r(B tr $B$G<B8=(B.
1.3 takayama 368:
1.4 takayama 369: $BNc(B; $BQQ5i?t$N7W;;$r(B quote $B$G<B8=(B.
1.3 takayama 370: sort $B$d(B expand $B$OAH$_9~$_$G(B.
371:
1.4 takayama 372: $BNc(B; Mathematica $B$N(B Expand[], Toghether[] $BAjEv$N$b$N(B.
1.3 takayama 373:
1.4 takayama 374: $BNc(B; D $B$N3]$1;;$r(B $B%Q%?!<%s%^%C%A$G<B8=(B.
1.5 ! takayama 375: holonomic $B4X?t$r78?t$H$9$kHyJ,:nMQAG4D$G$N7W;;(B.
1.3 takayama 376:
1.4 takayama 377: $BNc(B; (x^(1/n))^n --> x $BEy(B.
1.3 takayama 378:
1.4 takayama 379: $BNc(B; $B5-9fHyJ,$HHyJ,4D$G$N7W;;(B.
380: y''+xy=0, y''=y^2+x $BEy(B. index $BIU$-$NJQ?t@8@.$,I,MW(B. idxtov
1.3 takayama 381:
1.4 takayama 382: $BNc(B; QE, $BO@M}<0(B.
1.3 takayama 383:
1.5 ! takayama 384: $BNc(B; $B30@QBe?t(B.
! 385:
! 386: $BNc(B; $B4dGH(B, $B1~MQ?t3X(B, $B?@J]$N%=%j%H%s$NK\$K$"$k$h$&$J(B fermion $BEy$NNc(B.
1.3 takayama 387:
388:
1.5 ! takayama 389: $BNc(B;
! 390: Bergman, George M.
! 391: The diamond lemma for ring theory.
! 392: Advances in Math. 29 (1978), no. 2, 178--218.
! 393: $B$K$"$k$h$&$JHs2D49Be?t$NNc(B.
1.4 takayama 394:
395: end:
396:
1.5 ! takayama 397: begin: new-functions|
! 398:
1.3 takayama 399: @section $B$^$@%9%1%C%A$N$_$N4X?t;EMM(B
400:
1.5 ! takayama 401: qt_ltor, qt_rtol ; $BLZ$N9=B$$NJQ49(B; $BNc(B (x*y)*z --> x*(y*z)
! 402:
! 403:
! 404: @subsection Index $B$D$-JQ?t(B
1.3 takayama 405:
406: idxtov(x,i) x_i $B$r@8@.(B. x_i $B$N(B index (idx) $BB0@-(B $B$r(B i $B$K(B.
407: base_name $BB0@-$r(B x $B$K(B.
408: idxtov(x,[i,j]) 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.
409: vtoidx(x_i) $B$O(B i $B$rLa$9(B. $BB0@-$N8!:w$J$N$G9bB.(B. idx $BB0@-$,L5$$>l9g$O(B i $B$r@_Dj(B.
410:
411: idxtov $B4X?t$O(B $B4X?tL>$K$b;H$($k$h$&$K$9$k(B --> $BHyJ,4DBP1~(B.
412:
413: qt_function($BL>A0(B, $B0z?t(B) --> quote($BL>A0(B($B0z?t(B)) $B$r@8@.(B.
414: index $BIU$-4X?t$OHyJ,4D$N<h07$KI,MW(B.
415:
1.5 ! takayama 416: @subsection $BQQ5i?t(B, dp $B$N(B pretty print.
! 417:
1.3 takayama 418: $B6R5i?t$N<h07(B, dp $B$N(B pretty print $B$N$?$a(B.
419: qt_qttodp(Qobj | vlist, order?) quote $B$+$i(B dp $B$r:n$k(B.
420: exponent $B$,?t$G$J$$$H:n$l$:(B.
421: qt_dptoqt(Qobj | vlist) dp $B$+$i(B quote $B$r:n$k(B. vlist $B$OB0@-$GBP1~(B?
1.1 takayama 422:
1.3 takayama 423: qt_expand, qt_sort, qt_ht, qt_rest, qt_mtov $B$b4pAC4X?t$H$7$FM_$7$$(B.
1.5 ! takayama 424:
! 425: end:
1.1 takayama 426:
427: /*&generate-epilogue
428: */
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