Annotation of OpenXM/src/asir-contrib/testing/tr-ja.oxt, Revision 1.6
1.6 ! takayama 1: $Id: tr.oxt,v 1.21 2005/04/15 12:42:59 taka Exp $
! 2: $OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.5 2005/04/06 09:26:28 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$$(B. qt_is_function(x) $B$G(B OK.
26: fn(f) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
27: fn(f,pn(x),pn(y)) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
28: f $B$N0z?t$r(B x, y $B$K(B bind
29:
30:
31: $B%Q%?!<%s$O(B quote $B$GM?$($k(B.
32: $BM=Ls8l(B tr_and, tr_or, tr_not $B$O%Q%?!<%s$N%^%C%A$K4X$7$FO@M}1i;;$r$*$3$J$&(B.
33: $B$?$H$($P(B
34: quote(tr_and(pn(x,qt_is_integer),pn(x,qt_is_non_negative(x))))
35: $B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.
36:
37: end:
38:
39: begin: AAA02|
1.4 takayama 40:
1.1 takayama 41: @section quote $B$KBP$9$k4pK\4X?t(B
42:
1.5 takayama 43: end:
44:
45:
1.4 takayama 46: begin: qt_node(Q)
1.1 takayama 47: quote $B%G!<%?(B {Q} $B$N(B node $B$r<h$j=P$9(B.
48: example: qt_node(quote(1+2*3))
1.4 takayama 49: end:
1.1 takayama 50:
51:
1.4 takayama 52: begin: qt_nchild(Q)
1.1 takayama 53: quote $B%G!<%?(B {Q} $B$N(B $B;R6!$N?t$rLa$9(B.
54: example: qt_nchild(quote(1+2*3)) 2 $B$rLa$9(B.
1.4 takayama 55: end:
1.1 takayama 56:
57:
1.4 takayama 58: begin: qt_child(Q,K)
1.1 takayama 59: quote $B%G!<%?(B {Q} $B$N(B {K} $BHVL\$N;R6!$rLa$9(B.
60: example: qt_child(quote(1+2*3),1) quote(2*3) $B$rLa$9(B.
1.3 takayama 61: example: qt_child(quote(1+2*3),0) quote(1) $B$rLa$9(B.
1.4 takayama 62: end:
1.1 takayama 63:
64: @c --------------------------------------------------------------------
65: @subsection quote $B$KBP$9$k=R8l(B
66:
1.4 takayama 67: begin: qt_is_integer(Q)
1.1 takayama 68: quote $B%G!<%?(B {Q} $B$,@0?t$J$i(B 1
69: example: qt_is_integer(quote(0))
1.4 takayama 70: end:
1.1 takayama 71:
1.6 ! takayama 72: begin: qt_is_dependent(Q,x)
1.1 takayama 73: quote $B%G!<%?(B {Q} $B$,ITDj85(B {x} $B$r4^$`$H(B 1, $B4^$^$J$$$H(B 0.
1.6 ! takayama 74: example: qt_is_dependent(quote(1+1/x),x)
1.4 takayama 75: end:
76:
77: begin: qt_is_function(Q)
78: quote $B%G!<%?(B {Q} $B$,4X?t$N$H$-(B 1, $B$=$&$G$J$$$H$-(B 0.
79: example: qt_is_function(f(x,y));
80: end:
1.1 takayama 81:
82: @c --------------------------------------------------------------------
83: @subsection quote $B$KBP$9$k%3%s%9%H%i%/%?(B
84:
1.4 takayama 85: begin: qt_zero()
1.1 takayama 86: quote 0 $B$rLa$9(B.
1.4 takayama 87: end:
1.1 takayama 88:
1.4 takayama 89: begin: qt_id(Qobj)
1.1 takayama 90: quote object {Qobj} $B$r$=$N$^$^La$9(B.
1.4 takayama 91: end:
1.1 takayama 92:
1.4 takayama 93: begin: qt_replace(Qobj,[[x,Valuex],[y,Valuey],...])
1.1 takayama 94: quote object {Qobj} $B$NCf$N(B x $B$r(B Valuex, y $B$r(B Valuey, ... $B$KCV$-49$($?(B
95: quote object $B$rLa$9(B.
1.5 takayama 96: description:
97: $B2]Bj(B; x, y $B$OBgJ8;z$b5v$9$+(B? @var{Qobj} $B$b85!94^$^$l$F$$$kBgJ8;z$rI>2A$7$FCV$-49$($k(B
98: $B4X?t$bI,MW$+(B?
99:
1.3 takayama 100: example: qt_replace(quote(sin(x*@pi)), [[x,quote( (2*t+3) )]])
1.4 takayama 101: end:
1.1 takayama 102:
1.3 takayama 103: qt_replace $B$O(B asir-contrib $B$N(B base_replace $B$H;w$?5!G=(B.
104: quote $B$NFbIt$KBgJ8;z$G$O$8$^$kJQ?t(B($BI>2A$9$k(B)$B$,=q$1$J$$$?$a(B.
105:
1.4 takayama 106: begin: qt_parenthesis(Qobj)
1.1 takayama 107: quote object {Qobj} $B$NCf$N3g8L$,B-$j$J$$$H$-$K$OJd$$(B, $BB?$$$H$-$K$O<h$j5n$C$?(B
108: quote object $B$r:n$k(B.
1.3 takayama 109: +, *, /, ^, - $BEy$K$D$$$F(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
1.5 takayama 110: description:
111: $B;29M(B;
112: noro_simplify.rr $B$N(B @code{remove_paren()} $B$,$9$G$K<B8=$E$_(B?
113: @code{flatten()} $B$d(B @code{quote_to_funargs()} $B$rMxMQ$7$F$kLOMM(B.
114:
1.4 takayama 115: end:
1.1 takayama 116:
1.4 takayama 117: begin: qt_eval(Qobj,type)
1.2 takayama 118: Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
1.5 takayama 119: description:
120: @code{eval_quote()} $B$,$9$G$K<B8=$E$_(B.
121:
1.4 takayama 122: end:
1.2 takayama 123:
1.4 takayama 124: begin: qt_(Obj)
1.2 takayama 125: asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.
1.5 takayama 126: description:
127: @code{objtoquote()} $B$,$9$G$K<B8=$E$_(B.
128:
1.4 takayama 129: end:
1.2 takayama 130:
1.1 takayama 131:
1.5 takayama 132: begin: tr|
133:
1.1 takayama 134: @c --------------------------------------------------------------------
135: @section tr (term rewriting) $B$N%H%C%W%l%Y%k$N4X?t(B
136:
1.5 takayama 137: end:
138:
1.4 takayama 139: begin: tr_match0(Qobj,P)
1.1 takayama 140: 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
141: $B$rLa$9(B.
1.3 takayama 142: example: tr_match0(quote(1+2*3),quote(pn(x)+pn(y)))
143: x $B$K(B quote(1), y $B$K(B quote(2*3)
144: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,qt_is_integer,y)))
145: qt_is_integer(2*3) $B$O(B 0 $B$J$N$G(B y $B$K$O%^%C%A$7$J$$(B.
1.4 takayama 146: end:
1.1 takayama 147:
1.4 takayama 148: begin: pn(X)
149: pn(x) $B$OG$0U$N(B quote object $B$K%^%C%A$7(B, $BL>A0(B x $B$r$D$1$k(B.
150: description:
151: tr_match0(quote(1+2*3),quote(pn(x)+pn(y))) $B$O(B 1 $B$rLa$9$,(B,
152: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,tr_is_integer,x))) $B$O(B 0 $B$r$b$I$9(B.
153: 2*3 $B$O(B integer $B$+$i:n$i$l$?(B fnode $B$G$O$"$k$,(B integer $B$G$O$J$$$N$G(B qt_is_integer
154: $B$,(B 0 $B$rLa$9$?$a(B.
155: end:
1.1 takayama 156:
1.4 takayama 157: begin: tr_match0_act(Qobj,P,Act)
1.1 takayama 158: 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.
159: $B%Q%?!<%s(B {P} $B$K%^%C%A$7$J$$$H$-$O(B 0.
160:
1.4 takayama 161: example: tr_match0_act(quote(1+2*3),quote(pn(x)+pn(y)),[myadd,x,y])
162: end:
1.1 takayama 163:
1.4 takayama 164: begin: tr_or_match0_act(Qobj,Rules)
165: end:
1.1 takayama 166:
1.4 takayama 167: begin: tr_apply_rule1(Qobj,P,Act)
1.1 takayama 168: quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B,
169: $B%Q%?!<%s(B {P} $B$KE,9g$9$k$b$N$,$"$k$H$-$O(B {Act} $B$r8F$S=P$7$=$NCM$rLa$9(B.
170: $B$D$^$j(B top node $B$,(B {P} $B$KE,9g$9$k$+D4$Y(B, $BE,9g$7$J$$>l9g$O$=$N;R6!$K(B
1.3 takayama 171: 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 172: $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).
173:
1.4 takayama 174: description:
1.3 takayama 175: $B$3$3$G(B sin_int(X) $B$O(B X $B$,(B integer $B$N;~$O(B quote(0) $B$rLa$7(B,
1.5 takayama 176: $B$=$&$G$J$$$H$-$O(B quote(sin(X*@@pi)) $B$rLa$9(B.
1.1 takayama 177: $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
178: $B$h$$(B.
179:
1.4 takayama 180: example: tr_apply_rule1(quote(1+sin(2*@pi)),quote(sin(pn(x)*@pi)),[sin_int,x])
181: end:
182:
183:
184: begin: tr_apply_or_rules(Qobj,Rules)
185: end:
1.1 takayama 186:
1.2 takayama 187: @subsection $BFbIt4X?t(B
188:
1.4 takayama 189: begin: tr_apply_function0(Qobj,BindingTable)
190: end:
1.2 takayama 191:
1.4 takayama 192: begin: tr_rp(Qobj,P,A)
193: end:
1.2 takayama 194:
1.4 takayama 195: begin: tr_make_binding(Qobj,P)
196: end:
1.2 takayama 197:
1.1 takayama 198:
1.5 takayama 199: begin: zzz00|
1.4 takayama 200:
1.5 takayama 201: @section $BNcBj(B
1.1 takayama 202:
1.4 takayama 203: end:
1.1 takayama 204:
1.5 takayama 205: begin: zzz01|
206: $BNcBj(B sin($B@0?t(B*@@pi) $B$r(B 0 $B$K(B.
1.4 takayama 207: example:
1.2 takayama 208: /* $B=`Hw(B */
209: extern P,A;
210: P=quote(sin(pn(x)*@pi)); /* $B%Q%?!<%s(B */
211: A=[sin_int,x] /* action, action $B4X?t(B */
212: def sin_int(X) {
213: X = tr_apply_rule1(X,P,A); /* $B;R6!$K(B [P,A] $B$r:F5"E*$KE,MQ(B */
214: if (qt_is_integer(X)) return qt_zero();
215: else qt_replace(sin(y*@pi),[[y,X]]); /* sin(x*@pi) $B$r$=$N$^$^La$9(B.*/
216: }
217:
218: /* $B7W;;(B */
219: Qobj=quote(1+sin(sin(2*@pi)*@pi)*sin((1/2)*@pi));
220: tr_apply_rule1(Qobj,P,A);
1.4 takayama 221: end:
1.2 takayama 222:
1.4 takayama 223: @c ------------------------------------------------------
224: @section $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
225:
1.5 takayama 226: begin: zzz02|
1.4 takayama 227: $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
228: example:
229: nn(sin(cos(@pi)+sqrt(2)))
230: --> nn(sin(nn(cos(nn(@pi)))+nn(sqrt(nn(2)))))
231: Prog; test1-tr.rr $B$N(B test4().
232:
233: qt_map_arg $B4X?t$rMQ$$$k(B.
234: def test4() {
235: Rule=[quote(nn(pn(f))),[qt_map_arg,nn,f]];
236: /* nn $B$G0O$^$l$?$b$N$,$"$l$P(B, nn $B$r$=$NFbIt$K:F5"E*$K(B apply $B$9$k(B */
237: R0 = quote(nn(sin(1/2)*cos(1/3)));
238: print(print_input_form(R0));
239: R=tr_apply_rule1(R0,Rule[0],Rule[1]);
240: return R;
241: }
242:
243: end:
1.1 takayama 244:
245: @c ---------------------------------------------------------
246: @section $BNcBj(B $BITDj@QJ,(B
247:
1.5 takayama 248: begin: zzz03|
1.4 takayama 249: $BNcBj(B $BITDj@QJ,(B
250: example:
1.2 takayama 251: /* integral(f+g) => integral(f)+integral(g) */
252: S1=[quote(integral(pn(f)+pn(g))),
253: [int_linear1,f,g]];
254: def int_linear1(X,Y) {
255: return qt_replace(quote(integral(f)+integral(g)),[[f,X],[g,Y]]);
256: }
257:
258: /* integral(c*f) => c*integral(f) */
259: def qt_independent(F,X) { return !qt_dependent(F,X); }
260: S2=[quote(integral(pn(c,qt_independent(c,x))*f)),
261: [int_linear2,c,f]];
262: def int_linear2(X,Y) {
263: return qt_replace(quote(c*integral(f)),[[c,X],[f,Y]]);
264: }
265:
266: apply_or_rules(quote(integral(a*x^2+x+2/x)),[S1,S2]);
267: $B$3$l$r$3$l0J>e=q$-49$($,5/$-$J$$$^$G7+$jJV$9(B.
268: $B$3$N%k!<%k$N>l9gEz$($O(B
269: a*integral(x^2)+integral(x)+integral(2/x);
270:
271: quote(integral(x^pn(n))) --> x^(n+1)/(n+1) or log(x) $B$r=q$/(B.
1.4 takayama 272: end:
1.2 takayama 273:
1.1 takayama 274: @c ---------------------------------------------------------
275: @section $BNcBj(B $B4JC1$J9=J82r@O(B
276:
1.5 takayama 277: begin: zzz04|sortKey: zzz04
278: description:
279:
1.4 takayama 280: $BNcBj(B $B4JC1$J9=J82r@O(B
1.5 takayama 281:
1.4 takayama 282: example:
1.2 takayama 283: $B<0(B(expression) $B$O(B $B<0(B+$B<0(B | $B<0(B*$B<0(B | ($B<0(B) | $B@0?t(B
284:
285: extern R1,R2,R3,R4,S1,S2,S3,S4;
286: /* $BJ8K!$rK~$?$9$+$I$&$+$N(B check $BMQ(B. Action $BIt$O(B 1 $B$+(B 0 */
287: R1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), 1];
288: R2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), 1];
289: R3=[quote((pn(x,is_expression(x)))), 1];
290: R4=[quote(pn(x,qt_is_integer(x))), 1];
291: def is_expression(Qobj) {
292: R = [R1,R2,R3,R4];
293: A = apply_or_match0(Qobj,R);
294: if (A == 0) return 0; else return 1;
295: }
296:
297: /* $B7W;;MQ(B. R1,R2,R3,R4 $B$H:8$O6&DL(B. */
298: S1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), [myadd,x,y]];
299: S2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), [mymul,x,y]];
300: S3=[quote((pn(x,is_expression(x)))), [qt_id,x]];
301: S4=[quote(pn(x,qt_is_integer(x))), [qt_id,x]];
302:
303: def eval_expression(Qobj) {
304: S = [S1,S2,S3,S4];
305: return apply_or_rules(Qobj,S);
306: }
307:
308: def myadd(X,Y) {
309: return qt_(qt_eval(X,1)+qt_eval(Y,1));
310: }
311:
312: def mymul(X,Y) {
313: return qt_(qt_eval(X,1)*qt_eval(Y,1));
314: }
315:
316: /* $B7W;;(B */
317: tr_eval_expression(quote(1+2*(3+15)));
1.4 takayama 318: end:
1.1 takayama 319:
1.5 takayama 320: begin: misc|
321:
322: @section $B9M$(J}$K$D$$$F$N35@b(B
323:
324: $B%H%C%W%l%Y%k$N4X?tC#(B. (stylesheet $B$N9M$($K;w$F$k(B.)
325:
326: iterator $B$N0l<o(B.
327:
328: yacc $B$K;w$F$k(B.
329:
330: @section $B%G%P%C%,!<(B
331:
332: $BA*Br$9$Y$-%k!<%k$,Bt;3$"$k$H$-$O(B, $B7Y9p$9$k5!G=(B.
333:
334: $BL58B%k!<%W$N(B|$B8!=P(B.
335:
336: end:
337:
338: begin: exp|
339:
340: @c ------------------------------------------------
341: @section $B<B83E*4X?t(B
342:
343: end:
344:
345: begin: qt_map_arg(F,Q)
346: $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
347: apply $B$7$?(B quote $B%G!<%?$rLa$9(B.
348: example: qt_map_arg(nn,quote(sin(@pi)+2/3))
349: nn(nn(sin(nn(@pi)))+nn(nn(2)/nn(3)))
350: end:
351:
352: begin: todo|
353:
354: @section Todo
355:
356: @subsection $B%f!<%6Dj5A$NCfCV1i;;;R(B
357:
358: tfb $B$N=q$-J}$rF3F~(B.
1.1 takayama 359:
1.5 takayama 360: @subsection $B?t3X$h$j$NNcBj(B
1.1 takayama 361:
1.5 takayama 362: $B?t3XE*$K$*$b$7$m$$NcBj$r$J$k$Y$/Bt;3MQ0U$9$k(B.
363: $B$3$l$i$NNcBj$KBP$7$F(B tr $B$,;n:nIJ$r:n$k$N$KM-8z$G$"$k$H$$$&$3$H$r$$$&(B.
1.1 takayama 364:
1.5 takayama 365: $BNc(B; gcd $B7W;;$NB?9`<0(B reduction $B$r(B tr $B$G<B8=(B.
1.3 takayama 366:
1.4 takayama 367: $BNc(B; $BQQ5i?t$N7W;;$r(B quote $B$G<B8=(B.
1.3 takayama 368: sort $B$d(B expand $B$OAH$_9~$_$G(B.
369:
1.4 takayama 370: $BNc(B; Mathematica $B$N(B Expand[], Toghether[] $BAjEv$N$b$N(B.
1.3 takayama 371:
1.4 takayama 372: $BNc(B; D $B$N3]$1;;$r(B $B%Q%?!<%s%^%C%A$G<B8=(B.
1.5 takayama 373: holonomic $B4X?t$r78?t$H$9$kHyJ,:nMQAG4D$G$N7W;;(B.
1.3 takayama 374:
1.4 takayama 375: $BNc(B; (x^(1/n))^n --> x $BEy(B.
1.3 takayama 376:
1.4 takayama 377: $BNc(B; $B5-9fHyJ,$HHyJ,4D$G$N7W;;(B.
378: y''+xy=0, y''=y^2+x $BEy(B. index $BIU$-$NJQ?t@8@.$,I,MW(B. idxtov
1.3 takayama 379:
1.4 takayama 380: $BNc(B; QE, $BO@M}<0(B.
1.3 takayama 381:
1.5 takayama 382: $BNc(B; $B30@QBe?t(B.
383:
384: $BNc(B; $B4dGH(B, $B1~MQ?t3X(B, $B?@J]$N%=%j%H%s$NK\$K$"$k$h$&$J(B fermion $BEy$NNc(B.
1.3 takayama 385:
386:
1.5 takayama 387: $BNc(B;
388: Bergman, George M.
389: The diamond lemma for ring theory.
390: Advances in Math. 29 (1978), no. 2, 178--218.
391: $B$K$"$k$h$&$JHs2D49Be?t$NNc(B.
1.4 takayama 392:
393: end:
394:
1.5 takayama 395: begin: new-functions|
396:
1.3 takayama 397: @section $B$^$@%9%1%C%A$N$_$N4X?t;EMM(B
398:
1.5 takayama 399: qt_ltor, qt_rtol ; $BLZ$N9=B$$NJQ49(B; $BNc(B (x*y)*z --> x*(y*z)
400:
1.6 ! takayama 401: end:
! 402:
! 403: begin: idx|
1.5 takayama 404:
405: @subsection Index $B$D$-JQ?t(B
1.3 takayama 406:
1.6 ! takayama 407: end:
! 408:
! 409: begin: idxtov(X,I)
! 410: idxtov({X},{I}) $B$OJQ?t(B {X}_{I} $B$rLa$9(B.
! 411: {I} $B$O%9%+%i!<$+%j%9%H(B.
! 412: example:
! 413: idxtov(x,i) $B$O(B x_i $B$rLa$9(B.
! 414: description:
! 415: 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.
! 416:
! 417: @code{util_v()} $B$H$[$\F1$8(B.
! 418:
! 419: x_i $B$N(B index (idx) $BB0@-(B $B$r(B i $B$K(B.
! 420: base_name $BB0@-$r(B x $B$K(B.
! 421: $BITDj85$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
! 422: $BBe$j$,$G$-$k(B.
! 423:
! 424: end:
! 425:
! 426: begin: vtoidx(X)
! 427: vtoidx(x_i) $B$O(B [x,i] $B$rLa$9(B.
! 428: description:
! 429: @code{util_index()} $B$H$[$\F1MM(B.
! 430:
! 431: $BB0@-$N8!:w$J$N$G9bB.(B. idx $BB0@-$,L5$$>l9g$O(B i $B$r@_Dj(B.
1.3 takayama 432:
1.6 ! takayama 433: idxtov $B4X?t$O(B $B4X?tL>$K$b;H$($k$h$&$K$9$k(B? --> $BHyJ,4DBP1~(B.
1.3 takayama 434:
435: qt_function($BL>A0(B, $B0z?t(B) --> quote($BL>A0(B($B0z?t(B)) $B$r@8@.(B.
436: index $BIU$-4X?t$OHyJ,4D$N<h07$KI,MW(B.
1.6 ! takayama 437: end:
! 438:
! 439: begin: powerSeries|
1.3 takayama 440:
1.5 takayama 441: @subsection $BQQ5i?t(B, dp $B$N(B pretty print.
442:
1.3 takayama 443: $B6R5i?t$N<h07(B, dp $B$N(B pretty print $B$N$?$a(B.
444: qt_qttodp(Qobj | vlist, order?) quote $B$+$i(B dp $B$r:n$k(B.
445: exponent $B$,?t$G$J$$$H:n$l$:(B.
446: qt_dptoqt(Qobj | vlist) dp $B$+$i(B quote $B$r:n$k(B. vlist $B$OB0@-$GBP1~(B?
1.1 takayama 447:
1.3 takayama 448: qt_expand, qt_sort, qt_ht, qt_rest, qt_mtov $B$b4pAC4X?t$H$7$FM_$7$$(B.
1.5 takayama 449:
450: end:
1.1 takayama 451:
1.6 ! takayama 452: begin: MonomialSimplifier|
! 453:
! 454: @subsection $B%b%N%_%"%k$rI8=`7A$X(B (builtin$B$G(B?)
! 455:
! 456: example:
! 457: x^1 --> x
! 458: (x*y)*(z*t) --> x*y*z*t
! 459: x*2*y*4 --> 8*x*y ($B;XDj$7$?JQ?t0J30$O2D49$H$9$k(B)
! 460: x*x^3 --> x^4
! 461: x*(-y)*z --> -x*y*z
! 462: ((x)) --> x $B$3$l$O(B noro_simplify.rr noro_simplify.remove_paren() $B$,BP1~(B
! 463:
! 464:
! 465: end:
! 466:
! 467: 4/15 $BLk(B. $B<BAu$OL@F|9V5A$N=`Hw$N=*N;8e$+(B?
! 468: begin: qt.gtlex(f,g)
! 469: {f} $B$O(B {g} $B$h$j(B quote tree $B$N(B lex order $B$GBg$-$$(B.
! 470: description:
! 471: quote tree $B$N(B lex order $B$O<!$N$h$&$K7h$a$k(B.
! 472: @itemize
! 473: @item $BITDj85$OITDj85$N=g=x(B.
! 474: @item $BITDj85$h$j(B +, - , *, /, ^ $BEy$N(B node $B$OBg$-$$(B.
! 475: $B$?$H$($P(B x < power(x,2) (power(x,2) $B$O(B x^2 $B$N0UL#(B)
! 476: @item $B$"$H$O:F5"E*(B. times(x,y) < power(x,y) $B$@$,(B,
! 477: times(x,y) $B$H(B times(p,q) $B$O(B x $B$H(B p $B$NHf3S(B, $B$3$l$G$-$^$i$J$$$J$i(B,
! 478: y, q $B$NHf3S(B.
! 479: @end itemize
! 480:
! 481: end:
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