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Form.cpp
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1
6#include "HEP.h"
7#include "ginac/parse_context.h"
8
9namespace HepLib {
10
11 //-----------------------------------------------------------
12 // Extend Parser for form, copied from ginac/parser of GiNaC
13 //-----------------------------------------------------------
14 namespace {
15
16 alignas(2) static ex SP_reader(const exvector& ev) {
17 if(ev.size()<2) return SP(ev[0]).subs(SP_map);
18 else return SP(ev[0], ev[1]).subs(SP_map);
19 }
20
21 alignas(2) static ex LC_reader(const exvector& ev) {
22 if(ev.size()==4) return (-I)*LC(ev[0], ev[1], ev[2], ev[3]);
23 else return Eps(ev);
24 }
25
26 alignas(2) static ex SUNT_reader(const exvector& ev) {
27 int n = ev.size();
28 if(n==3) return SUNT(ev[0], ev[1], ev[2]);
29 else if(n>3) {
30 lst as;
31 for(int i=0; i<n-2; i++) as.append(ev[i]);
32 return SUNT(as,ev[n-2],ev[n-1]);
33 } else throw Error("SUNT_reader: number of arguments less than 3.");
34 }
35
36 alignas(2) static ex TTR_reader(const exvector& ev) {
37 if(ev.size()==1) return TTR(ev[0]);
38 lst as;
39 for(auto item : ev) as.append(item);
40 return TTR(as);
41 }
42
43 alignas(2) static ex DGamma_reader(const exvector& ev) {
44 int n = ev.size();
45 if(n==1) return GAS(ev[0]);
46 ex ret = 1;
47 int rl = ex2int(ev[0]);
48 for(int i=1; i<n; i++) ret = ret * GAS(ev[i],rl);
49 return ret;
50 }
51
52 alignas(2) static ex gi_reader(const exvector& ev) {
53 int n = ev.size();
54 if(n==0) return GAS(1);
55 else if(n==1) return GAS(1,ex2int(ev[0]));
56 else throw Error("DGamma_reader: number of arguments more than 2.");
57 }
58
59 alignas(2) static ex GMat_reader(const exvector& ev) {
60 return GMat(ev[0],ev[1],ev[2]);
61 }
62 }
63
64 //-----------------------------------------------------------
65 // Run Form Program
66 //-----------------------------------------------------------
67 namespace {
68
69 struct mapGamma : public map_function {
70 public:
71 ex operator()(const ex &e) {
72 if(is_a<DGamma>(e)) return DGamma(ex_to<DGamma>(e), gline);
73 else if(!DGamma::has(e)) return e;
74 else return e.map(*this);
75 }
76 mapGamma(int _gline) : gline(_gline) { };
77 private:
78 unsigned gline = 0;
79 };
80
81 struct mapTR : public map_function {
82 public:
83 ex operator()(const ex &e) {
84 if (e.match(TR(w))) {
85 ex trs = e.op(0);
86 gline++;
87 trs = mapGamma(gline)(trs);
88 trs = DGamma(1, gline) * trs;
89 if(glmax<gline) {
90 glmax = gline;
91 if(glmax>128) throw Error("too large index with glmax>128.");
92 }
93 return TR(trs);
94 } else if(is_a<add>(e)) {
95 ex res = 0;
96 unsigned gl = gline;
97 unsigned glmax = gline;
98 for(auto item : e) {
99 gline = gl;
100 res += (*this)(item);
101 if(glmax<gline) glmax = gline;
102 }
103 gline = glmax;
104 return res;
105 } else return e.map(*this);
106 }
107 unsigned glmax = 0;
108 private:
109 unsigned gline = 0;
110 };
111
112 string init_script = R"EOF(
113CFunction pow,sqrt,gamma,HF,GMat,WF;
114Tensor TTR(cyclic), f(antisymmetric), T, f4, colTp;
115Symbols reX,I2R,NF,NA,d;
116AutoDeclare Symbols gCF, trcN;
117Dimension NA;
118AutoDeclare Index colA;
119Dimension NF;
120AutoDeclare Index colF;
121
122#procedure SUNTrace
123Dimension NF;
124
125repeat;
126 id,once,TTR(?a) = T(?a,colF1,colF1);
127 sum colF1;
128 repeat;
129 id,once,T(colA1?,colA2?,?a,colF1?,colF2?) = T(colA1,colF1,colF3)*T(colA2,?a,colF3,colF2);
130 sum colF3;
131 id,once,f4(colA1?,colA2?,colA3?,colA4?) = f(colA1,colA2,colA5) * f(colA5,colA3,colA4);
132 sum colA5;
133 endrepeat;
134endrepeat;
135
136#do colXi = 1,1
137 if ( count(f,1) || match(T(colA1?,colF1?,colF2?)*T(colA1?,colF3?,colF4?)) ) redefine colXi "0";
138 id,once,f(colA1?,colA2?,colA3?) = 1/I2R/i_*T(colA1,colF1,colF2)*T(colA2,colF2,colF3)*T(colA3,colF3,colF1)-1/I2R/i_*T(colA3,colF1,colF2)*T(colA2,colF2,colF3)*T(colA1,colF3,colF1);
139 sum colF1,colF2,colF3;
140 id T(colA1?,colF1?,colF2?)*T(colA1?,colF3?,colF4?) = colTp(colF1,colF2,colF3,colF4);
141 #do colXj = 1,1
142 if ( count(colTp,1) ) redefine colXj "0";
143 .sort
144 id,once,colTp(colF1?,colF2?,colF3?,colF4?) = I2R*(d_(colF1,colF4)*d_(colF2,colF3)-d_(colF1,colF2)*d_(colF3,colF4)/NF);
145 #enddo
146#enddo
147
148repeat;
149 id T(colA1?,?a,colF1?,colF2?)*T(colA2?,?b,colF2?,colF3?) = T(colA1,?a,colA2,?b,colF1,colF3);
150endrepeat;
151id T(?a,colF1?,colF1?) = TTR(?a);
152id TTR(colA1?) = 0;
153id TTR(colA1?,colA2?) = I2R*d_(colA1,colA2);
154.sort
155
156Local I = i_;
157Local Pi = pi_;
158.sort
159
160#endprocedure
161.global
162 )EOF";
163 }
164
165 //-----------------------------------------------------------
166 // form
167 //-----------------------------------------------------------
168 namespace {
169 ex runform(const ex &expr_in, int verb) {
170 static map<pid_t, Form> form_map;
171 auto pid = getpid();
172 if((form_map.find(pid)==form_map.end())) { // init section
173 ostringstream ss;
174 ss << init_script << endl;
175 form_map[pid].Init("form");
176 form_map[pid].Execute(ss.str());
177 }
178 Form &fprc = form_map[pid];
179
180 ex expr = expr_in.subs(SP_map);
181 ex all_expr = expr;
182 stringstream sss;
183 FormFormat ids(sss);
184 for(auto kv : SP_map) {
185 ids << "id " << kv.first << "=" << kv.second << ";" << endl;
186 all_expr += iWF(kv.first) * iWF(kv.second);
187 }
188 string idstr = sss.str();
189
190 lst vec_lst, VD_lst, CF_lst, CA_lst, sym_lst;
191 for(const_preorder_iterator i = all_expr.preorder_begin(); i != all_expr.preorder_end(); ++i) {
192 if(is_a<Vector>(*i)) vec_lst.append(*i);
193 else if(is_a<Index>(*i)) {
194 if(ex_to<Index>(*i).dim==d) VD_lst.append(*i);
195 else if(ex_to<Index>(*i).dim==NF) CF_lst.append(*i);
196 else if(ex_to<Index>(*i).dim==NA) CA_lst.append(*i);
197 } else if(is_a<symbol>(*i)) sym_lst.append(*i);
198 else if(is_a<GiNaC::function>(*i)) {
199 static vector<string> fun_vec = {
200 "iWF", "WF", "TR", "sin", "cos", "HF", "TTR", "GMat"
201 };
202 auto func = ex_to<GiNaC::function>(*i).get_name();
203 bool ok = false;
204 for(auto fi : fun_vec) {
205 if(fi==func) { ok = true; break; }
206 }
207 if(!ok) {
208 cout << (*i) << endl;
209 throw Error("runform: Functions not defined in FORM: "+func);
210 }
211 }
212 }
213 vec_lst.sort(); vec_lst.unique();
214 VD_lst.sort(); VD_lst.unique();
215 CF_lst.sort(); CF_lst.unique();
216 CA_lst.sort(); CA_lst.unique();
217 sym_lst.append(d);
218 sym_lst.sort(); sym_lst.unique();
219
220 stringstream ss;
221 FormFormat ff(ss);
222 ff << ".store" << endl;
223 symtab st;
224 if(sym_lst.nops()>0) {
225 ff << "Symbols";
226 for(auto sx : sym_lst) {
227 auto s = ex_to<symbol>(sx);
228 ff << " " << s.get_name();
229 st[s.get_name()] = sx;
230 }
231 ff << ";" << endl;
232 }
233 if(vec_lst.nops()>0) {
234 ff << "Vectors";
235 for(auto vx : vec_lst) {
236 auto v = ex_to<Vector>(vx);
237 ff << " " << v;
238 st[v.name.get_name()] = v;
239 for(auto vvx : vec_lst) {
240 auto vv = ex_to<Vector>(vvx);
241 st[v.name.get_name()+"__"+vv.name.get_name()] = SP(v,vv).subs(SP_map);
242 }
243 }
244 ff << ";" << endl;
245 }
246 if(VD_lst.nops()>0) {
247 if(form_using_dim4) ff << "Dimension 4;" << endl;
248 else ff << "Dimension d;" << endl;
249 ff << "Indices";
250 for(auto ix : VD_lst) {
251 auto i = ex_to<Index>(ix);
252 ff << " " << i;
253 st[i.name.get_name()] = i;
254 auto itr = Index::Dimension.find(ix);
255 if(itr!=Index::Dimension.end()) ff << "=" << itr->second;
256 }
257 ff << ";" << endl;
258 }
259 if(CF_lst.nops()>0) {
260 ff << "Dimension NF;" << endl;
261 ff << "Indices";
262 for(auto ix : CF_lst) {
263 auto i = ex_to<Index>(ix);
264 ff << " " << i;
265 st[i.name.get_name()] = i;
266 auto itr = Index::Dimension.find(ix);
267 if(itr!=Index::Dimension.end()) ff << "=" << itr->second;
268 }
269 ff << ";" << endl;
270 }
271 if(CA_lst.nops()>0) {
272 ff << "Dimension NA;" << endl;
273 ff << "Indices";
274 for(auto ix : CA_lst) {
275 auto i = ex_to<Index>(ix);
276 ff << " " << i;
277 st[i.name.get_name()] = i;
278 auto itr = Index::Dimension.find(ix);
279 if(itr!=Index::Dimension.end()) ff << "=" << itr->second;
280 }
281 ff << ";" << endl;
282 }
283 ff << ".global" << endl;
284 ff << endl;
285
286 // trace and contract
287 bool islst = is_a<lst>(expr);
288 lst expr_lst;
289 if(islst) expr_lst = ex_to<lst>(expr);
290 else expr_lst.append(expr);
291 auto total = expr_lst.nops();
292
293 string ostr;
294 int gid = 1;
295 ostr = "{";
296 int c = 1;
297 int kid = 0;
298 map<ex,int,ex_is_less> e2i_map;
299 for(auto it : expr_lst) {
300 ff << ".store" << endl;
301 ex item = it;
302 item = MapFunction([](const ex & e, MapFunction &self)->ex{
303 if(!e.has(TR(w))) return e;
304 else if(e.match(TR(w))) {
305 ex nd = e.op(0).normal().numer_denom();
306 return TR(nd.op(0))/nd.op(1);
307 } else return e.map(self);
308 })(item);
309 item = normal(item); // TODO: normal
310 // pull out global common factor
311 item = collect_common_factors(item);
312 item = CoPat(item,[](const ex &e)->bool{return Index::has(e) || DGamma::has(e) || Eps::has(e);});
313 auto ckey = item.op(0);
314 if(!is_a<numeric>(ckey)) {
315 int ckid;
316 if(e2i_map.find(ckey)==e2i_map.end()) {
317 kid++;
318 e2i_map[ckey] = kid;
319 ckid = kid;
320 } else ckid = e2i_map[ckey];
321 string gCF = "gCF" + to_string(ckid);
322 st[gCF] = item.op(0);
323 item = Symbol(gCF) * item.op(1);
324 } else {
325 item = ckey * item.op(1);
326 }
327
328 // pull out color factor
329 auto cv_lst = collect_lst(item, [](const ex &e)->bool{return Index::hasc(e);});
330 item=0;
331 exvector color_vec;
332 for(int i=0; i<cv_lst.nops(); i++) {
333 auto it = cv_lst.op(i);
334 auto cc = it.op(0);
335 auto vv = it.op(1);
336 color_vec.push_back(vv);
337 item += cc * Symbol("[cl"+to_string(i)+"]");
338 }
339
340 ostringstream coss;
341 for(int i=0; i<color_vec.size(); i++) {
342 coss << " [cl" << i << "]";
343 ff << "L [cl" << i << "]=" << color_vec[i] << ";" << endl;
344 ff << ".sort" << endl;
345 ff << "#call SUNTrace" << endl;
346 ff << ".sort" << endl;
347 if(form_using_su3) {
348 ff << "id NF^reX?=3^reX;" << endl;
349 ff << "id I2R=1/2;" << endl;
350 ff << "id NA^reX?=8^reX;" << endl;
351 ff << ".sort" << endl;
352 }
353 }
354 ff << endl;
355
356 // methods to handle TR objects
357 auto tr_mode = form_trace_mode;
358 exset trs;
359 find(item,TR(w),trs);
360 if(form_trace_mode==form_trace_auto) {
361 if(trs.size()<2) tr_mode = form_trace_all;
362 else tr_mode = form_trace_each_each;
363 }
364 if(tr_mode==form_trace_all) {
365 mapTR tr;
366 item = tr(item);
367 ff << "L [o]=" << item << ";" << endl;
368 ff << ".sort" << endl;
369 ff << "#do i = 1,1" << endl;
370 ff << "id once HF(reX?)=reX;" << endl;
371 ff << idstr;
372 ff << "if(count(HF,1)>0) redefine i \"0\";" << endl;
373 ff << ".sort" << endl;
374 ff << "#enddo" << endl;
375 ff << "contract 0;" << endl;
376 ff << ".sort" << endl;
377 ff << idstr << ".sort" << endl;
378 ff << endl;
379 for(int gl=1; gl<=tr.glmax; gl++) {
380 if(form_using_gamma5) {
381 ff << ".sort" << endl;
382 if(form_using_dim4) ff << "Dimension 4;" << endl;
383 else ff << "Dimension d;" << endl;
384 ff << "Indices [g5_i1], [g5_i2], [g5_i3], [g5_i4];" << endl;
385 ff << "id g_(" << gl << ",5_) = e_([g5_i1],[g5_i2],[g5_i3],[g5_i4])*g_(" << gl << ",[g5_i1],[g5_i2],[g5_i3],[g5_i4])/24;" << endl;
386 ff << "sum [g5_i1],[g5_i2],[g5_i3],[g5_i4];" << endl;
387 ff << ".sort" << endl;
388 }
389 if(form_using_dim4) ff << "trace4 " << gl << ";" << endl;
390 else ff << "tracen " << gl << ";" << endl;
391 ff << ".sort" << endl;
392 ff << idstr << ".sort" << endl;
393 }
394 } else if(tr_mode==form_trace_each_all) {
395 exmap tr2v;
396 int trn=0;
397 exvector trvec;
398 for(auto tr : trs) {
399 tr2v[tr] = Symbol("[tr"+to_string(trn)+"]");
400 auto tri = mapGamma(gid)(tr.op(0));
401 trvec.push_back(tri);
402 trn++;
403 }
404 item = item.subs(tr2v);
405 for(int i=0; i<trvec.size(); i++) {
406 ff << "L [tr" << i << "]=" << trvec[i] << ";" << endl;
407 if(form_using_gamma5) {
408 ff << ".sort" << endl;
409 if(form_using_dim4) ff << "Dimension 4;" << endl;
410 else ff << "Dimension d;" << endl;
411 ff << "Indices [g5_i1], [g5_i2], [g5_i3], [g5_i4];" << endl;
412 ff << "id g_(" << gid << ",5_) = e_([g5_i1],[g5_i2],[g5_i3],[g5_i4])*g_(" << gid << ",[g5_i1],[g5_i2],[g5_i3],[g5_i4])/24;" << endl;
413 ff << "sum [g5_i1],[g5_i2],[g5_i3],[g5_i4];" << endl;
414 }
415 if(form_using_dim4) ff << "trace4 " << gid << ";" << endl;
416 else ff << "tracen " << gid << ";" << endl;
417 ff << ".sort" << endl;
418 ff << idstr << ".sort" << endl;
419 }
420 ff << "L [o]=" << item << ";" << endl;
421 ff << ".sort" << endl;
422 ff << "#do i = 1,1" << endl;
423 ff << "id once HF(reX?)=reX;" << endl;
424 ff << idstr;
425 ff << "if(count(HF,1)>0) redefine i \"0\";" << endl;
426 ff << ".sort" << endl;
427 ff << "#enddo" << endl;
428 ff << idstr << ".sort" << endl;
429 ff << endl;
430 } else if(tr_mode==form_trace_each_each) {
431 exmap tr2v;
432 int trn=0;
433 exvector trvec;
434 for(auto tr : trs) {
435 tr2v[tr] = Symbol("trcN"+to_string(trn));
436 auto tri = mapGamma(gid)(tr.op(0));
437 trvec.push_back(tri);
438 trn++;
439 }
440 item = item.subs(tr2v);
441
442 if(color_vec.size()>0) ff << "drop" << coss.str() << ";" << endl;
443 ff << "L [o]=" << item << ";" << endl;
444 ff << ".sort" << endl;
445 ff << "#do i = 1,1" << endl;
446 ff << "id once HF(reX?)=reX;" << endl;
447 ff << idstr;
448 ff << "if(count(HF,1)>0) redefine i \"0\";" << endl;
449 ff << ".sort" << endl;
450 ff << "#enddo" << endl;
451 ff << endl;
452
453 for(int i=0; i<trvec.size(); i++) {
454 ff << "L [tr" << i << "]=" << trvec[i] << ";" << endl;
455 if(form_using_gamma5) {
456 ff << ".sort" << endl;
457 if(form_using_dim4) ff << "Dimension 4;" << endl;
458 else ff << "Dimension d;" << endl;
459 ff << "Indices [g5_i1], [g5_i2], [g5_i3], [g5_i4];" << endl;
460 ff << "id g_(" << gid << ",5_) = e_([g5_i1],[g5_i2],[g5_i3],[g5_i4])*g_(" << gid << ",[g5_i1],[g5_i2],[g5_i3],[g5_i4])/24;" << endl;
461 ff << "sum [g5_i1],[g5_i2],[g5_i3],[g5_i4];" << endl;
462 }
463 if(form_using_dim4) ff << "trace4 " << gid << ";" << endl;
464 else ff << "tracen " << gid << ";" << endl;
465 ff << ".sort" << endl;
466 ff << idstr << ".sort" << endl;
467 ff << "drop [tr" << i << "];" << endl;
468 ff << "id trcN" << i << "=[tr" << i << "];" << endl;
469 ff << ".sort" << endl;
470 ff << idstr << ".sort" << endl;
471 ff << endl;
472 }
473 } else {
474 throw Error("runform: unsupported form_trace_mode = " + to_string(form_trace_mode));
475 }
476
477 ff << "contract 0;" << endl;
478 ff << ".sort" << endl;
479 ff << idstr << ".sort" << endl;
480
481 if(verb==1) {
482 cout << "\r \r";
483 cout << PRE << "\\--Form Script @ " << c << " / " << total << flush;
484 } else if(verb>1) {
485 cout << "--------------------------------------" << endl;
486 cout << "Form Script @ " << c << " / " << total << endl;
487 cout << "--------------------------------------" << endl;
488 cout << ss.str() << endl;
489 }
490
491 auto script = ss.str();
492 string_replace_all(script, "sin(", "sin_(");
493 string_replace_all(script, "cos(", "cos_(");
494 try {
495 auto otmp = fprc.Execute(script);
496 if(verb>2) {
497 cout << "--------------------------------------" << endl;
498 cout << "Form Output @ " << c << " / " << total << endl;
499 cout << "--------------------------------------" << endl;
500 cout << otmp << endl;
501 }
502
503 ostr += otmp;
504 ss.clear();
505 ss.str("");
506
507 if(c<total) ostr += ",";
508 c++;
509 } catch(Error& err) {
510 form_map.erase(pid);
511 throw;
512 }
513 }
514 if(verb==1) cout << endl;
515 ostr += "}";
516
517 string_replace_all(ostr, "[", "(");
518 string_replace_all(ostr, "]", ")");
519 string_replace_all(ostr, "\\\n", "");
520 string_replace_all(ostr, "\n", "");
521 string_replace_all(ostr, " ","");
522 for(auto v : vec_lst) {
523 string pat(ex_to<Vector>(v).name.get_name());
524 string from = pat+"(";
525 string to = "d_("+pat+",";
526 string_replace_all(ostr, from, to);
527 from = pat+".";
528 to = pat+"__";
529 string_replace_all(ostr, from, to);
530 }
531
532 string_replace_all(ostr, "d_(", "SP(");
533 string_replace_all(ostr, "e_(", "LC(");
534 string_replace_all(ostr, "sin_(", "sin(");
535 string_replace_all(ostr, "cos_(", "cos(");
536 string_replace_all(ostr, "g_(", "DG(");
537 string_replace_all(ostr, ",5_", ",5");
538 string_replace_all(ostr, ",6_", ",6");
539 string_replace_all(ostr, ",7_", ",7");
540 string_replace_all(ostr, "gi_(", "GI(");
541 string_replace_all(ostr, "TTR(", "TTRX(");
542
543 st["I2R"] = TF;
544 st["NA"] = NA;
545 st["NF"] = NF;
546 st["I"] = I;
547 st["i_"] = I;
548 st["pi_"] = Pi;
549
550 Parser fp(st);
551 fp.FTable.insert({{"SP", 2}, reader_func(SP_reader)});
552 fp.FTable.insert({{"SP", 1}, reader_func(SP_reader)});
553 //fp.FTable.insert({{"LC", 4}, reader_func(LC_reader)});
554 for(int i=3; i<10; i++) fp.FTable.insert({{"LC", i}, reader_func(LC_reader)});
555 fp.FTable.insert({{"GMat", 3}, reader_func(GMat_reader)});
556 for(int i=1; i<30; i++) fp.FTable.insert({{"T", i}, reader_func(SUNT_reader)});
557 for(int i=1; i<30; i++) fp.FTable.insert({{"TTRX", i}, reader_func(TTR_reader)});
558 for(int i=1; i<30; i++) fp.FTable.insert({{"DG", i}, reader_func(DGamma_reader)});
559 fp.FTable.insert({{"GI", 0}, reader_func(gi_reader)});
560 fp.FTable.insert({{"GI", 1}, reader_func(gi_reader)});
561 ex ret = fp.Read(ostr);
562 if(!islst) ret = ret.op(0);
563 return ret;
564 }}
565
572 ex form(const ex & iexpr, int verb) {
573 ex expr = iexpr;
574 if(!is_a<lst>(expr)) {
575 static MapFunction mf([](const ex & e, MapFunction & self)->ex{
576 if(!e.has(TR(w))) return e;
577 else if(e.match(TR(w))) {
578 if(is_a<mul>(e.op(0))) {
579 ex c = 1, v = 1;
580 for(auto const & ei : e.op(0)) {
581 if(DGamma::has(ei)) v *= ei;
582 else c *= ei;
583 }
584 return c*TR(v);
585 } else return e;
586 } else return e.map(self);
587 });
588 expr = mf(expr);
589 }
590 if(form_expand_mode==form_expand_none || is_a<lst>(expr)) return runform(expr, verb);
591 else if(form_expand_mode==form_expand_tr) {
592 auto cv_lst = collect_lst(expr.subs(SP_map), TR(w));
593 lst to_lst;
594 for(auto cv : cv_lst) to_lst.append(cv.op(0)*cv.op(1));
595 lst out_lst = ex_to<lst>(runform(to_lst, verb));
596
597 ex ret = 0;
598 for(int i=0; i<cv_lst.nops(); i++) ret += out_lst.op(i);
599
600 return ret.subs(SP_map);
601 } else if(form_expand_mode==form_expand_ci) {
602 auto cv_lst = collect_lst(expr.subs(SP_map), [](const ex & e)->bool {
603 return e.has(TR(w)) || Index::hasc(e);
604 });
605 lst to_lst;
606 for(auto cv : cv_lst) to_lst.append(cv.op(0)*cv.op(1));
607 lst out_lst = ex_to<lst>(runform(to_lst, verb));
608
609 ex ret = 0;
610 for(int i=0; i<cv_lst.nops(); i++) ret += out_lst.op(i);
611
612 return ret.subs(SP_map);
613 } else if(form_expand_mode==form_expand_li) {
614 auto cv_lst = collect_lst(expr.subs(SP_map), [](const ex & e)->bool {
615 return e.has(TR(w)) || Index::hasv(e);
616 });
617 lst to_lst;
618 for(auto cv : cv_lst) to_lst.append(cv.op(0)*cv.op(1));
619 lst out_lst = ex_to<lst>(runform(to_lst, verb));
620
621 ex ret = 0;
622 for(int i=0; i<cv_lst.nops(); i++) ret += out_lst.op(i);
623
624 return ret.subs(SP_map);
625 } else if(form_expand_mode==form_expand_all) {
626 auto cv_lst = collect_lst(expr.subs(SP_map), [](const ex & e)->bool {
627 return e.has(TR(w)) || SUNT::has(e) || SUNF::has(e) || SUNF4::has(e) || Index::has(e) || DGamma::has(e);
628 });
629 lst to_lst;
630 for(auto cv : cv_lst) to_lst.append(cv.op(1));
631 lst out_lst = ex_to<lst>(runform(to_lst, verb));
632
633 ex ret = 0;
634 for(int i=0; i<cv_lst.nops(); i++) ret += cv_lst.op(i).op(0) * out_lst.op(i);
635
636 return ret.subs(SP_map);
637 } else throw Error("form: unsupported form_expand_mode = " + to_string(form_expand_mode));
638 return 0;
639 }
640
646 ex charge_conjugate(const ex & expr) {
647 if(expr.has(GMat(w1,w2,w3))) throw Error("charge_conjugate: GMat found.");
648
649 if(!DGamma::has(expr) && !AsGamma::has(expr)) return expr;
650 if(is_a<DGamma>(expr)) {
651 DGamma g = ex_to<DGamma>(expr);
652 if(is_a<Vector>(g.pi) || is_a<Index>(g.pi)) return -expr;
653 else if(is_zero(g.pi-1) || is_zero(g.pi-5)) return expr;
654 } else if(is_a<AsGamma>(expr)) {
655 AsGamma ag = ex_to<AsGamma>(expr);
656 ex sign = 1;
657 lst pis_lst;
658 for(int i=ag.pis.size()-1; i>=0; --i) {
659 ex pi = ag.pis[i];
660 if(is_a<Vector>(pi) || is_a<Index>(pi)) sign *= -1;
661 else if(is_zero(pi-1) || is_zero(pi-5)) sign *= 1;
662 else throw Error("charge_conjugate: only p/i/1/5 supported.");
663 pis_lst.append(pi);
664 }
665 return sign * AsGamma::from(pis_lst);
666 }
667
668 if(is_a<add>(expr)) {
669 ex ret = 0;
670 for(auto item : expr) ret += charge_conjugate(item);
671 return ret;
672 } else if(is_a<mul>(expr)) {
673 ex ret = 1;
674 for(auto item : expr) ret *= charge_conjugate(item);
675 return ret;
676 } else if(is_a<ncmul>(expr)) {
677 ex ret = 1;
678 int n = expr.nops();
679 for(int i=n-1; i>-1; i--) ret *= charge_conjugate(expr.op(i));
680 return ret;
681 }
682 cout << expr << endl;
683 throw Error("charge_conjugate: unexpected region.");
684 return 0;
685 }
686
692 ex gamma_transpose(const ex & expr) {
693 if(expr.has(GMat(w1,w2,w3))) throw Error("charge_conjugate: GMat found.");
694 if(AsGamma::has(expr)) throw Error("gamma_transpose: Not supported for AsGamma.");
695
696 if(!DGamma::has(expr)) return expr;
697 if(is_a<DGamma>(expr)) {
698 if(expr.is_equal(DGamma::C)) return (-1)*DGamma::C;
699 DGamma g = ex_to<DGamma>(expr);
700 g.isTr = !g.isTr;
701 return g;
702 }
703
704 if(is_a<add>(expr)) {
705 ex ret = 0;
706 for(auto item : expr) ret += gamma_transpose(item);
707 return ret;
708 } else if(is_a<mul>(expr)) {
709 ex ret = 1;
710 for(auto item : expr) ret *= gamma_transpose(item);
711 return ret;
712 } else if(is_a<ncmul>(expr)) {
713 ex ret = 1;
714 int n = expr.nops();
715 for(int i=n-1; i>-1; i--) ret *= gamma_transpose(expr.op(i));
716 return ret;
717 }
718 cout << "gamma_transpose input:" << expr << endl;
719 throw Error("gamma_transpose: unexpected region.");
720 return 0;
721 }
722
723}
724
glmax
unsigned glmax
Definition Form.cpp:107
HEP.h
HEP header file.
HepLib::DGamma::has
static bool has(const ex &e)
HepLib::Eps::has
static bool has(const ex &e)
HepLib::Index::hasc
static bool hasc(const ex &e)
Definition Basic.cpp:234
HepLib::Index::Dimension
static GiNaC::exmap Dimension
Definition HEP.h:109
HepLib::Index::has
static bool has(const ex &e)
HepLib
HepLib namespace.
Definition BASIC.cpp:17
HepLib::form_using_dim4
bool form_using_dim4
Definition Init.cpp:214
HepLib::NA
const Symbol NA
HepLib::CoPat
lst CoPat(const ex &e, std::function< bool(const ex &)> f)
Definition BASIC.h:768
HepLib::NF
const Symbol NF
HepLib::SP_map
exmap SP_map
Definition Init.cpp:184
HepLib::form_trace_all
const int form_trace_all
Definition Init.cpp:201
HepLib::GAS
ex GAS(const ex &expr, unsigned rl)
function similar to GAD/GSD in FeynClac
Definition DGamma.cpp:280
HepLib::form_trace_mode
int form_trace_mode
Definition Init.cpp:204
HepLib::form_using_su3
bool form_using_su3
Definition Init.cpp:213
HepLib::w
ex w
Definition Init.cpp:93
HepLib::form_trace_each_all
const int form_trace_each_all
Definition Init.cpp:202
HepLib::d
const Symbol d
HepLib::TF
const Symbol TF
HepLib::gamma_transpose
ex gamma_transpose(const ex &expr)
make the transpose operaton M --> M^T
Definition Form.cpp:690
HepLib::as
const Symbol as
HepLib::charge_conjugate
ex charge_conjugate(const ex &expr)
make the charge conjugate operaton, M -> C^{-1} . M^T . C w.r.t. a GMat object
Definition Form.cpp:644
HepLib::collect_lst
lst collect_lst(ex const &expr_in, std::function< bool(const ex &)> has_func, int opt)
the collect function like Mathematica, reture the lst { {c1,v1}, {c2,v2}, ... }
Definition BASIC.cpp:1224
HepLib::form_using_gamma5
bool form_using_gamma5
Definition Init.cpp:215
HepLib::string_replace_all
void string_replace_all(string &str, const string &from, const string &to)
Definition Functions.cpp:148
HepLib::form_trace_each_each
const int form_trace_each_each
Definition Init.cpp:203
HepLib::form_trace_auto
const int form_trace_auto
Definition Init.cpp:200
HepLib::LC
ex LC(ex pi1, ex pi2, ex pi3, ex pi4)
function similar to LCD in FeynCalc
Definition Eps.cpp:179
HepLib::form
ex form(const ex &iexpr, int verb)
evalulate expr in form program, see also the form_trace_mode and form_expand_mode
Definition Form.cpp:570
HepLib::PRE
string PRE
Definition Init.cpp:143
HepLib::SP
ex SP(const ex &a, bool use_map=false)
Definition Pair.cpp:166
HepLib::ex2int
int ex2int(ex num)
ex to integer
Definition BASIC.cpp:895
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