HepLib
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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,I,Pi;
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
156#endprocedure
157.global
158 )EOF";
159 }
160
161 //-----------------------------------------------------------
162 // form
163 //-----------------------------------------------------------
164 namespace {
165 ex runform(const ex &expr_in, int verb) {
166 static map<pid_t, Form> form_map;
167 auto pid = getpid();
168 if((form_map.find(pid)==form_map.end())) { // init section
169 ostringstream ss;
170 ss << init_script << endl;
171 form_map[pid].Init("form");
172 form_map[pid].Execute(ss.str());
173 }
174 Form &fprc = form_map[pid];
175
176 ex expr = expr_in.subs(SP_map);
177 ex all_expr = expr;
178 stringstream sss;
179 FormFormat ids(sss);
180 for(auto kv : SP_map) {
181 ids << "id " << kv.first << "=" << kv.second << ";" << endl;
182 all_expr += iWF(kv.first) * iWF(kv.second);
183 }
184 string idstr = sss.str();
185
186 lst vec_lst, VD_lst, CF_lst, CA_lst, sym_lst;
187 for(const_preorder_iterator i = all_expr.preorder_begin(); i != all_expr.preorder_end(); ++i) {
188 if(is_a<Vector>(*i)) vec_lst.append(*i);
189 else if(is_a<Index>(*i)) {
190 if(ex_to<Index>(*i).dim==d) VD_lst.append(*i);
191 else if(ex_to<Index>(*i).dim==NF) CF_lst.append(*i);
192 else if(ex_to<Index>(*i).dim==NA) CA_lst.append(*i);
193 } else if(is_a<symbol>(*i)) sym_lst.append(*i);
194 else if(is_a<GiNaC::function>(*i)) {
195 static vector<string> fun_vec = {
196 "iWF", "WF", "TR", "sin", "cos", "HF", "TTR", "GMat"
197 };
198 auto func = ex_to<GiNaC::function>(*i).get_name();
199 bool ok = false;
200 for(auto fi : fun_vec) {
201 if(fi==func) { ok = true; break; }
202 }
203 if(!ok) {
204 cout << (*i) << endl;
205 throw Error("runform: Functions not defined in FORM: "+func);
206 }
207 }
208 }
209 vec_lst.sort(); vec_lst.unique();
210 VD_lst.sort(); VD_lst.unique();
211 CF_lst.sort(); CF_lst.unique();
212 CA_lst.sort(); CA_lst.unique();
213 sym_lst.append(d);
214 sym_lst.sort(); sym_lst.unique();
215
216 stringstream ss;
217 FormFormat ff(ss);
218 ff << ".store" << endl;
219 symtab st;
220 if(sym_lst.nops()>0) {
221 ff << "Symbols";
222 for(auto sx : sym_lst) {
223 auto s = ex_to<symbol>(sx);
224 ff << " " << s.get_name();
225 st[s.get_name()] = sx;
226 }
227 ff << ";" << endl;
228 }
229 if(vec_lst.nops()>0) {
230 ff << "Vectors";
231 for(auto vx : vec_lst) {
232 auto v = ex_to<Vector>(vx);
233 ff << " " << v;
234 st[v.name.get_name()] = v;
235 for(auto vvx : vec_lst) {
236 auto vv = ex_to<Vector>(vvx);
237 st[v.name.get_name()+"__"+vv.name.get_name()] = SP(v,vv).subs(SP_map);
238 }
239 }
240 ff << ";" << endl;
241 }
242 if(VD_lst.nops()>0) {
243 if(form_using_dim4) ff << "Dimension 4;" << endl;
244 else ff << "Dimension d;" << endl;
245 ff << "Indices";
246 for(auto ix : VD_lst) {
247 auto i = ex_to<Index>(ix);
248 ff << " " << i;
249 st[i.name.get_name()] = i;
250 auto itr = Index::Dimension.find(ix);
251 if(itr!=Index::Dimension.end()) ff << "=" << itr->second;
252 }
253 ff << ";" << endl;
254 }
255 if(CF_lst.nops()>0) {
256 ff << "Dimension NF;" << endl;
257 ff << "Indices";
258 for(auto ix : CF_lst) {
259 auto i = ex_to<Index>(ix);
260 ff << " " << i;
261 st[i.name.get_name()] = i;
262 auto itr = Index::Dimension.find(ix);
263 if(itr!=Index::Dimension.end()) ff << "=" << itr->second;
264 }
265 ff << ";" << endl;
266 }
267 if(CA_lst.nops()>0) {
268 ff << "Dimension NA;" << endl;
269 ff << "Indices";
270 for(auto ix : CA_lst) {
271 auto i = ex_to<Index>(ix);
272 ff << " " << i;
273 st[i.name.get_name()] = i;
274 auto itr = Index::Dimension.find(ix);
275 if(itr!=Index::Dimension.end()) ff << "=" << itr->second;
276 }
277 ff << ";" << endl;
278 }
279 ff << ".global" << endl;
280 ff << endl;
281
282 // trace and contract
283 bool islst = is_a<lst>(expr);
284 lst expr_lst;
285 if(islst) expr_lst = ex_to<lst>(expr);
286 else expr_lst.append(expr);
287 auto total = expr_lst.nops();
288
289 string ostr;
290 int gid = 1;
291 ostr = "{";
292 int c = 1;
293 int kid = 0;
294 map<ex,int,ex_is_less> e2i_map;
295 for(auto it : expr_lst) {
296 ff << ".store" << endl;
297 ex item = it;
298 item = MapFunction([](const ex & e, MapFunction &self)->ex{
299 if(!e.has(TR(w))) return e;
300 else if(e.match(TR(w))) {
301 ex nd = e.op(0).normal().numer_denom();
302 return TR(nd.op(0))/nd.op(1);
303 } else return e.map(self);
304 })(item);
305 item = normal(item); // TODO: normal
306 // pull out global common factor
307 item = collect_common_factors(item);
308 item = CoPat(item,[](const ex &e)->bool{return Index::has(e) || DGamma::has(e) || Eps::has(e);});
309 auto ckey = item.op(0);
310 if(!is_a<numeric>(ckey)) {
311 int ckid;
312 if(e2i_map.find(ckey)==e2i_map.end()) {
313 kid++;
314 e2i_map[ckey] = kid;
315 ckid = kid;
316 } else ckid = e2i_map[ckey];
317 string gCF = "gCF" + to_string(ckid);
318 st[gCF] = item.op(0);
319 item = Symbol(gCF) * item.op(1);
320 } else {
321 item = ckey * item.op(1);
322 }
323
324 // pull out color factor
325 auto cv_lst = collect_lst(item, [](const ex &e)->bool{return Index::hasc(e);});
326 item=0;
327 exvector color_vec;
328 for(int i=0; i<cv_lst.nops(); i++) {
329 auto it = cv_lst.op(i);
330 auto cc = it.op(0);
331 auto vv = it.op(1);
332 color_vec.push_back(vv);
333 item += cc * Symbol("[cl"+to_string(i)+"]");
334 }
335
336 ostringstream coss;
337 for(int i=0; i<color_vec.size(); i++) {
338 coss << " [cl" << i << "]";
339 ff << "L [cl" << i << "]=" << color_vec[i] << ";" << endl;
340 ff << ".sort" << endl;
341 ff << "#call SUNTrace" << endl;
342 ff << ".sort" << endl;
343 if(form_using_su3) {
344 ff << "id NF^reX?=3^reX;" << endl;
345 ff << "id I2R=1/2;" << endl;
346 ff << "id NA^reX?=8^reX;" << endl;
347 ff << ".sort" << endl;
348 }
349 }
350 ff << endl;
351
352 // methods to handle TR objects
353 auto tr_mode = form_trace_mode;
354 exset trs;
355 find(item,TR(w),trs);
356 if(form_trace_mode==form_trace_auto) {
357 if(trs.size()<2) tr_mode = form_trace_all;
358 else tr_mode = form_trace_each_each;
359 }
360 if(tr_mode==form_trace_all) {
361 mapTR tr;
362 item = tr(item);
363 ff << "L [o]=" << item << ";" << endl;
364 ff << ".sort" << endl;
365 ff << "#do i = 1,1" << endl;
366 ff << "id once HF(reX?)=reX;" << endl;
367 ff << idstr;
368 ff << "if(count(HF,1)>0) redefine i \"0\";" << endl;
369 ff << ".sort" << endl;
370 ff << "#enddo" << endl;
371 ff << "contract 0;" << endl;
372 ff << ".sort" << endl;
373 ff << idstr << ".sort" << endl;
374 ff << endl;
375 for(int gl=1; gl<=tr.glmax; gl++) {
376 if(form_using_gamma5) {
377 ff << ".sort" << endl;
378 if(form_using_dim4) ff << "Dimension 4;" << endl;
379 else ff << "Dimension d;" << endl;
380 ff << "Indices [g5_i1], [g5_i2], [g5_i3], [g5_i4];" << endl;
381 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;
382 ff << "sum [g5_i1],[g5_i2],[g5_i3],[g5_i4];" << endl;
383 ff << ".sort" << endl;
384 }
385 if(form_using_dim4) ff << "trace4 " << gl << ";" << endl;
386 else ff << "tracen " << gl << ";" << endl;
387 ff << ".sort" << endl;
388 ff << idstr << ".sort" << endl;
389 }
390 } else if(tr_mode==form_trace_each_all) {
391 exmap tr2v;
392 int trn=0;
393 exvector trvec;
394 for(auto tr : trs) {
395 tr2v[tr] = Symbol("[tr"+to_string(trn)+"]");
396 auto tri = mapGamma(gid)(tr.op(0));
397 trvec.push_back(tri);
398 trn++;
399 }
400 item = item.subs(tr2v);
401 for(int i=0; i<trvec.size(); i++) {
402 ff << "L [tr" << i << "]=" << trvec[i] << ";" << endl;
403 if(form_using_gamma5) {
404 ff << ".sort" << endl;
405 if(form_using_dim4) ff << "Dimension 4;" << endl;
406 else ff << "Dimension d;" << endl;
407 ff << "Indices [g5_i1], [g5_i2], [g5_i3], [g5_i4];" << endl;
408 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;
409 ff << "sum [g5_i1],[g5_i2],[g5_i3],[g5_i4];" << endl;
410 }
411 if(form_using_dim4) ff << "trace4 " << gid << ";" << endl;
412 else ff << "tracen " << gid << ";" << endl;
413 ff << ".sort" << endl;
414 ff << idstr << ".sort" << endl;
415 }
416 ff << "L [o]=" << item << ";" << endl;
417 ff << ".sort" << endl;
418 ff << "#do i = 1,1" << endl;
419 ff << "id once HF(reX?)=reX;" << endl;
420 ff << idstr;
421 ff << "if(count(HF,1)>0) redefine i \"0\";" << endl;
422 ff << ".sort" << endl;
423 ff << "#enddo" << endl;
424 ff << idstr << ".sort" << endl;
425 ff << endl;
426 } else if(tr_mode==form_trace_each_each) {
427 exmap tr2v;
428 int trn=0;
429 exvector trvec;
430 for(auto tr : trs) {
431 tr2v[tr] = Symbol("trcN"+to_string(trn));
432 auto tri = mapGamma(gid)(tr.op(0));
433 trvec.push_back(tri);
434 trn++;
435 }
436 item = item.subs(tr2v);
437
438 if(color_vec.size()>0) ff << "drop" << coss.str() << ";" << endl;
439 ff << "L [o]=" << item << ";" << endl;
440 ff << ".sort" << endl;
441 ff << "#do i = 1,1" << endl;
442 ff << "id once HF(reX?)=reX;" << endl;
443 ff << idstr;
444 ff << "if(count(HF,1)>0) redefine i \"0\";" << endl;
445 ff << ".sort" << endl;
446 ff << "#enddo" << endl;
447 ff << endl;
448
449 for(int i=0; i<trvec.size(); i++) {
450 ff << "L [tr" << i << "]=" << trvec[i] << ";" << endl;
451 if(form_using_gamma5) {
452 ff << ".sort" << endl;
453 if(form_using_dim4) ff << "Dimension 4;" << endl;
454 else ff << "Dimension d;" << endl;
455 ff << "Indices [g5_i1], [g5_i2], [g5_i3], [g5_i4];" << endl;
456 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;
457 ff << "sum [g5_i1],[g5_i2],[g5_i3],[g5_i4];" << endl;
458 }
459 if(form_using_dim4) ff << "trace4 " << gid << ";" << endl;
460 else ff << "tracen " << gid << ";" << endl;
461 ff << ".sort" << endl;
462 ff << idstr << ".sort" << endl;
463 ff << "drop [tr" << i << "];" << endl;
464 ff << "id trcN" << i << "=[tr" << i << "];" << endl;
465 ff << ".sort" << endl;
466 ff << idstr << ".sort" << endl;
467 ff << endl;
468 }
469 } else {
470 throw Error("runform: unsupported form_trace_mode = " + to_string(form_trace_mode));
471 }
472
473 ff << "contract 0;" << endl;
474 ff << ".sort" << endl;
475 ff << idstr << ".sort" << endl;
476
477 if(verb==1) {
478 cout << "\r \r";
479 cout << PRE << "\\--Form Script @ " << c << " / " << total << flush;
480 } else if(verb>1) {
481 cout << "--------------------------------------" << endl;
482 cout << "Form Script @ " << c << " / " << total << endl;
483 cout << "--------------------------------------" << endl;
484 cout << ss.str() << endl;
485 }
486
487 auto script = ss.str();
488 string_replace_all(script, "sin(", "sin_(");
489 string_replace_all(script, "cos(", "cos_(");
490 try {
491 auto otmp = fprc.Execute(script);
492 if(verb>2) {
493 cout << "--------------------------------------" << endl;
494 cout << "Form Output @ " << c << " / " << total << endl;
495 cout << "--------------------------------------" << endl;
496 cout << otmp << endl;
497 }
498
499 ostr += otmp;
500 ss.clear();
501 ss.str("");
502
503 if(c<total) ostr += ",";
504 c++;
505 } catch(Error& err) {
506 form_map.erase(pid);
507 throw;
508 }
509 }
510 if(verb==1) cout << endl;
511 ostr += "}";
512
513 string_replace_all(ostr, "[", "(");
514 string_replace_all(ostr, "]", ")");
515 string_replace_all(ostr, "\\\n", "");
516 string_replace_all(ostr, "\n", "");
517 string_replace_all(ostr, " ","");
518 for(auto v : vec_lst) {
519 string pat(ex_to<Vector>(v).name.get_name());
520 string from = pat+"(";
521 string to = "d_("+pat+",";
522 string_replace_all(ostr, from, to);
523 from = pat+".";
524 to = pat+"__";
525 string_replace_all(ostr, from, to);
526 }
527
528 string_replace_all(ostr, "d_(", "SP(");
529 string_replace_all(ostr, "e_(", "LC(");
530 string_replace_all(ostr, "sin_(", "sin(");
531 string_replace_all(ostr, "cos_(", "cos(");
532 string_replace_all(ostr, "g_(", "DG(");
533 string_replace_all(ostr, ",5_", ",5");
534 string_replace_all(ostr, ",6_", ",6");
535 string_replace_all(ostr, ",7_", ",7");
536 string_replace_all(ostr, "gi_(", "GI(");
537 string_replace_all(ostr, "TTR(", "TTRX(");
538
539 st["I2R"] = TF;
540 st["NA"] = NA;
541 st["NF"] = NF;
542 st["I"] = I;
543 st["i_"] = I;
544
545 Parser fp(st);
546 fp.FTable.insert({{"SP", 2}, reader_func(SP_reader)});
547 fp.FTable.insert({{"SP", 1}, reader_func(SP_reader)});
548 //fp.FTable.insert({{"LC", 4}, reader_func(LC_reader)});
549 for(int i=3; i<10; i++) fp.FTable.insert({{"LC", i}, reader_func(LC_reader)});
550 fp.FTable.insert({{"GMat", 3}, reader_func(GMat_reader)});
551 for(int i=1; i<30; i++) fp.FTable.insert({{"T", i}, reader_func(SUNT_reader)});
552 for(int i=1; i<30; i++) fp.FTable.insert({{"TTRX", i}, reader_func(TTR_reader)});
553 for(int i=1; i<30; i++) fp.FTable.insert({{"DG", i}, reader_func(DGamma_reader)});
554 fp.FTable.insert({{"GI", 0}, reader_func(gi_reader)});
555 fp.FTable.insert({{"GI", 1}, reader_func(gi_reader)});
556 ex ret = fp.Read(ostr);
557 if(!islst) ret = ret.op(0);
558 return ret;
559 }}
560
567 ex form(const ex & iexpr, int verb) {
568 ex expr = iexpr;
569 if(!is_a<lst>(expr)) {
570 static MapFunction mf([](const ex & e, MapFunction & self)->ex{
571 if(!e.has(TR(w))) return e;
572 else if(e.match(TR(w))) {
573 if(is_a<mul>(e.op(0))) {
574 ex c = 1, v = 1;
575 for(auto const & ei : e.op(0)) {
576 if(DGamma::has(ei)) v *= ei;
577 else c *= ei;
578 }
579 return c*TR(v);
580 } else return e;
581 } else return e.map(self);
582 });
583 expr = mf(expr);
584 }
585 if(form_expand_mode==form_expand_none || is_a<lst>(expr)) return runform(expr, verb);
586 else if(form_expand_mode==form_expand_tr) {
587 auto cv_lst = collect_lst(expr.subs(SP_map), TR(w));
588 lst to_lst;
589 for(auto cv : cv_lst) to_lst.append(cv.op(0)*cv.op(1));
590 lst out_lst = ex_to<lst>(runform(to_lst, verb));
591
592 ex ret = 0;
593 for(int i=0; i<cv_lst.nops(); i++) ret += out_lst.op(i);
594
595 return ret.subs(SP_map);
596 } else if(form_expand_mode==form_expand_ci) {
597 auto cv_lst = collect_lst(expr.subs(SP_map), [](const ex & e)->bool {
598 return e.has(TR(w)) || Index::hasc(e);
599 });
600 lst to_lst;
601 for(auto cv : cv_lst) to_lst.append(cv.op(0)*cv.op(1));
602 lst out_lst = ex_to<lst>(runform(to_lst, verb));
603
604 ex ret = 0;
605 for(int i=0; i<cv_lst.nops(); i++) ret += out_lst.op(i);
606
607 return ret.subs(SP_map);
608 } else if(form_expand_mode==form_expand_li) {
609 auto cv_lst = collect_lst(expr.subs(SP_map), [](const ex & e)->bool {
610 return e.has(TR(w)) || Index::hasv(e);
611 });
612 lst to_lst;
613 for(auto cv : cv_lst) to_lst.append(cv.op(0)*cv.op(1));
614 lst out_lst = ex_to<lst>(runform(to_lst, verb));
615
616 ex ret = 0;
617 for(int i=0; i<cv_lst.nops(); i++) ret += out_lst.op(i);
618
619 return ret.subs(SP_map);
620 } else if(form_expand_mode==form_expand_all) {
621 auto cv_lst = collect_lst(expr.subs(SP_map), [](const ex & e)->bool {
622 return e.has(TR(w)) || SUNT::has(e) || SUNF::has(e) || SUNF4::has(e) || Index::has(e) || DGamma::has(e);
623 });
624 lst to_lst;
625 for(auto cv : cv_lst) to_lst.append(cv.op(1));
626 lst out_lst = ex_to<lst>(runform(to_lst, verb));
627
628 ex ret = 0;
629 for(int i=0; i<cv_lst.nops(); i++) ret += cv_lst.op(i).op(0) * out_lst.op(i);
630
631 return ret.subs(SP_map);
632 } else throw Error("form: unsupported form_expand_mode = " + to_string(form_expand_mode));
633 return 0;
634 }
635
641 ex charge_conjugate(const ex & expr) {
642 if(expr.has(GMat(w1,w2,w3))) throw Error("charge_conjugate: GMat found.");
643
644 if(!DGamma::has(expr) && !AsGamma::has(expr)) return expr;
645 if(is_a<DGamma>(expr)) {
646 DGamma g = ex_to<DGamma>(expr);
647 if(is_a<Vector>(g.pi) || is_a<Index>(g.pi)) return -expr;
648 else if(is_zero(g.pi-1) || is_zero(g.pi-5)) return expr;
649 } else if(is_a<AsGamma>(expr)) {
650 AsGamma ag = ex_to<AsGamma>(expr);
651 ex sign = 1;
652 lst pis_lst;
653 for(int i=ag.pis.size()-1; i>=0; --i) {
654 ex pi = ag.pis[i];
655 if(is_a<Vector>(pi) || is_a<Index>(pi)) sign *= -1;
656 else if(is_zero(pi-1) || is_zero(pi-5)) sign *= 1;
657 else throw Error("charge_conjugate: only p/i/1/5 supported.");
658 pis_lst.append(pi);
659 }
660 return sign * AsGamma::from(pis_lst);
661 }
662
663 if(is_a<add>(expr)) {
664 ex ret = 0;
665 for(auto item : expr) ret += charge_conjugate(item);
666 return ret;
667 } else if(is_a<mul>(expr)) {
668 ex ret = 1;
669 for(auto item : expr) ret *= charge_conjugate(item);
670 return ret;
671 } else if(is_a<ncmul>(expr)) {
672 ex ret = 1;
673 int n = expr.nops();
674 for(int i=n-1; i>-1; i--) ret *= charge_conjugate(expr.op(i));
675 return ret;
676 }
677 cout << expr << endl;
678 throw Error("charge_conjugate: unexpected region.");
679 return 0;
680 }
681
687 ex gamma_transpose(const ex & expr) {
688 if(expr.has(GMat(w1,w2,w3))) throw Error("charge_conjugate: GMat found.");
689 if(AsGamma::has(expr)) throw Error("gamma_transpose: Not supported for AsGamma.");
690
691 if(!DGamma::has(expr)) return expr;
692 if(is_a<DGamma>(expr)) {
693 if(expr.is_equal(DGamma::C)) return (-1)*DGamma::C;
694 DGamma g = ex_to<DGamma>(expr);
695 g.isTr = !g.isTr;
696 return g;
697 }
698
699 if(is_a<add>(expr)) {
700 ex ret = 0;
701 for(auto item : expr) ret += gamma_transpose(item);
702 return ret;
703 } else if(is_a<mul>(expr)) {
704 ex ret = 1;
705 for(auto item : expr) ret *= gamma_transpose(item);
706 return ret;
707 } else if(is_a<ncmul>(expr)) {
708 ex ret = 1;
709 int n = expr.nops();
710 for(int i=n-1; i>-1; i--) ret *= gamma_transpose(expr.op(i));
711 return ret;
712 }
713 cout << "gamma_transpose input:" << expr << endl;
714 throw Error("gamma_transpose: unexpected region.");
715 return 0;
716 }
717
718}
719
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:725
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:685
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:639
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:1222
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:565
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:893
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