/** @file lortensor.cpp
*
- * Implementation of GiNaC´s lortensor objects.
- * No real implementation yet, do be done. */
+ * Implementation of GiNaC's Lorentz tensors. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include "add.h"
#include "mul.h"
#include "debugmsg.h"
-#include "flags.h"
#include "lst.h"
#include "lortensor.h"
-#include "utils.h"
#include "operators.h"
#include "tinfos.h"
#include "power.h"
-#include "symbol.h"
+#include "archive.h"
+#include "utils.h"
+#include "config.h"
-#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+
+GINAC_IMPLEMENT_REGISTERED_CLASS(lortensor, indexed)
//////////
// default constructor, destructor, copy constructor assignment operator and helpers
// public
-lortensor::lortensor()
-{
- debugmsg("lortensor default constructor",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- name=autoname_prefix()+ToString(serial);
- tinfo_key=TINFO_lortensor;
-}
-
-lortensor::~lortensor()
-{
- debugmsg("lortensor destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
-}
-
-lortensor::lortensor(lortensor const & other)
+lortensor::lortensor() : inherited(TINFO_lortensor), type(invalid)
{
- debugmsg("lortensor copy constructor",LOGLEVEL_CONSTRUCT);
- copy (other);
-}
-
-lortensor const & lortensor::operator=(lortensor const & other)
-{
- debugmsg("lortensor operator=",LOGLEVEL_ASSIGNMENT);
- if (this != & other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ debugmsg("lortensor default constructor",LOGLEVEL_CONSTRUCT);
+ serial=next_serial++;
+ name=autoname_prefix()+ToString(serial);
}
//protected
-void lortensor::copy(lortensor const & other)
+void lortensor::copy(const lortensor & other)
{
- indexed::copy(other);
- type=other.type;
- name=other.name;
- serial=other.serial;
+ inherited::copy(other);
+ type=other.type;
+ name=other.name;
+ serial=other.serial;
}
void lortensor::destroy(bool call_parent)
{
- if (call_parent) {
- indexed::destroy(call_parent);
- }
+ if (call_parent) inherited::destroy(call_parent);
}
//////////
// protected
-lortensor::lortensor(lortensor_types const lt, string const & n) : type(lt), name(n)
+/** Construct object without any Lorentz index. This constructor is for
+ * internal use only. */
+lortensor::lortensor(lortensor_types const lt, const std::string & n) : type(lt), name(n)
+{
+ debugmsg("lortensor constructor from lortensor_types,string",LOGLEVEL_CONSTRUCT);
+ if (lt == lortensor_symbolic)
+ serial = next_serial++;
+ else
+ serial = 0;
+ tinfo_key = TINFO_lortensor;
+}
+
+/** Construct object with one Lorentz index. This constructor is for
+ * internal use only. Use the lortensor_vector() or lortensor_symbolic()
+ * functions instead.
+ * @see lortensor_vector
+ * @see lortensor_symbolic */
+lortensor::lortensor(lortensor_types const lt, const std::string & n, const ex & mu) : inherited(mu), type(lt), name(n)
+{
+ debugmsg("lortensor constructor from lortensor_types,string,ex",LOGLEVEL_CONSTRUCT);
+ GINAC_ASSERT(all_of_type_lorentzidx());
+ if (lt == lortensor_symbolic)
+ serial = next_serial++;
+ else
+ serial = 0;
+ tinfo_key=TINFO_lortensor;
+}
+
+/** Construct object with two Lorentz indices. This constructor is for
+ * internal use only. Use the lortensor_g(), lortensor_delta() or
+ * lortensor_symbolic() functions instead.
+ * @see lortensor_g
+ * @see lortensor_delta
+ * @see lortensor_symbolic */
+lortensor::lortensor(lortensor_types const lt, const std::string & n, const ex & mu, const ex & nu) : inherited(mu,nu), type(lt), name(n)
+{
+ debugmsg("lortensor constructor from lortensor_types,string,ex,ex",LOGLEVEL_CONSTRUCT);
+ GINAC_ASSERT(all_of_type_lorentzidx());
+ if (lt == lortensor_symbolic)
+ serial = next_serial++;
+ else
+ serial = 0;
+ tinfo_key=TINFO_lortensor;
+}
+
+/** Construct object with three Lorentz indices. This constructor is for
+ * internal use only. Use the lortensor_symbolic() function instead.
+ * @see lortensor_symbolic */
+lortensor::lortensor(lortensor_types const lt, const std::string & n, const ex & mu, const ex & nu, const ex & rho) : inherited(mu,nu,rho), type(lt), name(n)
+{
+ debugmsg("lortensor constructor from lortensor_types,string,ex,ex,ex",LOGLEVEL_CONSTRUCT);
+ GINAC_ASSERT(all_of_type_lorentzidx());
+ if (lt == lortensor_symbolic)
+ serial = next_serial++;
+ else
+ serial = 0;
+ tinfo_key=TINFO_lortensor;
+}
+
+/** Construct object with four Lorentz indices. This constructor is for
+ * internal use only. Use the lortensor_epsilon() or lortensor_symbolic()
+ * functions instead.
+ * @see lortensor_epsilon
+ * @see lortensor_symbolic */
+lortensor::lortensor(lortensor_types const lt, const std::string & n, const ex & mu, const ex & nu, const ex & rho, const ex & sigma) : inherited(mu,nu,rho,sigma), type(lt), name(n)
+{
+ debugmsg("lortensor constructor from lortensor_types,string,ex,ex,ex,ex",LOGLEVEL_CONSTRUCT);
+ GINAC_ASSERT(all_of_type_lorentzidx());
+ if (lt == lortensor_symbolic)
+ serial = next_serial++;
+ else
+ serial = 0;
+ tinfo_key=TINFO_lortensor;
+}
+
+/** Construct object with arbitrary number of Lorentz indices. This
+ * constructor is for internal use only. Use the lortensor_symbolic()
+ * function instead.
+ *
+ * @see lortensor_symbolic */
+lortensor::lortensor(lortensor_types const lt, const std::string & n, const exvector & iv) : inherited(iv), type(lt), name(n)
{
- debugmsg("lortensor constructor from lortensor_types,string",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- tinfo_key=TINFO_lortensor;
+ debugmsg("lortensor constructor from lortensor_types,string,exvector",LOGLEVEL_CONSTRUCT);
+ GINAC_ASSERT(all_of_type_lorentzidx());
+ if (lt == lortensor_symbolic)
+ serial = next_serial++;
+ else
+ serial = 0;
+ tinfo_key=TINFO_lortensor;
}
-lortensor::lortensor(lortensor_types const lt, string const & n, ex const & mu) : indexed(mu), type(lt), name(n)
+lortensor::lortensor(lortensor_types const lt, const std::string & n, unsigned s, const exvector & iv) : indexed(iv), type(lt), name(n), serial(s)
{
- debugmsg("lortensor constructor from lortensor_types,string,ex",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- GINAC_ASSERT(all_of_type_lorentzidx());
- tinfo_key=TINFO_lortensor;
+ debugmsg("lortensor constructor from lortensor_types,string,unsigned,exvector",LOGLEVEL_CONSTRUCT);
+ GINAC_ASSERT(all_of_type_lorentzidx());
+ tinfo_key=TINFO_lortensor;
}
-lortensor::lortensor(lortensor_types const lt, string const & n, ex const & mu, ex const & nu) : indexed(mu,nu), type(lt), name(n)
+lortensor::lortensor(lortensor_types const lt, const std::string & n, unsigned s, exvector *ivp) : indexed(ivp), type(lt), name(n), serial(s)
{
- debugmsg("lortensor constructor from lortensor_types,string,ex,ex",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- GINAC_ASSERT(all_of_type_lorentzidx());
- tinfo_key=TINFO_lortensor;
+ debugmsg("lortensor constructor from lortensor_types,string,unsigned,exvector",LOGLEVEL_CONSTRUCT);
+ GINAC_ASSERT(all_of_type_lorentzidx());
+ tinfo_key=TINFO_lortensor;
}
-lortensor::lortensor(lortensor_types const lt, string const & n, ex const & mu, ex const & nu, ex const & rho) : indexed(mu,nu,rho), type(lt), name(n)
-{
- debugmsg("lortensor constructor from lortensor_types,string,ex,ex,ex",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- GINAC_ASSERT(all_of_type_lorentzidx());
- tinfo_key=TINFO_lortensor;
-}
-lortensor::lortensor(lortensor_types const lt, string const & n, ex const & mu, ex const & nu, ex const & rho, ex const & sigma) : indexed(mu,nu,rho,sigma), type(lt), name(n)
-{
- debugmsg("lortensor constructor from lortensor_types,string,ex,ex,ex,ex",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- GINAC_ASSERT(all_of_type_lorentzidx());
- tinfo_key=TINFO_lortensor;
-}
+//////////
+// archiving
+//////////
-lortensor::lortensor(lortensor_types const lt, string const & n, exvector const & iv) : indexed(iv), type(lt), name(n)
-{
- debugmsg("lortensor constructor from lortensor_types,string,exvector",LOGLEVEL_CONSTRUCT);
- serial=next_serial++;
- GINAC_ASSERT(all_of_type_lorentzidx());
- tinfo_key=TINFO_lortensor;
+/** Construct object from archive_node. */
+lortensor::lortensor(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+{
+ debugmsg("lortensor constructor from archive_node", LOGLEVEL_CONSTRUCT);
+ unsigned int ty;
+ if (!(n.find_unsigned("type", ty)))
+ throw (std::runtime_error("unknown lortensor type in archive"));
+ type = (lortensor_types)ty;
+ if (type == lortensor_symbolic) {
+ serial = next_serial++;
+ if (!(n.find_string("name", name)))
+ name = autoname_prefix() + ToString(serial);
+ } else
+ serial = 0;
+}
+
+/** Unarchive the object. */
+ex lortensor::unarchive(const archive_node &n, const lst &sym_lst)
+{
+ ex s = (new lortensor(n, sym_lst))->setflag(status_flags::dynallocated);
+
+ if (ex_to_lortensor(s).type == lortensor_symbolic) {
+ // If lortensor is in sym_lst, return the existing lortensor
+ for (unsigned i=0; i<sym_lst.nops(); i++) {
+ if (is_ex_of_type(sym_lst.op(i), lortensor) && (ex_to_lortensor(sym_lst.op(i)).name == ex_to_lortensor(s).name))
+ return sym_lst.op(i);
+ }
+ }
+ return s;
}
-lortensor::lortensor(lortensor_types const lt, string const & n, unsigned s, exvector const & iv) : indexed(iv), type(lt), name(n), serial(s)
+/** Archive the object. */
+void lortensor::archive(archive_node &n) const
{
- debugmsg("lortensor constructor from lortensor_types,string,unsigned,exvector",LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(all_of_type_lorentzidx());
- tinfo_key=TINFO_lortensor;
+ inherited::archive(n);
+ n.add_unsigned("type", type);
+ if (type == lortensor_symbolic)
+ n.add_string("name", name);
}
-lortensor::lortensor(lortensor_types const lt, string const & n, unsigned s, exvector *ivp) : indexed(ivp), type(lt), name(n), serial(s)
-{
- debugmsg("lortensor constructor from lortensor_types,string,unsigned,exvector",LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(all_of_type_lorentzidx());
- tinfo_key=TINFO_lortensor;
-}
//////////
// functions overriding virtual functions from bases classes
//public
-basic * lortensor::duplicate() const
-{
- debugmsg("lortensor duplicate",LOGLEVEL_DUPLICATE);
- return new lortensor(*this);
-}
-
-void lortensor::printraw(ostream & os) const
-{
- debugmsg("lortensor printraw",LOGLEVEL_PRINT);
- os << "lortensor(type=" << (unsigned)type
- << ",indices=";
- printrawindices(os);
- os << ",hash=" << hashvalue << ",flags=" << flags << ")";
-}
-
-void lortensor::printtree(ostream & os, unsigned indent) const
-{
- debugmsg("lortensor printtree",LOGLEVEL_PRINT);
- os << string(indent,' ') <<"lortensor object: "
- << "type=" << (unsigned)type << ","
- << seq.size() << " indices" << endl;
- printtreeindices(os,indent);
- os << string(indent,' ') << "hash=" << hashvalue
- << " (0x" << hex << hashvalue << dec << ")"
- << ", flags=" << flags << endl;
-}
-
-void lortensor::print(ostream & os, unsigned upper_precedence) const
-{
- debugmsg("lortensor print",LOGLEVEL_PRINT);
- switch (type) {
- case lortensor_g:
- os << "g";
- break;
- case lortensor_rankn:
- os << name;
- break;
- case lortensor_rank1:
- os << name;
- break;
- case lortensor_rank2:
- os << name;
- break;
- case lortensor_epsilon:
- os << "epsilon";
- break;
- case invalid:
- default:
- os << "INVALID_LORTENSOR_OBJECT";
- break;
- }
- printindices(os);
-}
-
-void lortensor::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
-{
- debugmsg("lortensor print csrc",LOGLEVEL_PRINT);
- print(os,upper_precedence);
+void lortensor::printraw(std::ostream & os) const
+{
+ debugmsg("lortensor printraw",LOGLEVEL_PRINT);
+ os << "lortensor(type=" << (unsigned)type
+ << ",indices=";
+ printrawindices(os);
+ os << ",serial=" << serial;
+ os << ",hash=" << hashvalue << ",flags=" << flags << ")";
+}
+
+void lortensor::printtree(std::ostream & os, unsigned indent) const
+{
+ debugmsg("lortensor printtree",LOGLEVEL_PRINT);
+ os << std::string(indent,' ') <<"lortensor object: "
+ << "type=" << (unsigned)type << ","
+ << seq.size() << " indices" << std::endl;
+ printtreeindices(os,indent);
+ os << std::string(indent,' ') << "hash=" << hashvalue
+ << " (0x" << std::hex << hashvalue << std::dec << ")"
+ << ", flags=" << flags << std::endl;
+}
+
+void lortensor::print(std::ostream & os, unsigned upper_precedence) const
+{
+ debugmsg("lortensor print",LOGLEVEL_PRINT);
+ switch (type) {
+ case lortensor_g:
+ os << "g";
+ break;
+ case lortensor_delta:
+ os << "delta";
+ break;
+ case lortensor_epsilon:
+ os << "epsilon";
+ break;
+ case lortensor_symbolic:
+ os << name;
+ break;
+ case invalid:
+ default:
+ os << "INVALID_LORTENSOR_OBJECT";
+ break;
+ }
+ printindices(os);
}
bool lortensor::info(unsigned inf) const
{
- return indexed::info(inf);
+ return inherited::info(inf);
}
ex lortensor::eval(int level) const
{
- if (type==lortensor_g) {
- // canonicalize indices
- exvector iv=seq;
- int sig=canonicalize_indices(iv,false); //symmetric
- if (sig!=INT_MAX) {
- //something has changed while sorting indices, more evaluations later
- return ex(sig) *lortensor(type,name,iv);
- }
- lorentzidx const & idx1=ex_to_lorentzidx(seq[0]);
- lorentzidx const & idx2=ex_to_lorentzidx(seq[1]);
- if ((!idx1.is_symbolic()) && (!idx2.is_symbolic())) {
- //both indices are numeric
- if ((idx1.get_value()==idx2.get_value())) {
- //both on diagonal
- if (idx1.get_value()==0){
- // (0,0)
- return exONE();
- } else {
- if (idx1.is_covariant() != idx2.is_covariant()) {
- // (_i,~i) or (~i,_i), i = 1...3
- return exONE();
- } else {
- // (_i,_i) or (~i,~i), i= 1...3
- return exMINUSONE();
- }
- }
- } else {
- // at least one off-diagonal
- return exZERO();
- }
- } else if (idx1.is_symbolic() && idx1.is_co_contra_pair(idx2)) {
- return Dim()-idx1.get_dim_parallel_space();
- }
- }
- return this -> hold();
+ if (type==lortensor_g) {
+ // canonicalize indices
+ exvector iv=seq;
+ int sig=canonicalize_indices(iv,false); //symmetric
+ if (sig!=INT_MAX) {
+ //something has changed while sorting indices, more evaluations later
+ return ex(sig) *lortensor(type,name,iv);
+ }
+ const lorentzidx & idx1=ex_to_lorentzidx(seq[0]);
+ const lorentzidx & idx2=ex_to_lorentzidx(seq[1]);
+ if ((!idx1.is_symbolic()) && (!idx2.is_symbolic())) {
+ //both indices are numeric
+ if ((idx1.get_value()==idx2.get_value())) {
+ //both on diagonal
+ if (idx1.get_value()==0){
+ // (0,0)
+ return _ex1();
+ } else {
+ if (idx1.is_covariant() != idx2.is_covariant()) {
+ // (_i,~i) or (~i,_i), i = 1...3
+ return _ex1();
+ } else {
+ // (_i,_i) or (~i,~i), i= 1...3
+ return _ex_1();
+ }
+ }
+ } else {
+ // at least one off-diagonal
+ return _ex0();
+ }
+ } else if (idx1.is_symbolic() && idx1.is_co_contra_pair(idx2)) {
+ if (idx1.is_orthogonal_only())
+ return Dim() - idx1.get_dim_parallel_space();
+ else
+ return Dim();
+ }
+ }
+ return this -> hold();
}
//protected
-int lortensor::compare_same_type(basic const & other) const
+int lortensor::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other,lortensor));
- const lortensor *o = static_cast <const lortensor *> (&other);
- if (type==o->type) {
- if (type==lortensor_rankn) {
- if (serial!=o->serial) {
- return serial < o->serial ? -1 : 1;
- }
- }
- return indexed::compare_same_type(other);
- }
- return type < o->type ? -1 : 1;
+ GINAC_ASSERT(is_of_type(other,lortensor));
+ const lortensor &o = static_cast<const lortensor &>(other);
+
+ if (type!=o.type) {
+ // different type
+ return type < o.type ? -1 : 1;
+ }
+
+ if (type == lortensor_symbolic) {
+ // symbolic, compare serials
+ if (serial != o.serial) {
+ return serial < o.serial ? -1 : 1;
+ }
+ }
+
+ return inherited::compare_same_type(other);
}
-bool lortensor::is_equal_same_type(basic const & other) const
+bool lortensor::is_equal_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other,lortensor));
- const lortensor *o=static_cast<const lortensor *> (&other);
- if (type!=o->type) return false;
- if (type==lortensor_rankn) {
- if (serial!=o->serial) return false;
- }
- return indexed::is_equal_same_type(other);
+ GINAC_ASSERT(is_of_type(other,lortensor));
+ const lortensor &o = static_cast<const lortensor &>(other);
+
+ if (type != o.type) return false;
+ if (type == lortensor_symbolic && serial != o.serial) return false;
+ return inherited::is_equal_same_type(other);
}
unsigned lortensor::return_type(void) const
{
- return return_types::commutative;
+ return return_types::commutative;
}
+
unsigned lortensor::return_type_tinfo(void) const
{
- return tinfo_key;
+ return tinfo_key;
}
-ex lortensor::thisexprseq(exvector const & v) const
+
+ex lortensor::thisexprseq(const exvector & v) const
{
- return lortensor(type,name,serial,v);
+ return lortensor(type,name,serial,v);
}
+
ex lortensor::thisexprseq(exvector *vp) const
{
- return lortensor(type,name,serial,vp);
+ return lortensor(type,name,serial,vp);
}
-
+
//////////
// non-virtual functions in this class
//////////
// protected
-void lortensor::setname(string const & n)
-{
- name=n;
-}
-
+/** Check whether all indices are of class lorentzidx or a subclass. This
+ * function is used internally to make sure that all constructed Lorentz
+ * tensors really carry Lorentz indices and not some other classes. */
bool lortensor::all_of_type_lorentzidx(void) const
{
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++ cit) {
- if (!is_ex_of_type(*cit,lorentzidx)) {
- return false;
- }
- }
- return true;
+ for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++ cit) {
+ if (!is_ex_of_type(*cit,lorentzidx)) return false;
+ }
+ return true;
}
// private
-string & lortensor::autoname_prefix(void)
+std::string & lortensor::autoname_prefix(void)
{
- static string * s=new string("lortensor");
- return *s;
+ static std::string * s = new std::string("lortensor");
+ return *s;
}
//////////
// friend functions
//////////
-lortensor lortensor_g(ex const & mu, ex const & nu)
+/** Construct an object representing the metric tensor g. The indices must
+ * be of class lorentzidx.
+ *
+ * @param mu First index
+ * @param nu Second index
+ * @return newly constructed object */
+lortensor lortensor_g(const ex & mu, const ex & nu)
{
- return lortensor(lortensor::lortensor_g,"",mu,nu);
+ return lortensor(lortensor::lortensor_g,"",mu,nu);
}
-lortensor lortensor_epsilon(ex const & mu, ex const & nu, ex const & rho, ex const & sigma)
+/** Construct an object representing the unity matrix delta. The indices
+ * must be of class lorentzidx.
+ *
+ * @param mu First index
+ * @param nu Second index
+ * @return newly constructed object */
+lortensor lortensor_delta(const ex & mu, const ex & nu)
{
- return lortensor(lortensor::lortensor_epsilon,"",mu,nu,rho,sigma);
+ return lortensor(lortensor::lortensor_delta,"",mu,nu);
}
-lortensor lortensor_rank1(string const & n, ex const & mu)
+/** Construct an object representing the four-dimensional totally
+ * antisymmetric tensor epsilon. The indices must be of class lorentzidx.
+ *
+ * @param mu First index
+ * @param nu Second index
+ * @param rho Third index
+ * @param sigma Fourth index
+ * @return newly constructed object */
+lortensor lortensor_epsilon(const ex & mu, const ex & nu, const ex & rho, const ex & sigma)
{
- return lortensor(lortensor::lortensor_rank1,n,mu);
+ return lortensor(lortensor::lortensor_epsilon,"",mu,nu,rho,sigma);
}
-lortensor lortensor_rank2(string const & n, ex const & mu, ex const & nu)
+/** Construct an object representing a symbolic Lorentz vector. The index
+ * must be of class lorentzidx.
+ *
+ * @param n Symbolic name
+ * @param mu Index
+ * @return newly constructed object */
+lortensor lortensor_vector(const std::string & n, const ex & mu)
{
- return lortensor(lortensor::lortensor_rank2,n,mu,nu);
+ return lortensor(lortensor::lortensor_symbolic,n,mu);
+}
+
+/** Construct an object representing a symbolic Lorentz tensor of arbitrary
+ * rank. The indices must be of class lorentzidx.
+ *
+ * @param n Symbolic name
+ * @param iv Vector of indices
+ * @return newly constructed object */
+lortensor lortensor_symbolic(const std::string & n, const exvector & iv)
+{
+ return lortensor(lortensor::lortensor_symbolic,n,iv);
+}
+
+ex simplify_lortensor_mul(const ex & m)
+{
+ GINAC_ASSERT(is_ex_exactly_of_type(m,mul));
+ exvector v_contracted;
+
+ // collect factors in an exvector, store squares twice
+ int n=m.nops();
+ v_contracted.reserve(2*n);
+ for (int i=0; i<n; ++i) {
+ ex f=m.op(i);
+ if (is_ex_exactly_of_type(f,power)&&f.op(1).is_equal(_ex2())) {
+ v_contracted.push_back(f.op(0));
+ v_contracted.push_back(f.op(0));
+ } else {
+ v_contracted.push_back(f);
+ }
+ }
+
+ unsigned replacements;
+ bool something_changed=false;
+
+ exvector::iterator it=v_contracted.begin();
+ while (it!=v_contracted.end()) {
+ // process only lor_g objects
+ if (is_ex_exactly_of_type(*it,lortensor) &&
+ (ex_to_lortensor(*it).type==lortensor::lortensor_g)) {
+ const lortensor & g=ex_to_lortensor(*it);
+ GINAC_ASSERT(g.seq.size()==2);
+ const idx & first_idx=ex_to_lorentzidx(g.seq[0]);
+ const idx & second_idx=ex_to_lorentzidx(g.seq[1]);
+ // g_{mu,mu} should have been contracted in lortensor::eval()
+ GINAC_ASSERT(!first_idx.is_equal(second_idx));
+ ex saved_g=*it; // save to restore it later
+
+ // try to contract first index
+ replacements=0;
+ if (first_idx.is_symbolic()) {
+ replacements = subs_index_in_exvector(v_contracted,
+ first_idx.toggle_covariant(),second_idx);
+ if (replacements==0) {
+ // not contracted, restore g object
+ *it=saved_g;
+ } else {
+ // a contracted index should occur exactly once
+ GINAC_ASSERT(replacements==1);
+ *it=_ex1();
+ something_changed=true;
+ }
+ }
+
+ // try second index only if first was not contracted
+ if ((replacements==0)&&(second_idx.is_symbolic())) {
+ // first index not contracted, *it is again the original g object
+ replacements = subs_index_in_exvector(v_contracted,
+ second_idx.toggle_covariant(),first_idx);
+ if (replacements==0) {
+ // not contracted except in itself, restore g object
+ *it=saved_g;
+ } else {
+ // a contracted index should occur exactly once
+ GINAC_ASSERT(replacements==1);
+ *it=_ex1();
+ something_changed=true;
+ }
+ }
+ }
+ ++it;
+ }
+ if (something_changed) {
+ return mul(v_contracted);
+ }
+ return m;
}
-ex simplify_lortensor_mul(ex const & m)
+/** Perform some simplifications on an expression containing Lorentz tensors. */
+ex simplify_lortensor(const ex & e)
{
- GINAC_ASSERT(is_ex_exactly_of_type(m,mul));
- exvector v_contracted;
+ // all simplification is done on expanded objects
+ ex e_expanded = e.expand();
+
+ // simplification of sum=sum of simplifications
+ if (is_ex_exactly_of_type(e_expanded,add)) {
+ ex sum=_ex0();
+ for (unsigned i=0; i<e_expanded.nops(); ++i) {
+ sum += simplify_lortensor(e_expanded.op(i));
+ }
+ return sum;
+ }
- // collect factors in an exvector, store squares twice
- int n=m.nops();
- v_contracted.reserve(2*n);
- for (int i=0; i<n; ++i) {
- ex f=m.op(i);
- if (is_ex_exactly_of_type(f,power)&&f.op(1).is_equal(exTWO())) {
- v_contracted.push_back(f.op(0));
- v_contracted.push_back(f.op(0));
- } else {
- v_contracted.push_back(f);
+ // simplification of (commutative) product
+ if (is_ex_exactly_of_type(e_expanded,mul)) {
+ return simplify_lortensor_mul(e);
}
- }
-
- unsigned replacements;
- bool something_changed=false;
-
- exvector::iterator it=v_contracted.begin();
- while (it!=v_contracted.end()) {
- // process only lor_g objects
- if (is_ex_exactly_of_type(*it,lortensor) &&
- (ex_to_lortensor(*it).type==lortensor::lortensor_g)) {
- lortensor const & g=ex_to_lortensor(*it);
- GINAC_ASSERT(g.seq.size()==2);
- idx const & first_idx=ex_to_lorentzidx(g.seq[0]);
- idx const & second_idx=ex_to_lorentzidx(g.seq[1]);
- // g_{mu,mu} should have been contracted in lortensor::eval()
- GINAC_ASSERT(!first_idx.is_equal(second_idx));
- ex saved_g=*it; // save to restore it later
-
- // try to contract first index
- replacements=0;
- if (first_idx.is_symbolic()) {
- replacements = subs_index_in_exvector(v_contracted,
- first_idx.toggle_covariant(),second_idx);
- if (replacements==0) {
- // not contracted, restore g object
- *it=saved_g;
- } else {
- // a contracted index should occur exactly once
- GINAC_ASSERT(replacements==1);
- *it=exONE();
- something_changed=true;
- }
- }
-
- // try second index only if first was not contracted
- if ((replacements==0)&&(second_idx.is_symbolic())) {
- // first index not contracted, *it is again the original g object
- replacements = subs_index_in_exvector(v_contracted,
- second_idx.toggle_covariant(),first_idx);
- if (replacements==0) {
- // not contracted except in itself, restore g object
- *it=saved_g;
- } else {
- // a contracted index should occur exactly once
- GINAC_ASSERT(replacements==1);
- *it=exONE();
- something_changed=true;
- }
- }
- }
- ++it;
- }
- if (something_changed) {
- return mul(v_contracted);
- }
- return m;
-}
-
-ex simplify_lortensor(ex const & e)
-{
- // all simplification is done on expanded objects
- ex e_expanded=e.expand();
-
- // simplification of sum=sum of simplifications
- if (is_ex_exactly_of_type(e_expanded,add)) {
- ex sum=exZERO();
- for (int i=0; i<e_expanded.nops(); ++i) {
- sum += simplify_lortensor(e_expanded.op(i));
- }
- return sum;
- }
-
- // simplification of commutative product=commutative product of simplifications
- if (is_ex_exactly_of_type(e_expanded,mul)) {
- return simplify_lortensor_mul(e);
- }
-
- // cannot do anything
- return e_expanded;
-}
-
-ex Dim(void)
-{
- static symbol * d=new symbol("dim");
- return *d;
-}
-
-#ifndef NO_GINAC_NAMESPACE
+
+ // cannot do anything
+ return e_expanded;
+}
+
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
git://www.ginac.de / ginac.git / blobdiff