* Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2024 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
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(clifford, indexed,
print_func<print_dflt>(&clifford::do_print_dflt).
- print_func<print_latex>(&clifford::do_print_latex))
+ print_func<print_latex>(&clifford::do_print_latex).
+ print_func<print_tree>(&clifford::do_print_tree))
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracone, tensor,
print_func<print_dflt>(&diracone::do_print).
}
}
+void clifford::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << class_name() << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << ", " << seq.size()-1 << " indices"
+ << ", symmetry=" << symtree << std::endl;
+ metric.print(c, level + c.delta_indent);
+ seq[0].print(c, level + c.delta_indent);
+ printindices(c, level + c.delta_indent);
+}
+
DEFAULT_COMPARE(diracone)
DEFAULT_COMPARE(cliffordunit)
DEFAULT_COMPARE(diracgamma)
i = _ex0;
b = _ex1;
} else { // slash object, generate new dummy index
- varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(c.op(1)).get_dim());
+ varidx ix(dynallocate<symbol>(), ex_to<idx>(c.op(1)).get_dim());
b = indexed(c.op(0), ix.toggle_variance());
i = ix;
}
}
/** Predicate for finding non-clifford objects. */
-struct is_not_a_clifford : public std::unary_function<ex, bool> {
+struct is_not_a_clifford {
bool operator()(const ex & e)
{
return !is_a<clifford>(e);
if (std::find_if(self + 1, other, is_not_a_clifford()) != other)
return false;
- exvector::iterator next_to_last = other - 1;
+ auto next_to_last = other - 1;
ex S = ncmul(exvector(self + 1, next_to_last));
ex SR = ncmul(exvector(std::reverse_iterator<exvector::const_iterator>(next_to_last), std::reverse_iterator<exvector::const_iterator>(self + 1)));
if (std::find_if(self + 1, other, is_not_a_clifford()) != other)
return false;
- exvector::iterator next_to_last = other - 1;
+ auto next_to_last = other - 1;
ex S = ncmul(exvector(self + 1, next_to_last));
*self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last);
&& unit.same_metric(*other))
return false;
- exvector::iterator before_other = other - 1;
+ auto before_other = other - 1;
ex mu = self->op(1);
ex mu_toggle = other->op(1);
ex alpha = before_other->op(1);
// Anticommutate gamma5/L/R's to the front
if (s.size() >= 2) {
- exvector::iterator first = s.begin(), next_to_last = s.end() - 2;
+ auto first = s.begin(), next_to_last = s.end() - 2;
while (true) {
- exvector::iterator it = next_to_last;
+ auto it = next_to_last;
while (true) {
- exvector::iterator it2 = it + 1;
+ auto it2 = it + 1;
if (is_a<clifford>(*it) && is_a<clifford>(*it2)) {
ex e1 = it->op(0), e2 = it2->op(0);
} else if (!a_is_cliffordunit && !b_is_cliffordunit && ag.is_equal(bg)) {
// a\ a\ -> a^2
- varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(a.op(1)).minimal_dim(ex_to<idx>(b.op(1))));
+ varidx ix(dynallocate<symbol>(), ex_to<idx>(a.op(1)).minimal_dim(ex_to<idx>(b.op(1))));
a = indexed(ag, ix) * indexed(ag, ix.toggle_variance());
b = dirac_ONE(representation_label);
ex diracgammaL::conjugate() const
{
- return (new diracgammaR)->setflag(status_flags::dynallocated);
+ return dynallocate<diracgammaR>();
}
ex diracgammaR::conjugate() const
{
- return (new diracgammaL)->setflag(status_flags::dynallocated);
+ return dynallocate<diracgammaL>();
}
//////////
ex dirac_ONE(unsigned char rl)
{
- static ex ONE = (new diracone)->setflag(status_flags::dynallocated);
+ static ex ONE = dynallocate<diracone>();
return clifford(ONE, rl);
}
ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
{
- //static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
- ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
+ ex unit = dynallocate<cliffordunit>();
if (!is_a<idx>(mu))
throw(std::invalid_argument("clifford_unit(): index of Clifford unit must be of type idx or varidx"));
unsigned n = M.rows();
bool symmetric = true;
- //static idx xi((new symbol)->setflag(status_flags::dynallocated), n),
- // chi((new symbol)->setflag(status_flags::dynallocated), n);
- idx xi((new symbol)->setflag(status_flags::dynallocated), n),
- chi((new symbol)->setflag(status_flags::dynallocated), n);
+ //static idx xi(dynallocate<symbol>(), n),
+ // chi(dynallocate<symbol>(), n);
+ idx xi(dynallocate<symbol>(), n),
+ chi(dynallocate<symbol>(), n);
if ((n == M.cols()) && (n == get_dim_uint(mu))) {
for (unsigned i = 0; i < n; i++) {
for (unsigned j = i+1; j < n; j++) {
throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be a square matrix with the same dimensions as index"));
}
} else if (indices.size() == 0) { // a tensor or other expression without indices
- //static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim()),
- // chi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim());
- varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim()),
- chi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim());
+ //static varidx xi(dynallocate<symbol>(), ex_to<idx>(mu).get_dim()),
+ // chi(dynallocate<symbol>(), ex_to<idx>(mu).get_dim());
+ varidx xi(dynallocate<symbol>(), ex_to<idx>(mu).get_dim()),
+ chi(dynallocate<symbol>(), ex_to<idx>(mu).get_dim());
return clifford(unit, mu, indexed(metr, xi, chi), rl);
} else
throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type tensor, matrix or an expression with two free indices"));
ex dirac_gamma(const ex & mu, unsigned char rl)
{
- static ex gamma = (new diracgamma)->setflag(status_flags::dynallocated);
+ static ex gamma = dynallocate<diracgamma>();
if (!is_a<varidx>(mu))
throw(std::invalid_argument("dirac_gamma(): index of Dirac gamma must be of type varidx"));
- static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim()),
- chi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim());
- return clifford(gamma, mu, indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl);
+ static varidx xi(dynallocate<symbol>(), ex_to<varidx>(mu).get_dim()),
+ chi(dynallocate<symbol>(), ex_to<varidx>(mu).get_dim());
+ return clifford(gamma, mu, indexed(dynallocate<minkmetric>(), symmetric2(), xi, chi), rl);
}
ex dirac_gamma5(unsigned char rl)
{
- static ex gamma5 = (new diracgamma5)->setflag(status_flags::dynallocated);
+ static ex gamma5 = dynallocate<diracgamma5>();
return clifford(gamma5, rl);
}
ex dirac_gammaL(unsigned char rl)
{
- static ex gammaL = (new diracgammaL)->setflag(status_flags::dynallocated);
+ static ex gammaL = dynallocate<diracgammaL>();
return clifford(gammaL, rl);
}
ex dirac_gammaR(unsigned char rl)
{
- static ex gammaR = (new diracgammaR)->setflag(status_flags::dynallocated);
+ static ex gammaR = dynallocate<diracgammaR>();
return clifford(gammaR, rl);
}
// vector as its base expression and a (dummy) index that just serves
// for storing the space dimensionality
- static varidx xi((new symbol)->setflag(status_flags::dynallocated), dim),
- chi((new symbol)->setflag(status_flags::dynallocated), dim);
- return clifford(e, varidx(0, dim), indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl);
+ static varidx xi(dynallocate<symbol>(), dim),
+ chi(dynallocate<symbol>(), dim);
+ return clifford(e, varidx(0, dim), indexed(dynallocate<minkmetric>(), symmetric2(), xi, chi), rl);
}
/** Extract representation label from tinfo key (as returned by
{
// Convert list to set
std::set<unsigned char> rls;
- for (lst::const_iterator i = rll.begin(); i != rll.end(); ++i) {
- if (i->info(info_flags::nonnegint))
- rls.insert(ex_to<numeric>(*i).to_int());
+ for (const auto & i : rll) {
+ if (i.info(info_flags::nonnegint))
+ rls.insert(ex_to<numeric>(i).to_int());
}
return dirac_trace(e, rls, trONE);
// Scan for any ncmul objects
exmap srl;
ex aux = e.to_rational(srl);
- for (exmap::iterator i = srl.begin(); i != srl.end(); ++i) {
+ for (auto & i : srl) {
- ex lhs = i->first;
- ex rhs = i->second;
+ ex lhs = i.first;
+ ex rhs = i.second;
if (is_exactly_a<ncmul>(rhs)
&& rhs.return_type() == return_types::noncommutative
// Expand product, if necessary
ex rhs_expanded = rhs.expand();
if (!is_a<ncmul>(rhs_expanded)) {
- i->second = canonicalize_clifford(rhs_expanded);
+ i.second = canonicalize_clifford(rhs_expanded);
continue;
} else if (!is_a<clifford>(rhs.op(0)))
v.push_back(rhs.op(j));
// Stupid recursive bubble sort because we only want to swap adjacent gammas
- exvector::iterator it = v.begin(), next_to_last = v.end() - 1;
+ auto it = v.begin(), next_to_last = v.end() - 1;
if (is_a<diracgamma5>(it->op(0)) || is_a<diracgammaL>(it->op(0)) || is_a<diracgammaR>(it->op(0)))
++it;
it[0] = save1;
it[1] = save0;
sum += ex_to<clifford>(save0).get_commutator_sign() * ncmul(std::move(v));
- i->second = canonicalize_clifford(sum);
+ i.second = canonicalize_clifford(sum);
goto next_sym;
}
++it;
}
}
+ex clifford_star_bar(const ex & e, bool do_bar, unsigned options)
+{
+ pointer_to_map_function_2args<bool, unsigned> fcn(clifford_star_bar, do_bar, options | 1);
+
+ // is a child, no need to expand
+ ex e1= (options & 1 ? e : e.expand());
+
+ if (is_a<ncmul>(e1) ) { // reversing order of clifford units
+ exvector ev, cv;
+ ev.reserve(e1.nops());
+ cv.reserve(e1.nops());
+ // separate clifford and non-clifford entries
+ for (size_t i= 0; i < e1.nops(); ++i) {
+ if (is_a<clifford>(e1.op(i)) && is_a<cliffordunit>(e1.op(i).op(0)))
+ cv.push_back(e1.op(i));
+ else
+ ev.push_back(e1.op(i));
+ }
+ for (auto i=cv.rbegin(); i!=cv.rend(); ++i) { // reverse order of Clifford units
+ ev.push_back(i->conjugate());
+ }
+ // For clifford_bar an odd number of clifford units reverts the sign
+ if (do_bar && (cv.size() % 2 == 1))
+ return -dynallocate<ncmul>(std::move(ev));
+ else
+ return dynallocate<ncmul>(std::move(ev));
+ } else if (is_a<clifford>(e1) && is_a<cliffordunit>(e1.op(0))) {
+ if (do_bar)
+ return -e;
+ else
+ return e;
+ } else if (is_a<power>(e1)) {
+ // apply the procedure to the base of a power
+ return pow(clifford_star_bar(e1.op(0), do_bar, 0), e1.op(1));
+ } else if (is_a<add>(e1) || is_a<mul>(e1) || e.info(info_flags::list)) {
+ // recurse into subexpressions
+ return e1.map(fcn);
+ } else // nothing meaningful can be done
+ return e;
+}
+
ex clifford_prime(const ex & e)
{
pointer_to_map_function fcn(clifford_prime);
/** Auxiliary structure to define a function for striping one Clifford unit
* from vectors. Used in clifford_to_lst(). */
-static ex get_clifford_comp(const ex & e, const ex & c)
+static ex get_clifford_comp(const ex & e, const ex & c, bool root=true)
{
- pointer_to_map_function_1arg<const ex &> fcn(get_clifford_comp, c);
+ // make expansion on the top-level call only
+ ex e1=(root? e.expand() : e);
+
+ pointer_to_map_function_2args<const ex &, bool> fcn(get_clifford_comp, c, false);
int ival = ex_to<numeric>(ex_to<idx>(c.op(1)).get_value()).to_int();
-
- if (is_a<add>(e) || e.info(info_flags::list) // || is_a<pseries>(e) || is_a<integral>(e)
- || is_a<matrix>(e))
- return e.map(fcn);
- else if (is_a<ncmul>(e) || is_a<mul>(e)) {
- // find a Clifford unit with the same metric, delete it and substitute its index
- size_t ind = e.nops() + 1;
- for (size_t j = 0; j < e.nops(); j++) {
- if (is_a<clifford>(e.op(j)) && ex_to<clifford>(c).same_metric(e.op(j))) {
- if (ind > e.nops()) {
- ind = j;
- } else {
+ int rl=ex_to<clifford>(c).get_representation_label();
+
+ if ( (is_a<add>(e1) || e1.info(info_flags::list) || is_a<matrix>(e1))) {
+ return e1.map(fcn);
+ } else if (is_a<ncmul>(e1) || is_a<mul>(e1)) {
+ // searches are done within products only
+ exvector ev, all_dummy=get_all_dummy_indices(e1);
+ bool found=false, same_value_found=false;
+ ex dummy_ind=0;
+ ev.reserve(e1.nops());
+ for (size_t i=0; i < e1.nops(); ++i) {
+ // look for a Clifford unit with the same metric and representation label,
+ // if found remember its index
+ if (is_a<clifford>(e1.op(i)) && ex_to<clifford>(e1.op(i)).get_representation_label() == rl
+ && is_a<cliffordunit>(e1.op(i).op(0)) && ex_to<clifford>(e1.op(i)).same_metric(c)) { // same Clifford unit
+ if (found)
throw(std::invalid_argument("get_clifford_comp(): expression is a Clifford multi-vector"));
- }
- }
+ found=true;
+ if (ex_to<idx>(e1.op(i).op(1)).is_numeric() &&
+ (ival == ex_to<numeric>(ex_to<idx>(e1.op(i).op(1)).get_value()).to_int())) {
+ same_value_found = true; // desired index value is found
+ } else if ((std::find(all_dummy.begin(), all_dummy.end(), e1.op(i).op(1)) != all_dummy.end())
+ || (is_a<varidx>(e1.op(i).op(1))
+ && std::find(all_dummy.begin(), all_dummy.end(),
+ ex_to<varidx>(e1.op(i).op(1)).toggle_variance()) != all_dummy.end())) {
+ dummy_ind=(e1.op(i).op(1)); // suitable dummy index found
+ } else
+ ev.push_back(e.op(i)); // another index value
+ } else
+ ev.push_back(e1.op(i));
}
- if (ind < e.nops()) {
- ex S = 1;
- bool same_value_index, found_dummy;
- same_value_index = ( ex_to<idx>(e.op(ind).op(1)).is_numeric()
- && (ival == ex_to<numeric>(ex_to<idx>(e.op(ind).op(1)).get_value()).to_int()) );
- found_dummy = same_value_index;
- // Run through the expression collecting all non-clifford factors
- for (size_t j=0; j < e.nops(); j++) {
- if (j != ind) {
- if (same_value_index) {
- S = S * e.op(j);
- } else {
- exvector ind_vec;
- if (is_a<indexed>(e.op(j)))
- ind_vec = ex_to<indexed>(e.op(j)).get_dummy_indices(ex_to<indexed>(e.op(ind)));
-
- if (ind_vec.size() > 0) {
- found_dummy = true;
- for (auto & it : ind_vec) {
- ex curridx = it;
- ex curridx_toggle = is_a<varidx>(curridx)
- ? ex_to<varidx>(curridx).toggle_variance()
- : curridx;
- S = S * e.op(j).subs(lst{curridx == ival, curridx_toggle == ival},
- subs_options::no_pattern);
- }
- } else
- S = S * e.op(j);
- }
- }
- }
- return (found_dummy ? S : 0);
- } else
+
+ if (! found) // no Clifford units found at all
throw(std::invalid_argument("get_clifford_comp(): expression is not a Clifford vector to the given units"));
- } else if (e.is_zero())
- return e;
- else if (is_a<clifford>(e) && ex_to<clifford>(e).same_metric(c))
- if ( ex_to<idx>(e.op(1)).is_numeric() &&
- (ival != ex_to<numeric>(ex_to<idx>(e.op(1)).get_value()).to_int()) )
+
+ ex res=dynallocate<ncmul>(std::move(ev));
+ if (same_value_found) {
+ return res;
+ } else if (! dummy_ind.is_zero()) { // a dummy index was found
+ if (is_a<varidx>(dummy_ind))
+ dummy_ind = ex_to<varidx>(dummy_ind).toggle_variance();
+ return res.subs(dummy_ind==ival, subs_options::no_pattern);
+ } else // found a Clifford unit with another index
return 0;
- else
+ } else if (e1.is_zero()) {
+ return 0;
+ } else if (is_a<clifford>(e1) && is_a<cliffordunit>(e1.op(0)) && ex_to<clifford>(e1).same_metric(c)) {
+ if (ex_to<idx>(e1.op(1)).is_numeric() &&
+ (ival == ex_to<numeric>(ex_to<idx>(e1.op(1)).get_value()).to_int()) )
return 1;
- else
+ else
+ return 0;
+ } else
throw(std::invalid_argument("get_clifford_comp(): expression is not usable as a Clifford vector"));
}
-
lst clifford_to_lst(const ex & e, const ex & c, bool algebraic)
{
GINAC_ASSERT(is_a<clifford>(c));
|| (! is_a<numeric>(pow(c.subs(mu == i, subs_options::no_pattern), 2))))
algebraic = false;
lst V;
- ex v0 = remove_dirac_ONE(canonicalize_clifford(e+clifford_prime(e)).normal())/2;
+ ex v0 = remove_dirac_ONE(canonicalize_clifford(e+clifford_prime(e)))/2;
if (! v0.is_zero())
V.append(v0);
ex e1 = canonicalize_clifford(e - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label()));
/ (2*pow(c.subs(mu == i, subs_options::no_pattern), 2))));
} else {
try {
- for (unsigned int i = 0; i < D; i++)
+ for (unsigned int i = 0; i < D; i++)
V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern)));
} catch (std::exception &p) {
/* Try to expand dummy summations to simplify the expression*/
e1 = canonicalize_clifford(expand_dummy_sum(e, true));
V.remove_all();
- v0 = remove_dirac_ONE(canonicalize_clifford(e1+clifford_prime(e1)).normal())/2;
+ v0 = remove_dirac_ONE(canonicalize_clifford(e1+clifford_prime(e1)))/2;
if (! v0.is_zero()) {
V.append(v0);
e1 = canonicalize_clifford(e1 - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label()));
} else {
if (is_a<indexed>(G)) {
D = ex_to<idx>(G.op(1)).get_dim();
- varidx mu((new symbol)->setflag(status_flags::dynallocated), D);
+ varidx mu(dynallocate<symbol>(), D);
cu = clifford_unit(mu, G, rl);
} else if (is_a<matrix>(G)) {
D = ex_to<matrix>(G).rows();
- idx mu((new symbol)->setflag(status_flags::dynallocated), D);
+ idx mu(dynallocate<symbol>(), D);
cu = clifford_unit(mu, G, rl);
} else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit"));
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