+ // Remember whether the product was commutative or noncommutative
+ // (because we chop it into factors and need to reassemble later)
+ non_commutative = is_exactly_a<ncmul>(e);
+
+ // Collect factors in an exvector, store squares twice
+ v.reserve(e.nops() * 2);
+
+ if (is_exactly_a<power>(e)) {
+ // We only get called for simple squares, split a^2 -> a*a
+ GINAC_ASSERT(e.op(1).is_equal(_ex2));
+ v.push_back(e.op(0));
+ v.push_back(e.op(0));
+ } else {
+ for (size_t i=0; i<e.nops(); i++) {
+ ex f = e.op(i);
+ if (is_exactly_a<power>(f) && f.op(1).is_equal(_ex2)) {
+ v.push_back(f.op(0));
+ v.push_back(f.op(0));
+ } else if (is_exactly_a<ncmul>(f)) {
+ // Noncommutative factor found, split it as well
+ non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
+ for (size_t j=0; j<f.nops(); j++)
+ v.push_back(f.op(j));
+ } else
+ v.push_back(f);
+ }
+ }
+}
+
+template<class T> ex idx_symmetrization(const ex& r,const exvector& local_dummy_indices)
+{ exvector dummy_syms;
+ dummy_syms.reserve(r.nops());
+ for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
+ if(is_exactly_a<T>(*it))
+ dummy_syms.push_back(it->op(0));
+ if(dummy_syms.size() < 2)
+ return r;
+ ex q=symmetrize(r, dummy_syms);
+ return q;
+}
+
+// Forward declaration needed in absence of friend injection, C.f. [namespace.memdef]:
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
+
+/** Simplify product of indexed expressions (commutative, noncommutative and
+ * simple squares), return list of free indices. */
+ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
+{
+ // Collect factors in an exvector
+ exvector v;
+
+ // Remember whether the product was commutative or noncommutative
+ // (because we chop it into factors and need to reassemble later)
+ bool non_commutative;
+ product_to_exvector(e, v, non_commutative);
+
+ // Perform contractions
+ bool something_changed = false;
+ GINAC_ASSERT(v.size() > 1);
+ exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
+ for (it1 = v.begin(); it1 != next_to_last; it1++) {
+
+try_again:
+ if (!is_a<indexed>(*it1))
+ continue;
+
+ bool first_noncommutative = (it1->return_type() != return_types::commutative);
+
+ // Indexed factor found, get free indices and look for contraction
+ // candidates
+ exvector free1, dummy1;
+ find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free1, dummy1);
+
+ exvector::iterator it2;
+ for (it2 = it1 + 1; it2 != itend; it2++) {
+
+ if (!is_a<indexed>(*it2))
+ continue;
+
+ bool second_noncommutative = (it2->return_type() != return_types::commutative);
+
+ // Find free indices of second factor and merge them with free
+ // indices of first factor
+ exvector un;
+ find_free_and_dummy(ex_to<indexed>(*it2).seq.begin() + 1, ex_to<indexed>(*it2).seq.end(), un, dummy1);
+ un.insert(un.end(), free1.begin(), free1.end());
+
+ // Check whether the two factors share dummy indices
+ exvector free, dummy;
+ find_free_and_dummy(un, free, dummy);
+ size_t num_dummies = dummy.size();
+ if (num_dummies == 0)
+ continue;
+
+ // At least one dummy index, is it a defined scalar product?
+ bool contracted = false;
+ if (free.empty() && it1->nops()==2 && it2->nops()==2) {
+
+ ex dim = minimal_dim(
+ ex_to<idx>(it1->op(1)).get_dim(),
+ ex_to<idx>(it2->op(1)).get_dim()
+ );
+
+ // User-defined scalar product?
+ if (sp.is_defined(*it1, *it2, dim)) {
+
+ // Yes, substitute it
+ *it1 = sp.evaluate(*it1, *it2, dim);
+ *it2 = _ex1;
+ goto contraction_done;
+ }
+ }
+
+ // Try to contract the first one with the second one
+ contracted = ex_to<basic>(it1->op(0)).contract_with(it1, it2, v);
+ if (!contracted) {
+
+ // That didn't work; maybe the second object knows how to
+ // contract itself with the first one
+ contracted = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
+ }
+ if (contracted) {
+contraction_done:
+ if (first_noncommutative || second_noncommutative
+ || is_exactly_a<add>(*it1) || is_exactly_a<add>(*it2)
+ || is_exactly_a<mul>(*it1) || is_exactly_a<mul>(*it2)
+ || is_exactly_a<ncmul>(*it1) || is_exactly_a<ncmul>(*it2)) {
+
+ // One of the factors became a sum or product:
+ // re-expand expression and run again
+ // Non-commutative products are always re-expanded to give
+ // eval_ncmul() the chance to re-order and canonicalize
+ // the product
+ ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v)));
+ return simplify_indexed(r, free_indices, dummy_indices, sp);
+ }
+
+ // Both objects may have new indices now or they might
+ // even not be indexed objects any more, so we have to
+ // start over
+ something_changed = true;
+ goto try_again;
+ }
+ }
+ }
+
+ // Find free indices (concatenate them all and call find_free_and_dummy())
+ // and all dummy indices that appear
+ exvector un, individual_dummy_indices;
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ exvector free_indices_of_factor;
+ if (is_a<indexed>(*it1)) {
+ exvector dummy_indices_of_factor;
+ find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free_indices_of_factor, dummy_indices_of_factor);
+ individual_dummy_indices.insert(individual_dummy_indices.end(), dummy_indices_of_factor.begin(), dummy_indices_of_factor.end());
+ } else
+ free_indices_of_factor = it1->get_free_indices();
+ un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
+ }
+ exvector local_dummy_indices;
+ find_free_and_dummy(un, free_indices, local_dummy_indices);
+ local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end());
+
+ // Filter out the dummy indices with variance
+ exvector variant_dummy_indices;
+ find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+ // Any indices with variance present at all?
+ if (!variant_dummy_indices.empty()) {
+
+ // Yes, bring the product into a canonical order that only depends on
+ // the base expressions of indexed objects
+ if (!non_commutative)
+ std::sort(v.begin(), v.end(), ex_base_is_less());
+
+ exvector moved_indices;
+
+ // Iterate over all indexed objects in the product
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ if (!is_a<indexed>(*it1))
+ continue;
+
+ if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices))
+ something_changed = true;
+ }
+ }
+
+ ex r;
+ if (something_changed)
+ r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
+ else
+ r = e;
+
+ // The result should be symmetric with respect to exchange of dummy
+ // indices, so if the symmetrization vanishes, the whole expression is
+ // zero. This detects things like eps.i.j.k * p.j * p.k = 0.
+ ex q = idx_symmetrization<idx>(r, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ q = idx_symmetrization<varidx>(q, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ q = idx_symmetrization<spinidx>(q, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+
+ // Dummy index renaming
+ r = rename_dummy_indices<idx>(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<varidx>(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<spinidx>(r, dummy_indices, local_dummy_indices);
+
+ // Product of indexed object with a scalar?
+ if (is_exactly_a<mul>(r) && r.nops() == 2
+ && is_exactly_a<numeric>(r.op(1)) && is_a<indexed>(r.op(0)))
+ return ex_to<basic>(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
+ else
+ return r;
+}
+
+/** This structure stores the original and symmetrized versions of terms
+ * obtained during the simplification of sums. */
+class terminfo {
+public:
+ terminfo(const ex & orig_, const ex & symm_) : orig(orig_), symm(symm_) {}
+
+ ex orig; /**< original term */
+ ex symm; /**< symmtrized term */
+};
+
+class terminfo_is_less {
+public:
+ bool operator() (const terminfo & ti1, const terminfo & ti2) const
+ {
+ return (ti1.symm.compare(ti2.symm) < 0);
+ }
+};
+
+/** This structure stores the individual symmetrized terms obtained during
+ * the simplification of sums. */
+class symminfo {
+public:
+ symminfo() : num(0) {}
+
+ symminfo(const ex & symmterm_, const ex & orig_, size_t num_) : orig(orig_), num(num_)
+ {
+ if (is_exactly_a<mul>(symmterm_) && is_exactly_a<numeric>(symmterm_.op(symmterm_.nops()-1))) {
+ coeff = symmterm_.op(symmterm_.nops()-1);
+ symmterm = symmterm_ / coeff;
+ } else {
+ coeff = 1;
+ symmterm = symmterm_;
+ }
+ }
+
+ ex symmterm; /**< symmetrized term */
+ ex coeff; /**< coefficient of symmetrized term */
+ ex orig; /**< original term */
+ size_t num; /**< how many symmetrized terms resulted from the original term */
+};
+
+class symminfo_is_less_by_symmterm {
+public:
+ bool operator() (const symminfo & si1, const symminfo & si2) const
+ {
+ return (si1.symmterm.compare(si2.symmterm) < 0);
+ }
+};
+
+class symminfo_is_less_by_orig {
+public:
+ bool operator() (const symminfo & si1, const symminfo & si2) const
+ {
+ return (si1.orig.compare(si2.orig) < 0);
+ }
+};
+
+bool hasindex(const ex &x, const ex &sym)
+{
+ if(is_a<idx>(x) && x.op(0)==sym)
+ return true;
+ else
+ for(size_t i=0; i<x.nops(); ++i)
+ if(hasindex(x.op(i), sym))
+ return true;
+ return false;
+}
+
+/** Simplify indexed expression, return list of free indices. */
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
+{
+ // Expand the expression
+ ex e_expanded = e.expand();
+
+ // Simplification of single indexed object: just find the free indices
+ // and perform dummy index renaming/repositioning
+ if (is_a<indexed>(e_expanded)) {
+
+ // Find the dummy indices
+ const indexed &i = ex_to<indexed>(e_expanded);
+ exvector local_dummy_indices;
+ find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
+
+ // Filter out the dummy indices with variance
+ exvector variant_dummy_indices;
+ find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+ // Any indices with variance present at all?
+ if (!variant_dummy_indices.empty()) {
+
+ // Yes, reposition them
+ exvector moved_indices;
+ reposition_dummy_indices(e_expanded, variant_dummy_indices, moved_indices);
+ }
+
+ // Rename the dummy indices
+ e_expanded = rename_dummy_indices<idx>(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<varidx>(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<spinidx>(e_expanded, dummy_indices, local_dummy_indices);
+ return e_expanded;
+ }
+
+ // Simplification of sum = sum of simplifications, check consistency of
+ // free indices in each term
+ if (is_exactly_a<add>(e_expanded)) {
+ bool first = true;
+ ex sum;
+ free_indices.clear();
+
+ for (size_t i=0; i<e_expanded.nops(); i++) {
+ exvector free_indices_of_term;
+ ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, dummy_indices, sp);
+ if (!term.is_zero()) {
+ if (first) {
+ free_indices = free_indices_of_term;
+ sum = term;
+ first = false;
+ } else {
+ if (!indices_consistent(free_indices, free_indices_of_term)) {
+ std::ostringstream s;
+ s << "simplify_indexed: inconsistent indices in sum: ";
+ s << exprseq(free_indices) << " vs. " << exprseq(free_indices_of_term);
+ throw (std::runtime_error(s.str()));
+ }
+ if (is_a<indexed>(sum) && is_a<indexed>(term))
+ sum = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
+ else
+ sum += term;
+ }
+ }
+ }
+
+ // If the sum turns out to be zero, we are finished
+ if (sum.is_zero()) {
+ free_indices.clear();
+ return sum;
+ }
+
+ // More than one term and more than one dummy index?
+ size_t num_terms_orig = (is_exactly_a<add>(sum) ? sum.nops() : 1);
+ if (num_terms_orig < 2 || dummy_indices.size() < 2)
+ return sum;
+
+ // Chop the sum into terms and symmetrize each one over the dummy
+ // indices
+ std::vector<terminfo> terms;
+ for (size_t i=0; i<sum.nops(); i++) {
+ const ex & term = sum.op(i);
+ exvector dummy_indices_of_term;
+ dummy_indices_of_term.reserve(dummy_indices.size());
+ for(exvector::iterator i=dummy_indices.begin(); i!=dummy_indices.end(); ++i)
+ if(hasindex(term,i->op(0)))
+ dummy_indices_of_term.push_back(*i);
+ ex term_symm = idx_symmetrization<idx>(term, dummy_indices_of_term);
+ term_symm = idx_symmetrization<varidx>(term_symm, dummy_indices_of_term);
+ term_symm = idx_symmetrization<spinidx>(term_symm, dummy_indices_of_term);
+ if (term_symm.is_zero())
+ continue;
+ terms.push_back(terminfo(term, term_symm));
+ }
+
+ // Sort by symmetrized terms
+ std::sort(terms.begin(), terms.end(), terminfo_is_less());
+
+ // Combine equal symmetrized terms
+ std::vector<terminfo> terms_pass2;
+ for (std::vector<terminfo>::const_iterator i=terms.begin(); i!=terms.end(); ) {
+ size_t num = 1;
+ std::vector<terminfo>::const_iterator j = i + 1;
+ while (j != terms.end() && j->symm == i->symm) {
+ num++;
+ j++;
+ }
+ terms_pass2.push_back(terminfo(i->orig * num, i->symm * num));
+ i = j;
+ }
+
+ // If there is only one term left, we are finished
+ if (terms_pass2.size() == 1)
+ return terms_pass2[0].orig;
+
+ // Chop the symmetrized terms into subterms
+ std::vector<symminfo> sy;
+ for (std::vector<terminfo>::const_iterator i=terms_pass2.begin(); i!=terms_pass2.end(); ++i) {
+ if (is_exactly_a<add>(i->symm)) {
+ size_t num = i->symm.nops();
+ for (size_t j=0; j<num; j++)
+ sy.push_back(symminfo(i->symm.op(j), i->orig, num));
+ } else
+ sy.push_back(symminfo(i->symm, i->orig, 1));
+ }
+
+ // Sort by symmetrized subterms
+ std::sort(sy.begin(), sy.end(), symminfo_is_less_by_symmterm());
+
+ // Combine equal symmetrized subterms
+ std::vector<symminfo> sy_pass2;
+ exvector result;
+ for (std::vector<symminfo>::const_iterator i=sy.begin(); i!=sy.end(); ) {
+
+ // Combine equal terms
+ std::vector<symminfo>::const_iterator j = i + 1;
+ if (j != sy.end() && j->symmterm == i->symmterm) {
+
+ // More than one term, collect the coefficients
+ ex coeff = i->coeff;
+ while (j != sy.end() && j->symmterm == i->symmterm) {
+ coeff += j->coeff;
+ j++;
+ }
+
+ // Add combined term to result
+ if (!coeff.is_zero())
+ result.push_back(coeff * i->symmterm);
+
+ } else {
+
+ // Single term, store for second pass
+ sy_pass2.push_back(*i);
+ }
+
+ i = j;
+ }
+
+ // Were there any remaining terms that didn't get combined?
+ if (sy_pass2.size() > 0) {
+
+ // Yes, sort by their original terms
+ std::sort(sy_pass2.begin(), sy_pass2.end(), symminfo_is_less_by_orig());
+
+ for (std::vector<symminfo>::const_iterator i=sy_pass2.begin(); i!=sy_pass2.end(); ) {
+
+ // How many symmetrized terms of this original term are left?
+ size_t num = 1;
+ std::vector<symminfo>::const_iterator j = i + 1;
+ while (j != sy_pass2.end() && j->orig == i->orig) {
+ num++;
+ j++;
+ }
+
+ if (num == i->num) {
+
+ // All terms left, then add the original term to the result
+ result.push_back(i->orig);
+
+ } else {
+
+ // Some terms were combined with others, add up the remaining symmetrized terms
+ std::vector<symminfo>::const_iterator k;
+ for (k=i; k!=j; k++)
+ result.push_back(k->coeff * k->symmterm);
+ }
+
+ i = j;
+ }
+ }
+
+ // Add all resulting terms
+ ex sum_symm = (new add(result))->setflag(status_flags::dynallocated);
+ if (sum_symm.is_zero())
+ free_indices.clear();
+ return sum_symm;
+ }
+
+ // Simplification of products
+ if (is_exactly_a<mul>(e_expanded)
+ || is_exactly_a<ncmul>(e_expanded)
+ || (is_exactly_a<power>(e_expanded) && is_a<indexed>(e_expanded.op(0)) && e_expanded.op(1).is_equal(_ex2)))
+ return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
+
+ // Cannot do anything
+ free_indices.clear();
+ return e_expanded;
+}
+
+/** Simplify/canonicalize expression containing indexed objects. This
+ * performs contraction of dummy indices where possible and checks whether
+ * the free indices in sums are consistent.
+ *
+ * @param options Simplification options (currently unused)
+ * @return simplified expression */
+ex ex::simplify_indexed(unsigned options) const
+{
+ exvector free_indices, dummy_indices;
+ scalar_products sp;
+ return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
+}
+
+/** Simplify/canonicalize expression containing indexed objects. This
+ * performs contraction of dummy indices where possible, checks whether
+ * the free indices in sums are consistent, and automatically replaces
+ * scalar products by known values if desired.
+ *
+ * @param sp Scalar products to be replaced automatically
+ * @param options Simplification options (currently unused)
+ * @return simplified expression */
+ex ex::simplify_indexed(const scalar_products & sp, unsigned options) const
+{
+ exvector free_indices, dummy_indices;
+ return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
+}
+
+/** Symmetrize expression over its free indices. */
+ex ex::symmetrize() const
+{
+ return GiNaC::symmetrize(*this, get_free_indices());
+}
+
+/** Antisymmetrize expression over its free indices. */
+ex ex::antisymmetrize() const
+{
+ return GiNaC::antisymmetrize(*this, get_free_indices());
+}
+
+/** Symmetrize expression by cyclic permutation over its free indices. */
+ex ex::symmetrize_cyclic() const
+{
+ return GiNaC::symmetrize_cyclic(*this, get_free_indices());
+}
+
+//////////
+// helper classes
+//////////
+
+spmapkey::spmapkey(const ex & v1_, const ex & v2_, const ex & dim_) : dim(dim_)
+{
+ // If indexed, extract base objects
+ ex s1 = is_a<indexed>(v1_) ? v1_.op(0) : v1_;
+ ex s2 = is_a<indexed>(v2_) ? v2_.op(0) : v2_;
+
+ // Enforce canonical order in pair
+ if (s1.compare(s2) > 0) {
+ v1 = s2;
+ v2 = s1;
+ } else {
+ v1 = s1;
+ v2 = s2;
+ }
+}
+
+bool spmapkey::operator==(const spmapkey &other) const
+{
+ if (!v1.is_equal(other.v1))
+ return false;
+ if (!v2.is_equal(other.v2))
+ return false;
+ if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
+ return true;
+ else
+ return dim.is_equal(other.dim);
+}
+
+bool spmapkey::operator<(const spmapkey &other) const
+{
+ int cmp = v1.compare(other.v1);
+ if (cmp)
+ return cmp < 0;
+ cmp = v2.compare(other.v2);
+ if (cmp)
+ return cmp < 0;
+
+ // Objects are equal, now check dimensions
+ if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
+ return false;
+ else
+ return dim.compare(other.dim) < 0;
+}
+
+void spmapkey::debugprint() const
+{
+ std::cerr << "(" << v1 << "," << v2 << "," << dim << ")";
+}
+
+void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
+{
+ spm[spmapkey(v1, v2)] = sp;
+}
+
+void scalar_products::add(const ex & v1, const ex & v2, const ex & dim, const ex & sp)
+{
+ spm[spmapkey(v1, v2, dim)] = sp;
+}
+
+void scalar_products::add_vectors(const lst & l, const ex & dim)
+{
+ // Add all possible pairs of products
+ for (lst::const_iterator it1 = l.begin(); it1 != l.end(); ++it1)
+ for (lst::const_iterator it2 = l.begin(); it2 != l.end(); ++it2)
+ add(*it1, *it2, *it1 * *it2);
+}
+
+void scalar_products::clear()
+{
+ spm.clear();
+}
+
+/** Check whether scalar product pair is defined. */
+bool scalar_products::is_defined(const ex & v1, const ex & v2, const ex & dim) const
+{
+ return spm.find(spmapkey(v1, v2, dim)) != spm.end();
+}
+
+/** Return value of defined scalar product pair. */
+ex scalar_products::evaluate(const ex & v1, const ex & v2, const ex & dim) const
+{
+ return spm.find(spmapkey(v1, v2, dim))->second;
+}
+
+void scalar_products::debugprint() const
+{
+ std::cerr << "map size=" << spm.size() << std::endl;
+ spmap::const_iterator i = spm.begin(), end = spm.end();
+ while (i != end) {
+ const spmapkey & k = i->first;
+ std::cerr << "item key=";
+ k.debugprint();
+ std::cerr << ", value=" << i->second << std::endl;
+ ++i;
+ }
+}
+
+exvector get_all_dummy_indices_safely(const ex & e)
+{
+ if (is_a<indexed>(e))
+ return ex_to<indexed>(e).get_dummy_indices();
+ else if (is_a<power>(e) && e.op(1)==2) {
+ return e.op(0).get_free_indices();
+ }
+ else if (is_a<mul>(e) || is_a<ncmul>(e)) {
+ exvector dummies;
+ exvector free_indices;
+ for (std::size_t i = 0; i < e.nops(); ++i) {
+ exvector dummies_of_factor = get_all_dummy_indices_safely(e.op(i));
+ dummies.insert(dummies.end(), dummies_of_factor.begin(),
+ dummies_of_factor.end());
+ exvector free_of_factor = e.op(i).get_free_indices();
+ free_indices.insert(free_indices.begin(), free_of_factor.begin(),
+ free_of_factor.end());
+ }
+ exvector free_out, dummy_out;
+ find_free_and_dummy(free_indices.begin(), free_indices.end(), free_out,
+ dummy_out);
+ dummies.insert(dummies.end(), dummy_out.begin(), dummy_out.end());
+ return dummies;
+ }
+ else if(is_a<add>(e)) {
+ exvector result;
+ for(std::size_t i = 0; i < e.nops(); ++i) {
+ exvector dummies_of_term = get_all_dummy_indices_safely(e.op(i));
+ sort(dummies_of_term.begin(), dummies_of_term.end());
+ exvector new_vec;
+ set_union(result.begin(), result.end(), dummies_of_term.begin(),
+ dummies_of_term.end(), std::back_inserter<exvector>(new_vec),
+ ex_is_less());
+ result.swap(new_vec);
+ }
+ return result;
+ }
+ return exvector();
+}
+
+/** Returns all dummy indices from the exvector */
+exvector get_all_dummy_indices(const ex & e)
+{
+ exvector p;
+ bool nc;
+ product_to_exvector(e, p, nc);
+ exvector::const_iterator ip = p.begin(), ipend = p.end();
+ exvector v, v1;
+ while (ip != ipend) {
+ if (is_a<indexed>(*ip)) {
+ v1 = ex_to<indexed>(*ip).get_dummy_indices();
+ v.insert(v.end(), v1.begin(), v1.end());
+ exvector::const_iterator ip1 = ip+1;
+ while (ip1 != ipend) {
+ if (is_a<indexed>(*ip1)) {
+ v1 = ex_to<indexed>(*ip).get_dummy_indices(ex_to<indexed>(*ip1));
+ v.insert(v.end(), v1.begin(), v1.end());
+ }
+ ++ip1;
+ }
+ }
+ ++ip;
+ }
+ return v;
+}
+
+lst rename_dummy_indices_uniquely(const exvector & va, const exvector & vb)
+{
+ exvector common_indices;
+ set_intersection(va.begin(), va.end(), vb.begin(), vb.end(), std::back_insert_iterator<exvector>(common_indices), ex_is_less());
+ if (common_indices.empty()) {
+ return lst(lst(), lst());
+ } else {
+ exvector new_indices, old_indices;
+ old_indices.reserve(2*common_indices.size());
+ new_indices.reserve(2*common_indices.size());
+ exvector::const_iterator ip = common_indices.begin(), ipend = common_indices.end();
+ while (ip != ipend) {
+ ex newsym=(new symbol)->setflag(status_flags::dynallocated);
+ ex newidx;
+ if(is_exactly_a<spinidx>(*ip))
+ newidx = (new spinidx(newsym, ex_to<spinidx>(*ip).get_dim(),
+ ex_to<spinidx>(*ip).is_covariant(),
+ ex_to<spinidx>(*ip).is_dotted()))
+ -> setflag(status_flags::dynallocated);
+ else if (is_exactly_a<varidx>(*ip))
+ newidx = (new varidx(newsym, ex_to<varidx>(*ip).get_dim(),
+ ex_to<varidx>(*ip).is_covariant()))
+ -> setflag(status_flags::dynallocated);
+ else
+ newidx = (new idx(newsym, ex_to<idx>(*ip).get_dim()))
+ -> setflag(status_flags::dynallocated);
+ old_indices.push_back(*ip);
+ new_indices.push_back(newidx);
+ if(is_a<varidx>(*ip)) {
+ old_indices.push_back(ex_to<varidx>(*ip).toggle_variance());
+ new_indices.push_back(ex_to<varidx>(newidx).toggle_variance());
+ }
+ ++ip;
+ }
+ return lst(lst(old_indices.begin(), old_indices.end()), lst(new_indices.begin(), new_indices.end()));
+ }
+}
+
+ex rename_dummy_indices_uniquely(const exvector & va, const exvector & vb, const ex & b)
+{
+ lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+ return (indices_subs.op(0).nops()>0 ? b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming) : b);
+}
+
+ex rename_dummy_indices_uniquely(const ex & a, const ex & b)
+{
+ exvector va = get_all_dummy_indices_safely(a);
+ if (va.size() > 0) {
+ exvector vb = get_all_dummy_indices_safely(b);
+ if (vb.size() > 0) {
+ sort(va.begin(), va.end(), ex_is_less());
+ sort(vb.begin(), vb.end(), ex_is_less());
+ lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+ if (indices_subs.op(0).nops() > 0)
+ return b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming);
+ }
+ }
+ return b;
+}
+
+ex rename_dummy_indices_uniquely(exvector & va, const ex & b, bool modify_va)
+{
+ if (va.size() > 0) {
+ exvector vb = get_all_dummy_indices_safely(b);
+ if (vb.size() > 0) {
+ sort(vb.begin(), vb.end(), ex_is_less());
+ lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+ if (indices_subs.op(0).nops() > 0) {
+ if (modify_va) {
+ for (lst::const_iterator i = ex_to<lst>(indices_subs.op(1)).begin(); i != ex_to<lst>(indices_subs.op(1)).end(); ++i)
+ va.push_back(*i);
+ exvector uncommon_indices;
+ set_difference(vb.begin(), vb.end(), indices_subs.op(0).begin(), indices_subs.op(0).end(), std::back_insert_iterator<exvector>(uncommon_indices), ex_is_less());
+ exvector::const_iterator ip = uncommon_indices.begin(), ipend = uncommon_indices.end();
+ while (ip != ipend) {
+ va.push_back(*ip);
+ ++ip;
+ }
+ sort(va.begin(), va.end(), ex_is_less());
+ }
+ return b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming);
+ }
+ }
+ }
+ return b;
+}
+
+ex expand_dummy_sum(const ex & e, bool subs_idx)
+{
+ ex e_expanded = e.expand();
+ pointer_to_map_function_1arg<bool> fcn(expand_dummy_sum, subs_idx);
+ if (is_a<add>(e_expanded) || is_a<lst>(e_expanded) || is_a<matrix>(e_expanded)) {
+ return e_expanded.map(fcn);
+ } else if (is_a<ncmul>(e_expanded) || is_a<mul>(e_expanded) || is_a<power>(e_expanded) || is_a<indexed>(e_expanded)) {
+ exvector v;
+ if (is_a<indexed>(e_expanded))
+ v = ex_to<indexed>(e_expanded).get_dummy_indices();
+ else
+ v = get_all_dummy_indices(e_expanded);
+ ex result = e_expanded;
+ for(exvector::const_iterator it=v.begin(); it!=v.end(); ++it) {
+ ex nu = *it;
+ if (ex_to<idx>(nu).get_dim().info(info_flags::nonnegint)) {
+ int idim = ex_to<numeric>(ex_to<idx>(nu).get_dim()).to_int();
+ ex en = 0;
+ for (int i=0; i < idim; i++) {
+ if (subs_idx && is_a<varidx>(nu)) {
+ ex other = ex_to<varidx>(nu).toggle_variance();
+ en += result.subs(lst(
+ nu == idx(i, idim),
+ other == idx(i, idim)
+ ));
+ } else {
+ en += result.subs( nu.op(0) == i );
+ }
+ }
+ result = en;
+ }
+ }
+ return result;
+ } else {
+ return e;