X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=0c1c904f1295caa0c4cf98cb26f0ab649a38eb46;hp=412aad52d9184206e34523beb75d494aa96fd6da;hb=b87f623d787279a123c8db77cef2c84bc5874239;hpb=b4be7b0f30fbb6178cf4ee83e1b3952e084bd8ca diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index 412aad52..0c1c904f 100644 --- a/ginac/indexed.cpp +++ b/ginac/indexed.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's indexed expressions. */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2005 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 @@ -17,7 +17,7 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ #include @@ -35,17 +35,23 @@ #include "operators.h" #include "lst.h" #include "archive.h" +#include "symbol.h" #include "utils.h" +#include "integral.h" +#include "matrix.h" namespace GiNaC { -GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq) +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(indexed, exprseq, + print_func(&indexed::do_print). + print_func(&indexed::do_print_latex). + print_func(&indexed::do_print_tree)) ////////// // default constructor ////////// -indexed::indexed() : symtree(sy_none()) +indexed::indexed() : symtree(not_symmetric()) { tinfo_key = TINFO_indexed; } @@ -54,31 +60,31 @@ indexed::indexed() : symtree(sy_none()) // other constructors ////////// -indexed::indexed(const ex & b) : inherited(b), symtree(sy_none()) +indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); @@ -102,7 +108,7 @@ indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & validate(); } -indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none()) +indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(not_symmetric()) { seq.insert(seq.end(), v.begin(), v.end()); tinfo_key = TINFO_indexed; @@ -126,7 +132,7 @@ indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : tinfo_key = TINFO_indexed; } -indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm) +indexed::indexed(const symmetry & symm, std::auto_ptr vp) : inherited(vp), symtree(symm) { tinfo_key = TINFO_indexed; } @@ -149,7 +155,7 @@ indexed::indexed(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) symtree = sy_anti(); break; default: - symtree = sy_none(); + symtree = not_symmetric(); break; } const_cast(ex_to(symtree)).validate(seq.size() - 1); @@ -168,38 +174,80 @@ DEFAULT_UNARCHIVE(indexed) // functions overriding virtual functions from base classes ////////// -void indexed::print(const print_context & c, unsigned level) const +void indexed::printindices(const print_context & c, unsigned level) const { - GINAC_ASSERT(seq.size() > 0); - - if (is_a(c)) { + if (seq.size() > 1) { - c.s << std::string(level, ' ') << class_name() - << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec - << ", " << seq.size()-1 << " indices" - << ", symmetry=" << symtree << std::endl; - unsigned delta_indent = static_cast(c).delta_indent; - seq[0].print(c, level + delta_indent); - printindices(c, level + delta_indent); + exvector::const_iterator it=seq.begin() + 1, itend = seq.end(); - } else { + if (is_a(c)) { - bool is_tex = is_a(c); - const ex & base = seq[0]; + // TeX output: group by variance + bool first = true; + bool covariant = true; - if (precedence() <= level) - c.s << (is_tex ? "{(" : "("); - if (is_tex) - c.s << "{"; - base.print(c, precedence()); - if (is_tex) + while (it != itend) { + bool cur_covariant = (is_a(*it) ? ex_to(*it).is_covariant() : true); + if (first || cur_covariant != covariant) { // Variance changed + // The empty {} prevents indices from ending up on top of each other + if (!first) + c.s << "}{}"; + covariant = cur_covariant; + if (covariant) + c.s << "_{"; + else + c.s << "^{"; + } + it->print(c, level); + c.s << " "; + first = false; + it++; + } c.s << "}"; - printindices(c, level); - if (precedence() <= level) - c.s << (is_tex ? ")}" : ")"); + + } else { + + // Ordinary output + while (it != itend) { + it->print(c, level); + it++; + } + } } } +void indexed::print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const +{ + if (precedence() <= level) + c.s << openbrace << '('; + c.s << openbrace; + seq[0].print(c, precedence()); + c.s << closebrace; + printindices(c, level); + if (precedence() <= level) + c.s << ')' << closebrace; +} + +void indexed::do_print(const print_context & c, unsigned level) const +{ + print_indexed(c, "", "", level); +} + +void indexed::do_print_latex(const print_latex & c, unsigned level) const +{ + print_indexed(c, "{", "}", level); +} + +void indexed::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; + seq[0].print(c, level + c.delta_indent); + printindices(c, level + c.delta_indent); +} + bool indexed::info(unsigned inf) const { if (inf == info_flags::indexed) return true; @@ -249,6 +297,9 @@ ex indexed::eval(int level) const return f * thiscontainer(v); } + if(this->tinfo()==TINFO_indexed && seq.size()==1) + return base; + // Canonicalize indices according to the symmetry properties if (seq.size() > 2) { exvector v = seq; @@ -271,29 +322,41 @@ ex indexed::thiscontainer(const exvector & v) const return indexed(ex_to(symtree), v); } -ex indexed::thiscontainer(exvector * vp) const +ex indexed::thiscontainer(std::auto_ptr vp) const { return indexed(ex_to(symtree), vp); } +unsigned indexed::return_type() const +{ + if(is_a(op(0))) + return return_types::commutative; + else + return op(0).return_type(); +} + ex indexed::expand(unsigned options) const { GINAC_ASSERT(seq.size() > 0); - if ((options & expand_options::expand_indexed) && is_exactly_a(seq[0])) { - - // expand_indexed expands (a+b).i -> a.i + b.i - const ex & base = seq[0]; - ex sum = _ex0; - for (size_t i=0; i(newbase)) { + ex sum = _ex0; + for (size_t i=0; i(thiscontainer(s)).inherited::expand(options); } - return sum; - - } else - return inherited::expand(options); + } + return inherited::expand(options); } ////////// @@ -306,48 +369,6 @@ ex indexed::expand(unsigned options) const // non-virtual functions in this class ////////// -void indexed::printindices(const print_context & c, unsigned level) const -{ - if (seq.size() > 1) { - - exvector::const_iterator it=seq.begin() + 1, itend = seq.end(); - - if (is_a(c)) { - - // TeX output: group by variance - bool first = true; - bool covariant = true; - - while (it != itend) { - bool cur_covariant = (is_a(*it) ? ex_to(*it).is_covariant() : true); - if (first || cur_covariant != covariant) { // Variance changed - // The empty {} prevents indices from ending up on top of each other - if (!first) - c.s << "}{}"; - covariant = cur_covariant; - if (covariant) - c.s << "_{"; - else - c.s << "^{"; - } - it->print(c, level); - c.s << " "; - first = false; - it++; - } - c.s << "}"; - - } else { - - // Ordinary output - while (it != itend) { - it->print(c, level); - it++; - } - } - } -} - /** Check whether all indices are of class idx and validate the symmetry * tree. This function is used internally to make sure that all constructed * indexed objects really carry indices and not some other classes. */ @@ -492,10 +513,43 @@ exvector ncmul::get_free_indices() const return free_indices; } +struct is_summation_idx : public std::unary_function { + bool operator()(const ex & e) + { + return is_dummy_pair(e, e); + } +}; + exvector power::get_free_indices() const { - // Return free indices of basis - return basis.get_free_indices(); + // Get free indices of basis + exvector basis_indices = basis.get_free_indices(); + + if (exponent.info(info_flags::even)) { + // If the exponent is an even number, then any "free" index that + // forms a dummy pair with itself is actually a summation index + exvector really_free; + std::remove_copy_if(basis_indices.begin(), basis_indices.end(), + std::back_inserter(really_free), is_summation_idx()); + return really_free; + } else + return basis_indices; +} + +exvector integral::get_free_indices() const +{ + if (a.get_free_indices().size() || b.get_free_indices().size()) + throw (std::runtime_error("integral::get_free_indices: boundary values should not have free indices")); + return f.get_free_indices(); +} + +template size_t number_of_type(const exvector&v) +{ + size_t number = 0; + for(exvector::const_iterator i=v.begin(); i!=v.end(); ++i) + if(is_exactly_a(*i)) + ++number; + return number; } /** Rename dummy indices in an expression. @@ -506,10 +560,10 @@ exvector power::get_free_indices() const * @param global_dummy_indices The set of dummy indices that have appeared * before and which we would like to use in "e", too. This gets updated * by the function */ -static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices) +template static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices) { - size_t global_size = global_dummy_indices.size(), - local_size = local_dummy_indices.size(); + size_t global_size = number_of_type(global_dummy_indices), + local_size = number_of_type(local_dummy_indices); // Any local dummy indices at all? if (local_size == 0) @@ -523,7 +577,7 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex int remaining = local_size - global_size; exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end(); while (it != itend && remaining > 0) { - if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(op0_is_equal(), *it)) == global_dummy_indices.end()) { + if (is_exactly_a(*it) && find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(idx_is_equal_ignore_dim(), *it)) == global_dummy_indices.end()) { global_dummy_indices.push_back(*it); global_size++; remaining--; @@ -541,11 +595,13 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex exvector local_syms, global_syms; local_syms.reserve(local_size); global_syms.reserve(local_size); - for (size_t i=0; i(local_dummy_indices[i])) + local_syms.push_back(local_dummy_indices[i].op(0)); shaker_sort(local_syms.begin(), local_syms.end(), ex_is_less(), ex_swap()); - for (size_t i=0; i(global_dummy_indices[i])) + global_syms.push_back(global_dummy_indices[i].op(0)); shaker_sort(global_syms.begin(), global_syms.end(), ex_is_less(), ex_swap()); // Remove common indices @@ -637,16 +693,15 @@ struct ex_base_is_less : public std::binary_function { } }; -/** 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) +/* An auxiliary function used by simplify_indexed() and expand_dummy_sum() + * It returns an exvector of factors from the supplied product */ +static void product_to_exvector(const ex & e, exvector & v, bool & non_commutative) { // Remember whether the product was commutative or noncommutative // (because we chop it into factors and need to reassemble later) - bool non_commutative = is_exactly_a(e); + non_commutative = is_exactly_a(e); // Collect factors in an exvector, store squares twice - exvector v; v.reserve(e.nops() * 2); if (is_exactly_a(e)) { @@ -659,7 +714,7 @@ ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & du ex f = e.op(i); if (is_exactly_a(f) && f.op(1).is_equal(_ex2)) { v.push_back(f.op(0)); - v.push_back(f.op(0)); + v.push_back(f.op(0)); } else if (is_exactly_a(f)) { // Noncommutative factor found, split it as well non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later @@ -669,6 +724,34 @@ ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & du v.push_back(f); } } +} + +template 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(*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; @@ -712,27 +795,29 @@ try_again: bool contracted = false; if (free.empty()) { - // Find minimal dimension of all indices of both factors - exvector::const_iterator dit = ex_to(*it1).seq.begin() + 1, ditend = ex_to(*it1).seq.end(); - ex dim = ex_to(*dit).get_dim(); - ++dit; - for (; dit != ditend; ++dit) { - dim = minimal_dim(dim, ex_to(*dit).get_dim()); - } - dit = ex_to(*it2).seq.begin() + 1; - ditend = ex_to(*it2).seq.end(); - for (; dit != ditend; ++dit) { - dim = minimal_dim(dim, ex_to(*dit).get_dim()); - } + try { + // Find minimal dimension of all indices of both factors + exvector::const_iterator dit = ex_to(*it1).seq.begin() + 1, ditend = ex_to(*it1).seq.end(); + ex dim = ex_to(*dit).get_dim(); + ++dit; + for (; dit != ditend; ++dit) { + dim = minimal_dim(dim, ex_to(*dit).get_dim()); + } + dit = ex_to(*it2).seq.begin() + 1; + ditend = ex_to(*it2).seq.end(); + for (; dit != ditend; ++dit) { + dim = minimal_dim(dim, ex_to(*dit).get_dim()); + } - // User-defined scalar product? - if (sp.is_defined(*it1, *it2, 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; - } + // Yes, substitute it + *it1 = sp.evaluate(*it1, *it2, dim); + *it2 = _ex1; + goto contraction_done; + } + } catch (const std::runtime_error&) {} } // Try to contract the first one with the second one @@ -818,19 +903,26 @@ contraction_done: // 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. - if (local_dummy_indices.size() >= 2) { - exvector dummy_syms; - dummy_syms.reserve(local_dummy_indices.size()); - for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it) - dummy_syms.push_back(it->op(0)); - if (symmetrize(r, dummy_syms).is_zero()) { - free_indices.clear(); - return _ex0; - } + ex q = idx_symmetrization(r, local_dummy_indices); + if (q.is_zero()) { + free_indices.clear(); + return _ex0; + } + q = idx_symmetrization(q, local_dummy_indices); + if (q.is_zero()) { + free_indices.clear(); + return _ex0; + } + q = idx_symmetrization(q, local_dummy_indices); + if (q.is_zero()) { + free_indices.clear(); + return _ex0; } // Dummy index renaming - r = rename_dummy_indices(r, dummy_indices, local_dummy_indices); + r = rename_dummy_indices(r, dummy_indices, local_dummy_indices); + r = rename_dummy_indices(r, dummy_indices, local_dummy_indices); + r = rename_dummy_indices(r, dummy_indices, local_dummy_indices); // Product of indexed object with a scalar? if (is_exactly_a(r) && r.nops() == 2 @@ -897,6 +989,17 @@ public: } }; +bool hasindex(const ex &x, const ex &sym) +{ + if(is_a(x) && x.op(0)==sym) + return true; + else + for(size_t i=0; i(e_expanded, dummy_indices, local_dummy_indices); + e_expanded = rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices); + e_expanded = rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices); + return e_expanded; } // Simplification of sum = sum of simplifications, check consistency of @@ -969,18 +1075,19 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi if (num_terms_orig < 2 || dummy_indices.size() < 2) return sum; - // Yes, construct vector of all dummy index symbols - exvector dummy_syms; - dummy_syms.reserve(dummy_indices.size()); - for (exvector::const_iterator it = dummy_indices.begin(); it != dummy_indices.end(); ++it) - dummy_syms.push_back(it->op(0)); - // Chop the sum into terms and symmetrize each one over the dummy // indices std::vector terms; for (size_t i=0; iop(0))) + dummy_indices_of_term.push_back(*i); + ex term_symm = idx_symmetrization(term, dummy_indices_of_term); + term_symm = idx_symmetrization(term_symm, dummy_indices_of_term); + term_symm = idx_symmetrization(term_symm, dummy_indices_of_term); if (term_symm.is_zero()) continue; terms.push_back(terminfo(term, term_symm)); @@ -1104,8 +1211,9 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi * 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() const +ex ex::simplify_indexed(unsigned options) const { exvector free_indices, dummy_indices; scalar_products sp; @@ -1118,8 +1226,9 @@ ex ex::simplify_indexed() const * 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) const +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); @@ -1244,4 +1353,166 @@ void scalar_products::debugprint() const } } +/** 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(*ip)) { + v1 = ex_to(*ip).get_dummy_indices(); + v.insert(v.end(), v1.begin(), v1.end()); + exvector::const_iterator ip1 = ip+1; + while (ip1 != ipend) { + if (is_a(*ip1)) { + v1 = ex_to(*ip).get_dummy_indices(ex_to(*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(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(*ip)) + newidx = (new spinidx(newsym, ex_to(*ip).get_dim(), + ex_to(*ip).is_covariant(), + ex_to(*ip).is_dotted())) + -> setflag(status_flags::dynallocated); + else if (is_exactly_a(*ip)) + newidx = (new varidx(newsym, ex_to(*ip).get_dim(), + ex_to(*ip).is_covariant())) + -> setflag(status_flags::dynallocated); + else + newidx = (new idx(newsym, ex_to(*ip).get_dim())) + -> setflag(status_flags::dynallocated); + old_indices.push_back(*ip); + new_indices.push_back(newidx); + if(is_a(*ip)) { + old_indices.push_back(ex_to(*ip).toggle_variance()); + new_indices.push_back(ex_to(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((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern) : b); +} + +ex rename_dummy_indices_uniquely(const ex & a, const ex & b) +{ + exvector va = get_all_dummy_indices(a); + if (va.size() > 0) { + exvector vb = get_all_dummy_indices(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((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern); + } + } + 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(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(indices_subs.op(1)).begin(); i != ex_to(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(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((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern); + } + } + } + return b; +} + +ex expand_dummy_sum(const ex & e, bool subs_idx) +{ + ex e_expanded = e.expand(); + pointer_to_map_function_1arg fcn(expand_dummy_sum, subs_idx); + if (is_a(e_expanded) || is_a(e_expanded) || is_a(e_expanded)) { + return e_expanded.map(fcn); + } else if (is_a(e_expanded) || is_a(e_expanded) || is_a(e_expanded)) { + exvector v = get_all_dummy_indices(e_expanded); + exvector::const_iterator it = v.begin(), itend = v.end(); + while (it != itend) { + varidx nu = ex_to(*it); + if (nu.is_dim_numeric()) { + ex en = 0; + for (int i=0; i < ex_to(nu.get_dim()).to_int(); i++) { + if (is_a(nu) && !subs_idx) { + en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim()))); + } else { + en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim()))); + } + } + return expand_dummy_sum(en, subs_idx); + } + ++it; + } + return e; + } else if (is_a(e_expanded)) { + exvector v = ex_to(e_expanded).get_dummy_indices(); + exvector::const_iterator it = v.begin(), itend = v.end(); + while (it != itend) { + varidx nu = ex_to(*it); + if (nu.is_dim_numeric()) { + ex en = 0; + for (int i=0; i < ex_to(nu.get_dim()).to_int(); i++) { + if (is_a(nu) && !subs_idx) { + en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim()))); + } else { + en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim()))); + } + } + return expand_dummy_sum(en, subs_idx); + } + ++it; + } + return e; + } else { + return e; + } +} + } // namespace GiNaC