X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=b85c38699b544d0cb30c56abac9f1f76f57d513f;hp=765a07c8bf4c7a1f8be7a17411a55dbcb64311b9;hb=d916416984a857e80962239a0ee93e7216f803bb;hpb=b89179d5c32459bd61f161278e2cae24abe36d4e diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index 765a07c8..b85c3869 100644 --- a/ginac/indexed.cpp +++ b/ginac/indexed.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's indexed expressions. */ /* - * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2011 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 @@ -17,132 +17,121 @@ * * 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 -#include - #include "indexed.h" #include "idx.h" #include "add.h" #include "mul.h" #include "ncmul.h" #include "power.h" +#include "relational.h" #include "symmetry.h" +#include "operators.h" #include "lst.h" -#include "print.h" #include "archive.h" +#include "symbol.h" #include "utils.h" +#include "integral.h" +#include "matrix.h" +#include "inifcns.h" + +#include +#include +#include +#include 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 ctor, dtor, copy ctor, assignment operator and helpers +// default constructor ////////// -indexed::indexed() : symtree(sy_none()) +indexed::indexed() : symtree(not_symmetric()) { - tinfo_key = TINFO_indexed; } -void indexed::copy(const indexed & other) -{ - inherited::copy(other); - symtree = other.symtree; -} - -DEFAULT_DESTROY(indexed) - ////////// // 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(); } indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm) { - tinfo_key = TINFO_indexed; validate(); } indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm) { - tinfo_key = TINFO_indexed; validate(); } indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(symm) { - tinfo_key = TINFO_indexed; 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; validate(); } indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm) { seq.insert(seq.end(), v.begin(), v.end()); - tinfo_key = TINFO_indexed; validate(); } indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm) { - tinfo_key = TINFO_indexed; } indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm) { - 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; } ////////// // archiving ////////// -indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +void indexed::read_archive(const archive_node &n, lst &sym_lst) { + inherited::read_archive(n, sym_lst); if (!n.find_ex("symmetry", symtree, sym_lst)) { // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property unsigned symm = 0; @@ -155,12 +144,13 @@ indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_l symtree = sy_anti(); break; default: - symtree = sy_none(); + symtree = not_symmetric(); break; } const_cast(ex_to(symtree)).validate(seq.size() - 1); } } +GINAC_BIND_UNARCHIVER(indexed); void indexed::archive(archive_node &n) const { @@ -168,46 +158,84 @@ void indexed::archive(archive_node &n) const n.add_ex("symmetry", symtree); } -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 (seq.size() > 1) { - if (is_of_type(c, print_tree)) { + exvector::const_iterator it=seq.begin() + 1, itend = seq.end(); - 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); + if (is_a(c)) { - } else { + // TeX output: group by variance + bool first = true; + bool covariant = true; - bool is_tex = is_of_type(c, print_latex); - const ex & base = seq[0]; - bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul) - || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power) - || is_ex_of_type(base, indexed); - if (is_tex) - c.s << "{"; - if (need_parens) - c.s << "("; - base.print(c); - if (need_parens) - c.s << ")"; - 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); + + } 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; @@ -250,23 +278,26 @@ ex indexed::eval(int level) const return _ex0; // If the base object is a product, pull out the numeric factor - if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) { + if (is_exactly_a(base) && is_exactly_a(base.op(base.nops() - 1))) { exvector v(seq); ex f = ex_to(base.op(base.nops() - 1)); v[0] = seq[0] / f; - return f * thisexprseq(v); + return f * thiscontainer(v); } + if((typeid(*this) == typeid(indexed)) && seq.size()==1) + return base; + // Canonicalize indices according to the symmetry properties if (seq.size() > 2) { exvector v = seq; GINAC_ASSERT(is_exactly_a(symtree)); int sig = canonicalize(v.begin() + 1, ex_to(symtree)); - if (sig != INT_MAX) { + if (sig != std::numeric_limits::max()) { // Something has changed while sorting indices, more evaluations later if (sig == 0) return _ex0; - return ex(sig) * thisexprseq(v); + return ex(sig) * thiscontainer(v); } } @@ -274,34 +305,60 @@ ex indexed::eval(int level) const return ex_to(base).eval_indexed(*this); } -ex indexed::thisexprseq(const exvector & v) const +ex indexed::real_part() const +{ + if(op(0).info(info_flags::real)) + return *this; + return real_part_function(*this).hold(); +} + +ex indexed::imag_part() const +{ + if(op(0).info(info_flags::real)) + return 0; + return imag_part_function(*this).hold(); +} + +ex indexed::thiscontainer(const exvector & v) const { return indexed(ex_to(symtree), v); } -ex indexed::thisexprseq(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_ex_exactly_of_type(seq[0], add)) { - - // expand_indexed expands (a+b).i -> a.i + b.i - const ex & base = seq[0]; - ex sum = _ex0; - for (unsigned 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); } ////////// @@ -314,63 +371,21 @@ 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_of_type(c, print_latex)) { - - // TeX output: group by variance - bool first = true; - bool covariant = true; - - while (it != itend) { - bool cur_covariant = (is_ex_of_type(*it, varidx) ? 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. */ -void indexed::validate(void) const +void indexed::validate() const { GINAC_ASSERT(seq.size() > 0); exvector::const_iterator it = seq.begin() + 1, itend = seq.end(); while (it != itend) { - if (!is_ex_of_type(*it, idx)) + if (!is_a(*it)) throw(std::invalid_argument("indices of indexed object must be of type idx")); it++; } if (!symtree.is_zero()) { - if (!is_ex_exactly_of_type(symtree, symmetry)) + if (!is_exactly_a(symtree)) throw(std::invalid_argument("symmetry of indexed object must be of type symmetry")); const_cast(ex_to(symtree)).validate(seq.size() - 1); } @@ -388,6 +403,22 @@ ex indexed::derivative(const symbol & s) const // global functions ////////// +struct idx_is_equal_ignore_dim : public std::binary_function { + bool operator() (const ex &lh, const ex &rh) const + { + if (lh.is_equal(rh)) + return true; + else + try { + // Replacing the dimension might cause an error (e.g. with + // index classes that only work in a fixed number of dimensions) + return lh.is_equal(ex_to(rh).replace_dim(ex_to(lh).get_dim())); + } catch (...) { + return false; + } + } +}; + /** Check whether two sorted index vectors are consistent (i.e. equal). */ static bool indices_consistent(const exvector & v1, const exvector & v2) { @@ -395,16 +426,16 @@ static bool indices_consistent(const exvector & v1, const exvector & v2) if (v1.size() != v2.size()) return false; - return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal()); + return equal(v1.begin(), v1.end(), v2.begin(), idx_is_equal_ignore_dim()); } -exvector indexed::get_indices(void) const +exvector indexed::get_indices() const { GINAC_ASSERT(seq.size() >= 1); return exvector(seq.begin() + 1, seq.end()); } -exvector indexed::get_dummy_indices(void) const +exvector indexed::get_dummy_indices() const { exvector free_indices, dummy_indices; find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices); @@ -432,17 +463,17 @@ bool indexed::has_dummy_index_for(const ex & i) const return false; } -exvector indexed::get_free_indices(void) const +exvector indexed::get_free_indices() const { exvector free_indices, dummy_indices; find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices); return free_indices; } -exvector add::get_free_indices(void) const +exvector add::get_free_indices() const { exvector free_indices; - for (unsigned i=0; i { + bool operator()(const ex & e) + { + return is_dummy_pair(e, e); + } +}; + +exvector integral::get_free_indices() const { - // Return free indices of basis - return basis.get_free_indices(); + 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. * - * @param e Expression to be worked on + * @param e Expression to work on * @param local_dummy_indices The set of dummy indices that appear in the * expression "e" * @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) { - unsigned 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) @@ -511,11 +559,11 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex // More local indices than we encountered before, add the new ones // to the global set - int old_global_size = global_size; + size_t old_global_size = global_size; 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(ex_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--; @@ -529,19 +577,23 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex } GINAC_ASSERT(local_size <= global_size); - // Construct lists of index symbols - exlist local_syms, global_syms; - for (unsigned 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 (unsigned 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 - exlist local_uniq, global_uniq; - set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator(local_uniq), ex_is_less()); - set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator(global_uniq), ex_is_less()); + exvector local_uniq, global_uniq; + set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator(local_uniq), ex_is_less()); + set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator(global_uniq), ex_is_less()); // Replace remaining non-common local index symbols by global ones if (local_uniq.empty()) @@ -549,54 +601,213 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex else { while (global_uniq.size() > local_uniq.size()) global_uniq.pop_back(); - return e.subs(lst(local_uniq), lst(global_uniq)); + return e.subs(lst(local_uniq.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()), subs_options::no_pattern); } } -/** 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) +/** Given a set of indices, extract those of class varidx. */ +static void find_variant_indices(const exvector & v, exvector & variant_indices) +{ + exvector::const_iterator it1, itend; + for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) { + if (is_exactly_a(*it1)) + variant_indices.push_back(*it1); + } +} + +/** Raise/lower dummy indices in a single indexed objects to canonicalize their + * variance. + * + * @param e Object to work on + * @param variant_dummy_indices The set of indices that might need repositioning (will be changed by this function) + * @param moved_indices The set of indices that have been repositioned (will be changed by this function) + * @return true if 'e' was changed */ +bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices) +{ + bool something_changed = false; + + // Find dummy symbols that occur twice in the same indexed object. + exvector local_var_dummies; + local_var_dummies.reserve(e.nops()/2); + for (size_t i=1; i(e.op(i))) + continue; + for (size_t j=i+1; jop(0)) { + variant_dummy_indices.erase(k); + break; + } + } + break; + } + } + } + + // In the case where a dummy symbol occurs twice in the same indexed object + // we try all posibilities of raising/lowering and keep the least one in + // the sense of ex_is_less. + ex optimal_e = e; + size_t numpossibs = 1 << local_var_dummies.size(); + for (size_t i=0; i(curr_idx).toggle_variance(); + m[curr_idx] = curr_toggle; + m[curr_toggle] = curr_idx; + } + try_e = e.subs(m, subs_options::no_pattern); + } + if(ex_is_less()(try_e, optimal_e)) + { optimal_e = try_e; + something_changed = true; + } + } + e = optimal_e; + + if (!is_a(e)) + return true; + + exvector seq = ex_to(e).seq; + + // If a dummy index is encountered for the first time in the + // product, pull it up, otherwise, pull it down + for (exvector::iterator it2 = seq.begin()+1, it2end = seq.end(); + it2 != it2end; ++it2) { + if (!is_exactly_a(*it2)) + continue; + + exvector::iterator vit, vitend; + for (vit = variant_dummy_indices.begin(), vitend = variant_dummy_indices.end(); vit != vitend; ++vit) { + if (it2->op(0).is_equal(vit->op(0))) { + if (ex_to(*it2).is_covariant()) { + /* + * N.B. we don't want to use + * + * e = e.subs(lst( + * *it2 == ex_to(*it2).toggle_variance(), + * ex_to(*it2).toggle_variance() == *it2 + * ), subs_options::no_pattern); + * + * since this can trigger non-trivial repositioning of indices, + * e.g. due to non-trivial symmetry properties of e, thus + * invalidating iterators + */ + *it2 = ex_to(*it2).toggle_variance(); + something_changed = true; + } + moved_indices.push_back(*vit); + variant_dummy_indices.erase(vit); + goto next_index; + } + } + + for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) { + if (it2->op(0).is_equal(vit->op(0))) { + if (ex_to(*it2).is_contravariant()) { + *it2 = ex_to(*it2).toggle_variance(); + something_changed = true; + } + goto next_index; + } + } + +next_index: ; + } + + if (something_changed) + e = ex_to(e).thiscontainer(seq); + + return something_changed; +} + +/* Ordering that only compares the base expressions of indexed objects. */ +struct ex_base_is_less : public std::binary_function { + bool operator() (const ex &lh, const ex &rh) const + { + return (is_a(lh) ? lh.op(0) : lh).compare(is_a(rh) ? rh.op(0) : rh) < 0; + } +}; + +/* 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_ex_exactly_of_type(e, ncmul); + non_commutative = is_exactly_a(e); // Collect factors in an exvector, store squares twice - exvector v; v.reserve(e.nops() * 2); - if (is_ex_exactly_of_type(e, power)) { + if (is_exactly_a(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 (unsigned i=0; i(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_ex_exactly_of_type(f, ncmul)) { + } 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 - for (unsigned j=0; j 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; + bool has_nonsymmetric = 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_ex_of_type(*it1, indexed)) + if (!is_a(*it1)) continue; bool first_noncommutative = (it1->return_type() != return_types::commutative); + bool first_nonsymmetric = ex_to(ex_to(*it1).get_symmetry()).has_nonsymmetric(); // Indexed factor found, get free indices and look for contraction // candidates @@ -606,7 +817,7 @@ try_again: exvector::iterator it2; for (it2 = it1 + 1; it2 != itend; it2++) { - if (!is_ex_of_type(*it2, indexed)) + if (!is_a(*it2)) continue; bool second_noncommutative = (it2->return_type() != return_types::commutative); @@ -620,15 +831,24 @@ try_again: // Check whether the two factors share dummy indices exvector free, dummy; find_free_and_dummy(un, free, dummy); - unsigned num_dummies = dummy.size(); + 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()) { - if (sp.is_defined(*it1, *it2)) { - *it1 = sp.evaluate(*it1, *it2); + if (free.empty() && it1->nops()==2 && it2->nops()==2) { + + ex dim = minimal_dim( + ex_to(it1->op(1)).get_dim(), + ex_to(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; } @@ -645,14 +865,14 @@ try_again: if (contracted) { contraction_done: if (first_noncommutative || second_noncommutative - || is_ex_exactly_of_type(*it1, add) || is_ex_exactly_of_type(*it2, add) - || is_ex_exactly_of_type(*it1, mul) || is_ex_exactly_of_type(*it2, mul) - || is_ex_exactly_of_type(*it1, ncmul) || is_ex_exactly_of_type(*it2, ncmul)) { + || is_exactly_a(*it1) || is_exactly_a(*it2) + || is_exactly_a(*it1) || is_exactly_a(*it2) + || is_exactly_a(*it1) || is_exactly_a(*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 - // simplify_ncmul() the chance to re-order and canonicalize + // 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); @@ -664,28 +884,55 @@ contraction_done: something_changed = true; goto try_again; } + else if (!has_nonsymmetric && + (first_nonsymmetric || + ex_to(ex_to(*it2).get_symmetry()).has_nonsymmetric())) { + has_nonsymmetric = true; + } } } // Find free indices (concatenate them all and call find_free_and_dummy()) // and all dummy indices that appear exvector un, individual_dummy_indices; - it1 = v.begin(); itend = v.end(); - while (it1 != itend) { + for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) { exvector free_indices_of_factor; - if (is_ex_of_type(*it1, indexed)) { + if (is_a(*it1)) { exvector dummy_indices_of_factor; find_free_and_dummy(ex_to(*it1).seq.begin() + 1, ex_to(*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()); - it1++; } 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(*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)); @@ -695,27 +942,105 @@ 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) { - lst dummy_syms; - for (int i=0; i(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_ex_exactly_of_type(r, mul) && r.nops() == 2 - && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed)) + if (is_exactly_a(r) && r.nops() == 2 + && is_exactly_a(r.op(1)) && is_a(r.op(0))) return ex_to(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to(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(symmterm_) && is_exactly_a(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(x) && x.op(0)==sym) + return true; + else + for(size_t i=0; i(e_expanded)) { + + // Find the dummy indices const indexed &i = ex_to(e_expanded); exvector local_dummy_indices; find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices); - return rename_dummy_indices(e_expanded, dummy_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(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 // free indices in each term - if (is_ex_exactly_of_type(e_expanded, add)) { + if (is_exactly_a(e_expanded)) { bool first = true; - ex sum = _ex0; + ex sum; free_indices.clear(); - for (unsigned i=0; i(sum) && is_a(term)) sum = ex_to(sum.op(0)).add_indexed(sum, term); else sum += term; @@ -757,13 +1105,142 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi } } - return sum; + // 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(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 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)); + } + + // Sort by symmetrized terms + std::sort(terms.begin(), terms.end(), terminfo_is_less()); + + // Combine equal symmetrized terms + std::vector terms_pass2; + for (std::vector::const_iterator i=terms.begin(); i!=terms.end(); ) { + size_t num = 1; + std::vector::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 sy; + for (std::vector::const_iterator i=terms_pass2.begin(); i!=terms_pass2.end(); ++i) { + if (is_exactly_a(i->symm)) { + size_t num = i->symm.nops(); + for (size_t j=0; jsymm.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 sy_pass2; + exvector result; + for (std::vector::const_iterator i=sy.begin(); i!=sy.end(); ) { + + // Combine equal terms + std::vector::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::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::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::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_ex_exactly_of_type(e_expanded, mul) - || is_ex_exactly_of_type(e_expanded, ncmul) - || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2))) + if (is_exactly_a(e_expanded) + || is_exactly_a(e_expanded) + || (is_exactly_a(e_expanded) && is_a(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 @@ -775,8 +1252,9 @@ 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(void) const +ex ex::simplify_indexed(unsigned options) const { exvector free_indices, dummy_indices; scalar_products sp; @@ -789,27 +1267,28 @@ ex ex::simplify_indexed(void) 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); } /** Symmetrize expression over its free indices. */ -ex ex::symmetrize(void) const +ex ex::symmetrize() const { return GiNaC::symmetrize(*this, get_free_indices()); } /** Antisymmetrize expression over its free indices. */ -ex ex::antisymmetrize(void) const +ex ex::antisymmetrize() const { return GiNaC::antisymmetrize(*this, get_free_indices()); } /** Symmetrize expression by cyclic permutation over its free indices. */ -ex ex::symmetrize_cyclic(void) const +ex ex::symmetrize_cyclic() const { return GiNaC::symmetrize_cyclic(*this, get_free_indices()); } @@ -818,65 +1297,292 @@ ex ex::symmetrize_cyclic(void) const // helper classes ////////// +spmapkey::spmapkey(const ex & v1_, const ex & v2_, const ex & dim_) : dim(dim_) +{ + // If indexed, extract base objects + ex s1 = is_a(v1_) ? v1_.op(0) : v1_; + ex s2 = is_a(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(dim) || is_a(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(dim) || is_a(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[make_key(v1, v2)] = 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) +void scalar_products::add_vectors(const lst & l, const ex & dim) { // Add all possible pairs of products - unsigned num = l.nops(); - for (unsigned i=0; isecond; + return spm.find(spmapkey(v1, v2, dim))->second; } -void scalar_products::debugprint(void) const +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.first << "," << k.second; - std::cerr << "), value=" << i->second << std::endl; + std::cerr << "item key="; + k.debugprint(); + std::cerr << ", value=" << i->second << std::endl; ++i; } } -/** Make key from object pair. */ -spmapkey scalar_products::make_key(const ex & v1, const ex & v2) +exvector get_all_dummy_indices_safely(const ex & e) { - // If indexed, extract base objects - ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1; - ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2; + if (is_a(e)) + return ex_to(e).get_dummy_indices(); + else if (is_a(e) && e.op(1)==2) { + return e.op(0).get_free_indices(); + } + else if (is_a(e) || is_a(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(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(new_vec), + ex_is_less()); + result.swap(new_vec); + } + return result; + } + return exvector(); +} - // Enforce canonical order in pair - if (s1.compare(s2) > 0) - return spmapkey(s2, s1); - else - return spmapkey(s1, s2); +/** 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(ex_to(indices_subs.op(0)), ex_to(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(indices_subs.op(0)), ex_to(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(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(ex_to(indices_subs.op(0)), ex_to(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 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) || is_a(e_expanded)) { + exvector v; + if (is_a(e_expanded)) + v = ex_to(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(nu).get_dim().info(info_flags::nonnegint)) { + int idim = ex_to(ex_to(nu).get_dim()).to_int(); + ex en = 0; + for (int i=0; i < idim; i++) { + if (subs_idx && is_a(nu)) { + ex other = ex_to(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; + } } } // namespace GiNaC