]> www.ginac.de Git - ginac.git/blobdiff - ginac/indexed.cpp
- added numer_denom() to get numerator and denominator in one pass
[ginac.git] / ginac / indexed.cpp
index c3fe1d9a26e6d49ca311b0e793913d6050ef402f..a2eda2c482b1621e7a94798a5db3ebece9ffbff4 100644 (file)
@@ -21,6 +21,7 @@
  */
 
 #include <stdexcept>
+#include <algorithm>
 
 #include "indexed.h"
 #include "idx.h"
@@ -28,6 +29,9 @@
 #include "mul.h"
 #include "ncmul.h"
 #include "power.h"
+#include "lst.h"
+#include "inifcns.h" // for symmetrize()
+#include "print.h"
 #include "archive.h"
 #include "utils.h"
 #include "debugmsg.h"
@@ -52,11 +56,7 @@ void indexed::copy(const indexed & other)
        symmetry = other.symmetry;
 }
 
-void indexed::destroy(bool call_parent)
-{
-       if (call_parent)
-               inherited::destroy(call_parent);
-}
+DEFAULT_DESTROY(indexed)
 
 //////////
 // other constructors
@@ -66,56 +66,56 @@ indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
 {
        debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
 {
        debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
 {
        debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
 {
        debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(unknown)
 {
        debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
 {
        debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
 {
        debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(symm)
 {
        debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
@@ -123,7 +123,7 @@ indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unkn
        debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
        seq.insert(seq.end(), v.begin(), v.end());
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
@@ -131,35 +131,34 @@ indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherit
        debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
        seq.insert(seq.end(), v.begin(), v.end());
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
 {
        debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
 {
        debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
 {
        debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_indexed;
-       GINAC_ASSERT(all_indices_of_type_idx());
+       assert_all_indices_of_type_idx();
 }
 
 //////////
 // archiving
 //////////
 
-/** Construct object from archive_node. */
 indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
        debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
@@ -168,59 +167,56 @@ indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_l
                throw (std::runtime_error("unknown indexed symmetry type in archive"));
 }
 
-/** Unarchive the object. */
-ex indexed::unarchive(const archive_node &n, const lst &sym_lst)
-{
-       return (new indexed(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
 void indexed::archive(archive_node &n) const
 {
        inherited::archive(n);
        n.add_unsigned("symmetry", symmetry);
 }
 
+DEFAULT_UNARCHIVE(indexed)
+
 //////////
 // functions overriding virtual functions from bases classes
 //////////
 
-void indexed::printraw(std::ostream & os) const
+void indexed::print(const print_context & c, unsigned level) const
 {
-       debugmsg("indexed printraw", LOGLEVEL_PRINT);
+       debugmsg("indexed print", LOGLEVEL_PRINT);
        GINAC_ASSERT(seq.size() > 0);
 
-       os << class_name() << "(";
-       seq[0].printraw(os);
-       os << ",indices=";
-       printrawindices(os);
-       os << ",hash=" << hashvalue << ",flags=" << flags << ")";
-}
-
-void indexed::printtree(std::ostream & os, unsigned indent) const
-{
-       debugmsg("indexed printtree", LOGLEVEL_PRINT);
-       GINAC_ASSERT(seq.size() > 0);
+       if (is_of_type(c, print_tree)) {
 
-       os << std::string(indent, ' ') << class_name() << ", " << seq.size()-1 << " indices";
-       os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
-       printtreeindices(os, indent);
-}
+               c.s << std::string(level, ' ') << class_name()
+                   << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+                   << ", " << seq.size()-1 << " indices";
+               switch (symmetry) {
+                       case symmetric: c.s << ", symmetric"; break;
+                       case antisymmetric: c.s << ", antisymmetric"; break;
+                       default: break;
+               }
+               c.s << std::endl;
+               unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
+               seq[0].print(c, level + delta_indent);
+               printindices(c, level + delta_indent);
 
-void indexed::print(std::ostream & os, unsigned upper_precedence) const
-{
-       debugmsg("indexed print", LOGLEVEL_PRINT);
-       GINAC_ASSERT(seq.size() > 0);
+       } else {
 
-       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);
-       if (need_parens)
-               os << "(";
-       os << base;
-       if (need_parens)
-               os << ")";
-       printindices(os);
+               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)
+                       c.s << "}";
+               printindices(c, level);
+       }
 }
 
 bool indexed::info(unsigned inf) const
@@ -230,6 +226,12 @@ bool indexed::info(unsigned inf) const
        return inherited::info(inf);
 }
 
+struct idx_is_not : public binary_function<ex, unsigned, bool> {
+       bool operator() (const ex & e, unsigned inf) const {
+               return !(ex_to_idx(e).get_value().info(inf));
+       }
+};
+
 bool indexed::all_index_values_are(unsigned inf) const
 {
        // No indices? Then no property can be fulfilled
@@ -237,14 +239,7 @@ bool indexed::all_index_values_are(unsigned inf) const
                return false;
 
        // Check all indices
-       exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
-       while (it != itend) {
-               GINAC_ASSERT(is_ex_of_type(*it, idx));
-               if (!ex_to_idx(*it).get_value().info(inf))
-                       return false;
-               it++;
-       }
-       return true;
+       return find_if(seq.begin() + 1, seq.end(), bind2nd(idx_is_not(), inf)) == seq.end();
 }
 
 int indexed::compare_same_type(const basic & other) const
@@ -259,31 +254,6 @@ int indexed::compare_same_type(const basic & other) const
 // reorder index pairs with known symmetry properties, while sort_index_vector()
 // always sorts the whole vector.
 
-/** Bring a vector of indices into a canonic order (don't care about the
- *  symmetry of the objects carrying the indices). Dummy indices will lie
- *  next to each other after the sorting.
- *
- *  @param v Index vector to be sorted */
-static void sort_index_vector(exvector &v)
-{
-       // Nothing to sort if less than 2 elements
-       if (v.size() < 2)
-               return;
-
-       // Simple bubble sort algorithm should be sufficient for the small
-       // number of indices expected
-       exvector::iterator it1 = v.begin(), itend = v.end(), next_to_last_idx = itend - 1;
-       while (it1 != next_to_last_idx) {
-               exvector::iterator it2 = it1 + 1;
-               while (it2 != itend) {
-                       if (it1->compare(*it2) > 0)
-                               it1->swap(*it2);
-                       it2++;
-               }
-               it1++;
-       }
-}
-
 /** Bring a vector of indices into a canonic order. This operation only makes
  *  sense if the object carrying these indices is either symmetric or totally
  *  antisymmetric with respect to the indices.
@@ -330,9 +300,23 @@ ex indexed::eval(int level) const
        if (level > 1)
                return indexed(symmetry, evalchildren(level));
 
+       const ex &base = seq[0];
+
+       // If the base object is 0, the whole object is 0
+       if (base.is_zero())
+               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)) {
+               exvector v(seq);
+               ex f = ex_to_numeric(base.op(base.nops() - 1));
+               v[0] = seq[0] / f;
+               return f * thisexprseq(v);
+       }
+
        // Canonicalize indices according to the symmetry properties
-       if (seq.size() > 2 && (symmetry != unknown && symmetry != mixed)) {
-               exvector v = seq;
+       if (seq.size() > 2 && (symmetry == symmetric || symmetry == antisymmetric)) {
+               exvector v(seq);
                int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
                if (sig != INT_MAX) {
                        // Something has changed while sorting indices, more evaluations later
@@ -343,7 +327,25 @@ ex indexed::eval(int level) const
        }
 
        // Let the class of the base object perform additional evaluations
-       return op(0).bp->eval_indexed(*this);
+       return base.bp->eval_indexed(*this);
+}
+
+int indexed::degree(const ex & s) const
+{
+       return is_equal(*s.bp) ? 1 : 0;
+}
+
+int indexed::ldegree(const ex & s) const
+{
+       return is_equal(*s.bp) ? 1 : 0;
+}
+
+ex indexed::coeff(const ex & s, int n) const
+{
+       if (is_equal(*s.bp))
+               return n==1 ? _ex1() : _ex0();
+       else
+               return n==0 ? ex(*this) : _ex0();
 }
 
 ex indexed::thisexprseq(const exvector & v) const
@@ -386,39 +388,43 @@ ex indexed::expand(unsigned options) const
 // non-virtual functions in this class
 //////////
 
-void indexed::printrawindices(std::ostream & os) const
+void indexed::printindices(const print_context & c, unsigned level) const
 {
        if (seq.size() > 1) {
-               exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
-               while (it != itend) {
-                       it->printraw(os);
-                       it++;
-                       if (it != itend)
-                               os << ",";
-               }
-       }
-}
 
-void indexed::printtreeindices(std::ostream & os, unsigned indent) const
-{
-       if (seq.size() > 1) {
                exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
-               while (it != itend) {
-                       os << std::string(indent + delta_indent, ' ');
-                       it->printraw(os);
-                       os << std::endl;
-                       it++;
-               }
-       }
-}
 
-void indexed::printindices(std::ostream & os) const
-{
-       if (seq.size() > 1) {
-               exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
-               while (it != itend) {
-                       it->print(os);
-                       it++;
+               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_varidx(*it).is_covariant() : true);
+                               if (first || cur_covariant != covariant) {
+                                       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++;
+                       }
                }
        }
 }
@@ -426,80 +432,63 @@ void indexed::printindices(std::ostream & os) const
 /** Check whether all indices are of class idx. This function is used
  *  internally to make sure that all constructed indexed objects really
  *  carry indices and not some other classes. */
-bool indexed::all_indices_of_type_idx(void) const
+void indexed::assert_all_indices_of_type_idx(void) 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))
-                       return false;
+                       throw(std::invalid_argument("indices of indexed object must be of type idx"));
                it++;
        }
-       return true;
 }
 
 //////////
 // global functions
 //////////
 
-/** Given a vector of indices, split them into two vectors, one containing
- *  the free indices, the other containing the dummy indices. */
-static void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
+/** Check whether two sorted index vectors are consistent (i.e. equal). */
+static bool indices_consistent(const exvector & v1, const exvector & v2)
 {
-       out_free.clear();
-       out_dummy.clear();
-
-       // No indices? Then do nothing
-       if (it == itend)
-               return;
+       // Number of indices must be the same
+       if (v1.size() != v2.size())
+               return false;
 
-       // Only one index? Then it is a free one if it's not numeric
-       if (itend - it == 1) {
-               if (ex_to_idx(*it).is_symbolic())
-                       out_free.push_back(*it);
-               return;
-       }
+       return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal());
+}
 
-       // Sort index vector. This will cause dummy indices come to lie next
-       // to each other (because the sort order is defined to guarantee this).
-       exvector v(it, itend);
-       sort_index_vector(v);
+exvector indexed::get_indices(void) const
+{
+       GINAC_ASSERT(seq.size() >= 1);
+       return exvector(seq.begin() + 1, seq.end());
+}
 
-       // Find dummy pairs and free indices
-       it = v.begin(); itend = v.end();
-       exvector::const_iterator last = it++;
-       while (it != itend) {
-               if (is_dummy_pair(*it, *last)) {
-                       out_dummy.push_back(*last);
-                       it++;
-                       if (it == itend)
-                               return;
-               } else {
-                       if (!it->is_equal(*last) && ex_to_idx(*last).is_symbolic())
-                               out_free.push_back(*last);
-               }
-               last = it++;
-       }
-       if (ex_to_idx(*last).is_symbolic())
-               out_free.push_back(*last);
+exvector indexed::get_dummy_indices(void) const
+{
+       exvector free_indices, dummy_indices;
+       find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+       return dummy_indices;
 }
 
-/** Check whether two sorted index vectors are consistent (i.e. equal). */
-static bool indices_consistent(const exvector & v1, const exvector & v2)
+exvector indexed::get_dummy_indices(const indexed & other) const
 {
-       // Number of indices must be the same
-       if (v1.size() != v2.size())
-               return false;
+       exvector indices = get_free_indices();
+       exvector other_indices = other.get_free_indices();
+       indices.insert(indices.end(), other_indices.begin(), other_indices.end());
+       exvector dummy_indices;
+       find_dummy_indices(indices, dummy_indices);
+       return dummy_indices;
+}
 
-       // And also the indices themselves
-       exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
-                                bit = v2.begin(), bitend = v2.end();
-       while (ait != aitend) {
-               if (!ait->is_equal(*bit))
-                       return false;
-               ait++; bit++;
+bool indexed::has_dummy_index_for(const ex & i) const
+{
+       exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
+       while (it != itend) {
+               if (is_dummy_pair(*it, i))
+                       return true;
+               it++;
        }
-       return true;
+       return false;
 }
 
 exvector indexed::get_free_indices(void) const
@@ -535,7 +524,7 @@ exvector mul::get_free_indices(void) const
 
        // And remove the dummy indices
        exvector free_indices, dummy_indices;
-       find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
+       find_free_and_dummy(un, free_indices, dummy_indices);
        return free_indices;
 }
 
@@ -550,7 +539,7 @@ exvector ncmul::get_free_indices(void) const
 
        // And remove the dummy indices
        exvector free_indices, dummy_indices;
-       find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
+       find_free_and_dummy(un, free_indices, dummy_indices);
        return free_indices;
 }
 
@@ -560,9 +549,61 @@ exvector power::get_free_indices(void) const
        return basis.get_free_indices();
 }
 
+/** Rename dummy indices in an expression.
+ *
+ *  @param e Expression to be worked 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)
+{
+       int global_size = global_dummy_indices.size(),
+           local_size = local_dummy_indices.size();
+
+       // Any local dummy indices at all?
+       if (local_size == 0)
+               return e;
+
+       if (global_size < local_size) {
+
+               // More local indices than we encountered before, add the new ones
+               // to the global set
+               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()) {
+                               global_dummy_indices.push_back(*it);
+                               global_size++;
+                               remaining--;
+                       }
+                       it++;
+               }
+       }
+
+       // Replace index symbols in expression
+       GINAC_ASSERT(local_size <= global_size);
+       bool all_equal = true;
+       lst local_syms, global_syms;
+       for (unsigned i=0; i<local_size; i++) {
+               ex loc_sym = local_dummy_indices[i].op(0);
+               ex glob_sym = global_dummy_indices[i].op(0);
+               if (!loc_sym.is_equal(glob_sym)) {
+                       all_equal = false;
+                       local_syms.append(loc_sym);
+                       global_syms.append(glob_sym);
+               }
+       }
+       if (all_equal)
+               return e;
+       else
+               return e.subs(local_syms, global_syms);
+}
+
 /** 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, const scalar_products & sp)
+ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 {
        // Remember whether the product was commutative or noncommutative
        // (because we chop it into factors and need to reassemble later)
@@ -586,7 +627,7 @@ ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_
                        } else if (is_ex_exactly_of_type(f, ncmul)) {
                                // Noncommutative factor found, split it as well
                                non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
-                               for (int j=0; j<f.nops(); i++)
+                               for (int j=0; j<f.nops(); j++)
                                        v.push_back(f.op(j));
                        } else
                                v.push_back(f);
@@ -603,33 +644,55 @@ try_again:
                if (!is_ex_of_type(*it1, indexed))
                        continue;
 
-               // Indexed factor found, look for contraction candidates
+               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_ex_of_type(*it2, indexed))
                                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 un(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end());
-                       un.insert(un.end(), ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end());
                        exvector free, dummy;
-                       find_free_and_dummy(un.begin(), un.end(), free, dummy);
+                       find_free_and_dummy(un, free, dummy);
                        if (dummy.size() == 0)
                                continue;
 
                        // At least one dummy index, is it a defined scalar product?
+                       bool contracted = false;
                        if (free.size() == 0) {
                                if (sp.is_defined(*it1, *it2)) {
                                        *it1 = sp.evaluate(*it1, *it2);
                                        *it2 = _ex1();
-                                       something_changed = true;
-                                       goto try_again;
+                                       goto contraction_done;
                                }
                        }
 
+                       // Contraction of symmetric with antisymmetric object is zero
+                       if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
+                            ex_to_indexed(*it2).symmetry == indexed::antisymmetric
+                         || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
+                            ex_to_indexed(*it2).symmetry == indexed::symmetric)
+                        && dummy.size() > 1) {
+                               free_indices.clear();
+                               return _ex0();
+                       }
+
                        // Try to contract the first one with the second one
-                       bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
+                       contracted = it1->op(0).bp->contract_with(it1, it2, v);
                        if (!contracted) {
 
                                // That didn't work; maybe the second object knows how to
@@ -637,63 +700,105 @@ try_again:
                                contracted = it2->op(0).bp->contract_with(it2, it1, v);
                        }
                        if (contracted) {
-                               something_changed = true;
+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)) {
+
+                                       // 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
+                                       // 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())
-       exvector un, dummy_indices;
+       // and all dummy indices that appear
+       exvector un, individual_dummy_indices;
        it1 = v.begin(); itend = v.end();
        while (it1 != itend) {
+               exvector free_indices_of_factor;
                if (is_ex_of_type(*it1, indexed)) {
-                       const indexed & o = ex_to_indexed(*it1);
-                       un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
-               }
+                       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());
                it1++;
        }
-       find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
+       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());
 
-       if (something_changed) {
-               if (non_commutative)
-                       return ncmul(v);
-               else
-                       return mul(v);
-       } else
-               return e;
+       ex r;
+       if (something_changed)
+               r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
+       else
+               r = e;
+
+       // Dummy index renaming
+       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))
+               return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
+       else
+               return r;
 }
 
 /** Simplify indexed expression, return list of free indices. */
-ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
+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
        if (is_ex_of_type(e_expanded, indexed)) {
                const indexed &i = ex_to_indexed(e_expanded);
-               exvector dummy_indices;
-               find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
-               return 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);
        }
 
        // Simplification of sum = sum of simplifications, check consistency of
        // free indices in each term
        if (is_ex_exactly_of_type(e_expanded, add)) {
+               bool first = true;
                ex sum = _ex0();
+               free_indices.clear();
 
                for (unsigned i=0; i<e_expanded.nops(); i++) {
                        exvector free_indices_of_term;
-                       sum += simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
-                       if (i == 0)
-                               free_indices = free_indices_of_term;
-                       else if (!indices_consistent(free_indices, free_indices_of_term))
-                               throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
+                       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))
+                                               throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
+                                       if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
+                                               sum = sum.op(0).bp->add_indexed(sum, term);
+                                       else
+                                               sum += term;
+                               }
+                       }
                }
 
                return sum;
@@ -703,24 +808,48 @@ ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_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())))
-               return simplify_indexed_product(e_expanded, free_indices, sp);
+               return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
 
        // Cannot do anything
        free_indices.clear();
        return e_expanded;
 }
 
-ex simplify_indexed(const ex & e)
+/** Simplify/canonicalize expression containing indexed objects. This
+ *  performs contraction of dummy indices where possible and checks whether
+ *  the free indices in sums are consistent.
+ *
+ *  @return simplified expression */
+ex ex::simplify_indexed(void) const
 {
-       exvector free_indices;
+       exvector free_indices, dummy_indices;
        scalar_products sp;
-       return simplify_indexed(e, free_indices, sp);
+       return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
 }
 
-ex simplify_indexed(const ex & e, const scalar_products & 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
+ *  @return simplified expression */
+ex ex::simplify_indexed(const scalar_products & sp) const
 {
-       exvector free_indices;
-       return simplify_indexed(e, free_indices, sp);
+       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
+{
+       return GiNaC::symmetrize(*this, get_free_indices());
+}
+
+/** Antisymmetrize expression over its free indices. */
+ex ex::antisymmetrize(void) const
+{
+       return GiNaC::antisymmetrize(*this, get_free_indices());
 }
 
 //////////
@@ -732,6 +861,19 @@ void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
        spm[make_key(v1, v2)] = sp;
 }
 
+void scalar_products::add_vectors(const lst & l)
+{
+       // Add all possible pairs of products
+       unsigned num = l.nops();
+       for (unsigned i=0; i<num; i++) {
+               ex a = l.op(i);
+               for (unsigned j=0; j<num; j++) {
+                       ex b = l.op(j);
+                       add(a, b, a*b);
+               }
+       }
+}
+
 void scalar_products::clear(void)
 {
        spm.clear();