*/
#include <stdexcept>
+#include <algorithm>
#include "indexed.h"
#include "idx.h"
#include "mul.h"
#include "ncmul.h"
#include "power.h"
+#include "symmetry.h"
#include "lst.h"
#include "print.h"
#include "archive.h"
// default constructor, destructor, copy constructor assignment operator and helpers
//////////
-indexed::indexed() : symmetry(unknown)
+indexed::indexed() : symtree(sy_none())
{
debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
void indexed::copy(const indexed & other)
{
inherited::copy(other);
- symmetry = other.symmetry;
+ symtree = other.symtree;
}
DEFAULT_DESTROY(indexed)
// other constructors
//////////
-indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
+indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
{
debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none())
{
debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none())
{
debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none())
{
debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-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)
+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())
{
debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
{
debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
{
debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-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)
+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)
{
debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
+indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none())
{
debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
seq.insert(seq.end(), v.begin(), v.end());
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
{
debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
seq.insert(seq.end(), v.begin(), v.end());
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
+indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
{
debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
}
-indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
+indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
{
debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
}
-indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
+indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm)
{
debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
}
//////////
indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
- unsigned int symm;
- if (!(n.find_unsigned("symmetry", symm)))
- throw (std::runtime_error("unknown indexed symmetry type in archive"));
+ if (!n.find_ex("symmetry", symtree, sym_lst)) {
+ // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property
+ unsigned symm = 0;
+ n.find_unsigned("symmetry", symm);
+ switch (symm) {
+ case 1:
+ symtree = sy_symm();
+ break;
+ case 2:
+ symtree = sy_anti();
+ break;
+ default:
+ symtree = sy_none();
+ break;
+ }
+ ex_to_nonconst_symmetry(symtree).validate(seq.size() - 1);
+ }
}
void indexed::archive(archive_node &n) const
{
inherited::archive(n);
- n.add_unsigned("symmetry", symmetry);
+ n.add_ex("symmetry", symtree);
}
DEFAULT_UNARCHIVE(indexed)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
void indexed::print(const print_context & c, unsigned level) const
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;
+ << ", " << seq.size()-1 << " indices"
+ << ", symmetry=" << symtree << 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);
} else {
+ 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_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);
}
}
return inherited::info(inf);
}
+struct idx_is_not : public std::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
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
return inherited::compare_same_type(other);
}
-// The main difference between sort_index_vector() and canonicalize_indices()
-// is that the latter takes the symmetry of the object into account. Once we
-// implement mixed symmetries, canonicalize_indices() will only be able to
-// 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.
- *
- * @param itbegin Start of index vector
- * @param itend End of index vector
- * @param antisymm Whether the object is antisymmetric
- * @return the sign introduced by the reordering of the indices if the object
- * is antisymmetric (or 0 if two equal indices are encountered). For
- * symmetric objects, this is always +1. If the index vector was
- * already in a canonic order this function returns INT_MAX. */
-static int canonicalize_indices(exvector::iterator itbegin, exvector::iterator itend, bool antisymm)
-{
- bool something_changed = false;
- int sig = 1;
-
- // Simple bubble sort algorithm should be sufficient for the small
- // number of indices expected
- exvector::iterator it1 = itbegin, next_to_last_idx = itend - 1;
- while (it1 != next_to_last_idx) {
- exvector::iterator it2 = it1 + 1;
- while (it2 != itend) {
- int cmpval = it1->compare(*it2);
- if (cmpval == 1) {
- it1->swap(*it2);
- something_changed = true;
- if (antisymm)
- sig = -sig;
- } else if (cmpval == 0 && antisymm) {
- something_changed = true;
- sig = 0;
- }
- it2++;
- }
- it1++;
- }
-
- return something_changed ? sig : INT_MAX;
-}
-
ex indexed::eval(int level) const
{
// First evaluate children, then we will end up here again
if (level > 1)
- return indexed(symmetry, evalchildren(level));
+ return indexed(ex_to<symmetry>(symtree), evalchildren(level));
const ex &base = seq[0];
// 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));
+ 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)) {
+ if (seq.size() > 2) {
exvector v = seq;
- int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
+ GINAC_ASSERT(is_ex_exactly_of_type(symtree, symmetry));
+ int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
if (sig != INT_MAX) {
// Something has changed while sorting indices, more evaluations later
if (sig == 0)
ex indexed::thisexprseq(const exvector & v) const
{
- return indexed(symmetry, v);
+ return indexed(ex_to<symmetry>(symtree), v);
}
ex indexed::thisexprseq(exvector * vp) const
{
- return indexed(symmetry, vp);
+ return indexed(ex_to<symmetry>(symtree), vp);
}
ex indexed::expand(unsigned options) 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->print(c, level);
- 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++;
+ }
}
}
}
-/** 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. */
-void indexed::assert_all_indices_of_type_idx(void) const
+/** 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
{
GINAC_ASSERT(seq.size() > 0);
exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
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))
+ throw(std::invalid_argument("symmetry of indexed object must be of type symmetry"));
+ ex_to_nonconst_symmetry(symtree).validate(seq.size() - 1);
+ }
+}
+
+/** Implementation of ex::diff() for an indexed object always returns 0.
+ *
+ * @see ex::diff */
+ex indexed::derivative(const symbol & s) const
+{
+ return _ex0();
}
//////////
if (v1.size() != v2.size())
return false;
- // 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++;
- }
- return true;
+ return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal());
}
exvector indexed::get_indices(void) const
return dummy_indices;
}
+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 false;
+}
+
exvector indexed::get_free_indices(void) const
{
exvector free_indices, dummy_indices;
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)
+{
+ unsigned 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)
+ && ex_to<idx>(local_dummy_indices[i]).get_dim().is_equal(ex_to<idx>(global_dummy_indices[i]).get_dim())) {
+ 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)
v.push_back(e.op(0));
v.push_back(e.op(0));
} else {
- for (int i=0; i<e.nops(); i++) {
+ for (unsigned i=0; i<e.nops(); i++) {
ex f = e.op(i);
if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
v.push_back(f.op(0));
} 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(); j++)
+ for (unsigned j=0; j<f.nops(); j++)
v.push_back(f.op(j));
} else
v.push_back(f);
if (!is_ex_of_type(*it1, indexed))
continue;
+ bool first_noncommutative = (it1->return_type() != return_types::commutative);
+
// Indexed factor found, get free indices and look for contraction
// candidates
exvector free1, dummy1;
- find_free_and_dummy(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end(), free1, dummy1);
+ 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);
+ find_free_and_dummy(ex_to<indexed>(*it2).seq.begin() + 1, ex_to<indexed>(*it2).seq.end(), un, dummy1);
un.insert(un.end(), free1.begin(), free1.end());
// Check whether the two factors share dummy indices
exvector free, dummy;
find_free_and_dummy(un, free, dummy);
- if (dummy.size() == 0)
+ unsigned 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.size() == 0) {
+ if (free.empty()) {
if (sp.is_defined(*it1, *it2)) {
*it1 = sp.evaluate(*it1, *it2);
*it2 = _ex1();
}
// 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();
+ if (num_dummies > 1
+ && ex_to<symmetry>(ex_to<indexed>(*it1).symtree).has_symmetry()
+ && ex_to<symmetry>(ex_to<indexed>(*it2).symtree).has_symmetry()) {
+
+ // Check all pairs of dummy indices
+ for (unsigned idx1=0; idx1<num_dummies-1; idx1++) {
+ for (unsigned idx2=idx1+1; idx2<num_dummies; idx2++) {
+
+ // Try and swap the index pair and check whether the
+ // relative sign changed
+ lst subs_lst(dummy[idx1].op(0), dummy[idx2].op(0)), repl_lst(dummy[idx2].op(0), dummy[idx1].op(0));
+ ex swapped1 = it1->subs(subs_lst, repl_lst);
+ ex swapped2 = it2->subs(subs_lst, repl_lst);
+ if (it1->is_equal(swapped1) && it2->is_equal(-swapped2)
+ || it1->is_equal(-swapped1) && it2->is_equal(swapped2)) {
+ free_indices.clear();
+ return _ex0();
+ }
+ }
+ }
}
// Try to contract the first one with the second one
}
if (contracted) {
contraction_done:
- if (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)) {
+ 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
- ex r = non_commutative ? ex(ncmul(v)) : ex(mul(v));
- return simplify_indexed(r, free_indices, sp);
+ // 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
}
// 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 = it1->get_free_indices();
+ exvector free_indices_of_factor;
+ if (is_ex_of_type(*it1, indexed)) {
+ 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, 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());
ex r;
if (something_changed)
- r = non_commutative ? ex(ncmul(v)) : ex(mul(v));
+ 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)));
+ 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;
+ const indexed &i = ex_to<indexed>(e_expanded);
+ exvector local_dummy_indices;
+ find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
+ return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
}
// Simplification of sum = sum of simplifications, check consistency of
for (unsigned i=0; i<e_expanded.nops(); i++) {
exvector free_indices_of_term;
- ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
+ 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;
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());
+}
+
+/** Symmetrize expression by cyclic permutation over its free indices. */
+ex ex::symmetrize_cyclic(void) const
+{
+ return GiNaC::symmetrize_cyclic(*this, get_free_indices());
}
//////////
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();
void scalar_products::debugprint(void) const
{
std::cerr << "map size=" << spm.size() << std::endl;
- for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
- const spmapkey & k = cit->first;
+ 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=" << cit->second << std::endl;
+ std::cerr << "), value=" << i->second << std::endl;
+ ++i;
}
}